MM4XL User`s Guide

Transcription

MM4XL User`s Guide

MM4XLTM User's Guide
Marketing Manager for Excel Software
Comprehensive analysis toolbox for
business analysts and strategic decision-makers
Marketing Manager for Excel – MM4XL© Software 8.0 Reference Manual
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For information about Marketing Manager for Excel, MM4XL software:
Write to: [email protected]
Visit:
www.mm4xl.com
MarketingStat GmbH
Christoph Merian-Ring 11
CH-4153 Reinach
Switzerland
Phone: +41 (0)61 401 6055
Fax: +41 (0)61 401 6073
MM4XLTM software is copyright of MarketingStat GmbH for its proprietary computer software. No material
describing such software may be produced or distributed without the written permission of the owner of the
copyright and license rights in the software and the copyright in the published materials.
MM4XL, Marketing Manager for Excel – Release 8.0, March 2011
Reference Manual
Copyright © 1997-2011 by MarketingStat GmbH
All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or
transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise,
without the prior written permission of the publisher.
February 2011. Printed in Switzerland.
First edition 1998
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ISBN 13: 978-3-033-00854-0
ISBN 9: 3-033-00854-0
MarketingStat is a proud member of:
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Summary of Contents
INTRODUCTION TO MM4XL SOFTWARE ................................................. 19
SECTION 1: STRATEGIC TOOLS............................................................... 31
1. BCG PRODUCT PORTFOLIO ANALYSIS ...........................................................................33
2. GE/MCKINSEY PRODUCT PORTFOLIO ANALYSIS ........................................................47
3. BRAND MAPPING..................................................................................................................57
4. BRAND SWITCH ANALYST.................................................................................................77
5. PROFILE MANAGER .............................................................................................................91
6. FORECAST MANAGER .........................................................................................................97
7. QUALITY MANAGER..........................................................................................................119
8. RISK ANALYST ....................................................................................................................159
9. DECISION TREE ...................................................................................................................253
SECTION 2: ANALYTICAL TOOLS........................................................... 269
10. GRAVITATION ANALYST................................................................................................271
11. CLUSTER ANALYSIS ........................................................................................................277
12. SEGMENTATION TREE.....................................................................................................287
13. PROPORTION ANALYST ..................................................................................................295
14. SAMPLE MANAGER..........................................................................................................301
15. CROSSTAB (CONTINGENCY TABLES)..........................................................................307
16. DESCRIPTIVE ANALYST..................................................................................................319
17. GROUP VARIATION ANALYST ......................................................................................327
SECTION 3: CHARTS & MAPS ................................................................. 337
18. SMART MAPPING ..............................................................................................................339
19. SEMANTIC DIFFERENTIAL .............................................................................................349
20. 4-DIMENSIONAL MAP ......................................................................................................353
21. STACKED CHARTS............................................................................................................357
22. BENCHMARK ANALYSIS.................................................................................................361
23. PROJECT MAPPING ...........................................................................................................367
APPENDIX: DETAILED OUTPUT BY TOOL............................................. 383
INDEX ......................................................................................................... 423
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Contents
INTRODUCTION TO MM4XL SOFTWARE ............................................... 19
OUR WORLD.................................................................................................................................................................. 19
INTRODUCTION TO MM4XL SOFTWARE ....................................................................................................................... 20
MM4XL Software Tools ............................................................................................................................................ 20
PROFICIENT WITH MM4XL IN FIVE STEPS .................................................................................................................... 21
MM4XL DOCUMENTATION .......................................................................................................................................... 22
Learning MM4XL Software ...................................................................................................................................... 22
Working with MM4XL Software ............................................................................................................................... 22
Getting Help ............................................................................................................................................................. 22
WHAT’S NEW IN MM4XL............................................................................................................................................. 23
MM4XL SOFTWARE BASICS ......................................................................................................................................... 24
Software Requirements ............................................................................................................................................. 24
Hardware Requirements ........................................................................................................................................... 24
Setting up MM4XL on a Network.............................................................................................................................. 25
Updating MM4XL..................................................................................................................................................... 25
BUY MM4XL SOFTWARE ............................................................................................................................................. 25
LICENSE FORM .............................................................................................................................................................. 26
License Benefits ........................................................................................................................................................ 26
Unlocking MM4XL ................................................................................................................................................... 26
Copyright .................................................................................................................................................................. 26
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SECTION 1: STRATEGIC TOOLS............................................................... 31
1. BCG PRODUCT PORTFOLIO ANALYSIS .............................................. 33
BCG IN A NUTSHELL ..................................................................................................................................................... 33
HOW TO RUN THE BCG PORTFOLIO ANALYSIS ............................................................................................................. 34
HOW TO INTERPRET THE BCG ANALYSIS ...................................................................................................................... 36
WHAT IS BCG INTERPRETER ......................................................................................................................................... 37
HOW TO RUN BCG INTERPRETER .................................................................................................................................. 37
THE PORTFOLIO BALANCE CONCEPT............................................................................................................................. 41
PORTFOLIO OPTIMIZATION ............................................................................................................................................ 42
TECHNICALITIES ............................................................................................................................................................ 43
REFERENCES TO THE PRODUCT PORTFOLIO ANALYSIS .................................................................................................. 44
2. GE/MCKINSEY PRODUCT PORTFOLIO ANALYSIS ............................ 47
MCKINSEY ANALYSIS IN A NUTSHELL .......................................................................................................................... 47
THE FACTORS OF THE ANALYSIS ................................................................................................................................... 48
HOW TO RUN THE MCKINSEY PRODUCT PORTFOLIO ANALYSIS ................................................................................... 49
HOW TO RUN DYNAMIC ANALYSES .............................................................................................................................. 51
OUTPUT OF THE ANALYSIS ............................................................................................................................................ 51
HOW TO INTERPRET THE ANALYSIS .............................................................................................................................. 52
STRATEGIC IMPLICATIONS ............................................................................................................................................. 53
REFERENCES TO THE GE/MCKINSEY PRODUCT PORTFOLIO ANALYSIS ......................................................................... 54
3. BRAND MAPPING.................................................................................... 57
BRAND MAPPING IN A NUTSHELL .................................................................................................................................. 57
HOW TO RUN BRAND MAPPING .................................................................................................................................... 58
HOW TO INTERPRET BRAND MAPPING .......................................................................................................................... 61
EXAMPLES ..................................................................................................................................................................... 64
EXAMPLE 1: PLAIN CONTINGENCY TABLE ...................................................................................................................... 64
BRAND MAPPING AND STRATEGY ................................................................................................................................. 67
EXAMPLE 2: TIME SERIES ANALYSIS .............................................................................................................................. 67
EXAMPLE 3: SUPPLEMENTARY DATA ............................................................................................................................. 69
EXAMPLE 3.1: DYNAMIC MAPS ...................................................................................................................................... 69
EXAMPLE 3.2: BRAND IMAGE MAPS ............................................................................................................................... 70
EXAMPLE 4: MISSING DATA ........................................................................................................................................... 72
REFERENCES TO THE BRAND MAPPING ANALYSIS ........................................................................................................ 73
4. BRAND SWITCH ANALYST .................................................................... 77
BRAND SWITCH ANALYST IN A NUTSHELL .................................................................................................................... 77
HOW TO RUN BRAND SWITCH ANALYST ....................................................................................................................... 78
Data Input................................................................................................................................................................. 78
Data Output .............................................................................................................................................................. 80
DYNAMIC BRAND SWITCH ANALYSIS ........................................................................................................................... 83
Dynamic Analysis Report.......................................................................................................................................... 83
ANALYSIS CASE: HAIR LOSS ......................................................................................................................................... 84
TECHNICALITIES ............................................................................................................................................................ 86
The Quadratic Programming Model ........................................................................................................................ 86
REFERENCES TO THE BRAND SWITCH ANALYSIS ........................................................................................................... 88
5. PROFILE MANAGER............................................................................... 91
PROFILE MANAGER IN A NUTSHELL .............................................................................................................................. 91
HOW TO RUN PROFILE MANAGER ................................................................................................................................. 92
ANATOMY OF A PROFILE MANAGER REPORT ................................................................................................................ 93
Input data.................................................................................................................................................................. 93
The Charts ................................................................................................................................................................ 93
Sensitivity Analysis ................................................................................................................................................... 94
TECHNICALITIES ............................................................................................................................................................ 95
The model ................................................................................................................................................................. 95
Known problems ....................................................................................................................................................... 95
REFERENCES.................................................................................................................................................................. 95
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6. FORECAST MANAGER ........................................................................... 97
FORECAST MANAGER IN A NUTSHELL ........................................................................................................................... 97
HOW TO RUN FORECAST MANAGER ............................................................................................................................. 98
Page 1: Input Data ................................................................................................................................................... 98
Page 2: Data Attributes ............................................................................................................................................ 99
Page 3: Method Gallery ......................................................................................................................................... 100
Page 4: Special Events ........................................................................................................................................... 101
OUTPUT REPORT ......................................................................................................................................................... 102
ANATOMY OF A FORECAST MANAGER OUTPUT REPORT ............................................................................................. 103
1. Report heading.................................................................................................................................................... 103
2. Best fitted model ................................................................................................................................................. 103
3. Accuracy & Seasonality tables ........................................................................................................................... 104
4. Control charts..................................................................................................................................................... 104
5. Special Events..................................................................................................................................................... 107
TECHNICALITIES .......................................................................................................................................................... 109
Forecasting? Never heard of it. .............................................................................................................................. 109
Forecasting Technique Selection............................................................................................................................ 109
Forecast horizon .....................................................................................................................................................................109
Level of accuracy ...................................................................................................................................................................109
Data pattern ............................................................................................................................................................................110
Forecast Manager: Opening the black box ............................................................................................................ 111
How to find optimized unknowns ..........................................................................................................................................112
General formulae: Models with unknowns.............................................................................................................................112
General formulae: Models without unknowns........................................................................................................................114
Seasonal coefficients ..............................................................................................................................................................114
Report heading .......................................................................................................................................................................115
Reliability & accuracy measures ............................................................................................................................................115
Control Charts ........................................................................................................................................................................116
Special Events ........................................................................................................................................................................116
Known problems ..................................................................................................................................................... 117
REFERENCES TO FORECAST MANAGER........................................................................................................................ 117
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7. QUALITY MANAGER............................................................................ 119
QUALITY MANAGER IN A NUTSHELL ........................................................................................................................... 119
INTRODUCTION TO QUALITY MANAGER ...................................................................................................................... 120
How to use Quality Manager.................................................................................................................................. 120
INTRODUCTION TO QUALITY CONTROL ....................................................................................................................... 123
What is statistical quality control (SQC)? .............................................................................................................. 123
Statistical process control (SPC) ............................................................................................................................ 123
Acceptance sampling (AS) ...................................................................................................................................... 124
Variation, source of improvement........................................................................................................................... 124
SPC, ATTRIBUTE CHARTS ........................................................................................................................................... 126
C chart .................................................................................................................................................................... 126
Input data................................................................................................................................................................................127
Output results .........................................................................................................................................................................128
U chart.................................................................................................................................................................... 130
Input data................................................................................................................................................................................130
Output results .........................................................................................................................................................................131
P chart with fixed and variable lot size .................................................................................................................. 133
Input data for the fixed lot ......................................................................................................................................................134
Output results for the fixed lot................................................................................................................................................135
Input data for the variable lot .................................................................................................................................................136
Output results for the variable lot ...........................................................................................................................................136
nP chart .................................................................................................................................................................. 137
Input data................................................................................................................................................................................138
Output results .........................................................................................................................................................................138
SPC, VARIABLE CHARTS ............................................................................................................................................. 140
Xbar and Range charts (X-R) ................................................................................................................................. 140
Input data................................................................................................................................................................................142
Output results .........................................................................................................................................................................142
Xbar and Sigma charts (X-S) .................................................................................................................................. 144
Input data................................................................................................................................................................................145
Output results .........................................................................................................................................................................145
PROCESS CAPABILITY ANALYSIS .................................................................................................................................. 147
Input data................................................................................................................................................................................147
Output results .........................................................................................................................................................................148
Kolmogorov-Smirnov test ......................................................................................................................................................149
ACCEPTANCE SAMPLING ............................................................................................................................................. 150
Operating characteristics curve (OCC, for large lots)........................................................................................... 150
Input data................................................................................................................................................................................150
Output results .........................................................................................................................................................................151
Hypergeometric operating characteristics curve (HOCC, for small lots).............................................................. 152
Input data................................................................................................................................................................................152
Output results .........................................................................................................................................................................153
Average outgoing quality (AOQ) ............................................................................................................................ 154
Input data................................................................................................................................................................................154
Output results .........................................................................................................................................................................154
TECHNICALITIES .......................................................................................................................................................... 156
REFERENCES................................................................................................................................................................ 157
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8. RISK ANALYST...................................................................................... 159
RISK ANALYST IN A NUTSHELL ................................................................................................................................... 159
RISK ANALYST EXPERT IN A FEW MINUTES ................................................................................................................ 160
Using an existing model.......................................................................................................................................... 160
Building your own model........................................................................................................................................ 161
INTRODUCTION TO DECISION ANALYSIS: RISK AND SCENARIO MODELING ................................................................. 162
INTRODUCING RISK ANALYST WITH AN EXAMPLE ...................................................................................................... 163
HOW TO RUN RISK ANALYST ....................................................................................................................................... 167
Model building........................................................................................................................................................ 167
Assessing variable cells..........................................................................................................................................................167
Output cells ............................................................................................................................................................................168
Locked cells ...........................................................................................................................................................................168
Naming variables....................................................................................................................................................................168
Formula bar ............................................................................................................................................................................168
Defining distributions.............................................................................................................................................................169
Data fitting .............................................................................................................................................................................170
Model simulation .................................................................................................................................................... 174
Sheet mode .............................................................................................................................................................................175
Sampling Page........................................................................................................................................................................175
Report Page ............................................................................................................................................................................176
Model report ........................................................................................................................................................... 178
Simulation report....................................................................................................................................................................178
Statistics .................................................................................................................................................................................178
Sensitivity...............................................................................................................................................................................179
Input charts.............................................................................................................................................................................179
Output charts ..........................................................................................................................................................................179
Time Series charts ..................................................................................................................................................................180
Short report.............................................................................................................................................................................180
Report Preview.......................................................................................................................................................................182
Getting help ............................................................................................................................................................ 185
Learning center.......................................................................................................................................................................185
Online help .............................................................................................................................................................................185
The Function Wizard..............................................................................................................................................................186
SIMULATION? NEVER HEARD OF IT.............................................................................................................................. 188
Contributing Factor Diagram ................................................................................................................................ 189
What are probability distribution functions?.......................................................................................................... 190
Random numbers .................................................................................................................................................... 191
Monte Carlo method ............................................................................................................................................... 192
Distribution types.................................................................................................................................................... 192
Interpreting distributions........................................................................................................................................ 193
Chance of failure .................................................................................................................................................... 195
Why the mode?........................................................................................................................................................ 196
Why correlated variables?...................................................................................................................................... 197
Summary of functions available in Risk Analyst..................................................................................................... 199
Property functions ..................................................................................................................................................................199
Utility functions......................................................................................................................................................................200
Distribution functions.............................................................................................................................................................201
EXAMPLES ................................................................................................................................................................... 202
Example 1: Media Choice....................................................................................................................................... 202
Example 2: Net Present Value ................................................................................................................................ 205
Example 3: Correlated variables............................................................................................................................ 209
TECHNICALITIES .......................................................................................................................................................... 211
Known issues........................................................................................................................................................ 211
PROPERTY FUNCTIONS ................................................................................................................................................ 213
Function mmOUTPUT() ......................................................................................................................................... 213
Function mmNAME(“CellName”, [Optional: ItemNum]) ..................................................................................... 214
Function mmLOCK() .............................................................................................................................................. 215
UTILITY FUNCTIONS .................................................................................................................................................... 216
Function mmHISTO(InputRng, [Optional: Classes])............................................................................................. 216
Function mmOPTNUM(InputRng, [Optional: StablePeriods], [Optional: SelectionLimit]) ................................. 218
Function mmCORREL(CorrMtx)............................................................................................................................ 219
DISTRIBUTION FUNCTIONS .......................................................................................................................................... 220
mmBETA(Scale, Shape) .......................................................................................................................................... 220
mmBETAGEN(Scale, Shape, [Optional: Lower], [Optional: Upper])................................................................... 221
mmBINOMIAL(Trials, Successes) .......................................................................................................................... 223
mmCHI2(Degrees).................................................................................................................................................. 224
mmDISCRETE(InputRange, Probabilities) ............................................................................................................ 225
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mmERF(Mean) ....................................................................................................................................................... 226
mmERLANG(Scale, Shape) .................................................................................................................................... 227
mmEXPON(Mean).................................................................................................................................................. 228
mmEXTVAL(ModalValue, StDeviation) ................................................................................................................. 229
mmGAMMA(Scale, Shape) ..................................................................................................................................... 230
mmGAUSSINV (Mean, Scale)................................................................................................................................. 231
mmGEO(Trials) ...................................................................................................................................................... 232
mmHYPERGEO(Sample, Defects, BatchSize) ........................................................................................................ 233
mmINTUNI(Lower, Upper) .................................................................................................................................... 234
mmLOGISTIC(Mean, StDeviation)......................................................................................................................... 235
mmLOGNORMAL(Mean, StDeviation) .................................................................................................................. 236
mmNEGBIN(Failures, Successes) .......................................................................................................................... 237
mmNORMAL(Mean, StDeviation) .......................................................................................................................... 238
mmPARETO(Location, ModalValue) ..................................................................................................................... 239
mmPARETO2(Location, ModalValue) ................................................................................................................... 240
mmPOISSON(Mean)............................................................................................................................................... 241
mmRANDBETWEEN(Lower, Upper) ..................................................................................................................... 242
mmRAYLEIGH(ModalValue) ................................................................................................................................. 243
mmSTUDENT(Degrees) ......................................................................................................................................... 244
mmTRI(Lower, ModalValue, Upper)...................................................................................................................... 245
mmTRI(Lower, ModalValue, Upper)...................................................................................................................... 245
mmUNIFORM(Lower, Upper)................................................................................................................................ 246
mmWEIBULL(Life, Shape) ..................................................................................................................................... 247
PROBABILITY FUNCTIONS............................................................................................................................................ 249
SOURCES ..................................................................................................................................................................... 250
9. DECISION TREE .................................................................................... 253
DECISION TREE IN A NUTSHELL .................................................................................................................................. 253
AN EXAMPLE AS APPETIZER ......................................................................................................................................... 254
Background............................................................................................................................................................. 254
Discussion............................................................................................................................................................... 254
Recommended strategy ........................................................................................................................................... 255
Take less risk .......................................................................................................................................................... 255
HOW TO RUN DTREE .................................................................................................................................................. 257
Create a new tree.................................................................................................................................................... 257
Add and modify a tree node .................................................................................................................................... 257
Decision path .......................................................................................................................................................... 258
ANATOMY OF A DECISION TREE .................................................................................................................................. 259
Naïve trees .............................................................................................................................................................. 259
Blank tree (no math)...............................................................................................................................................................259
Multiplicative tree ..................................................................................................................................................................259
Decision trees ......................................................................................................................................................... 260
Decision node.........................................................................................................................................................................260
Chance node ...........................................................................................................................................................................261
End node ................................................................................................................................................................................261
Optimum path.........................................................................................................................................................................261
ANATOMY OF A DTREE OUTPUT REPORT .................................................................................................................... 262
Risk profile.............................................................................................................................................................. 262
Charts ..................................................................................................................................................................... 262
TECHNICALITIES .......................................................................................................................................................... 263
Assessing probabilities ........................................................................................................................................... 264
Risk attitude ............................................................................................................................................................ 264
Utility functions ...................................................................................................................................................... 265
Risk Tolerance .......................................................................................................................................................................265
Exponential utility function....................................................................................................................................................265
Logarithmic utility function ...................................................................................................................................................266
Expected monetary value (EMV) ...........................................................................................................................................266
Expected utilities ....................................................................................................................................................................266
Certainty equivalent ...............................................................................................................................................................266
KNOWN PROBLEMS ...................................................................................................................................................... 267
REFERENCES................................................................................................................................................................ 267
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SECTION 2: ANALYTICAL TOOLS.......................................................... 269
10. GRAVITATION ANALYST .................................................................. 271
GRAVITATION ANALYST IN A NUTSHELL .................................................................................................................... 271
HOW TO RUN THE GRAVITY MODEL ............................................................................................................................ 272
DATA INPUT ................................................................................................................................................................ 272
DATA OUTPUT ............................................................................................................................................................. 274
TECHNICALITIES .......................................................................................................................................................... 274
REFERENCES TO THE GRAVITATION ANALYST ............................................................................................................ 275
11. CLUSTER ANALYSIS........................................................................... 277
CLUSTER ANALYSIS IN A NUTSHELL ............................................................................................................................ 277
HOW TO RUN CLUSTER ANALYSIS ............................................................................................................................... 278
WHAT IS SEGMENTATION?........................................................................................................................................... 279
AN EXAMPLE: CLUSTERING COMPANY PROFILES ......................................................................................................... 280
TECHNICALITIES .......................................................................................................................................................... 284
REFERENCES TO CLUSTER ANALYSIS .......................................................................................................................... 285
12. SEGMENTATION TREE ...................................................................... 287
SEGMENTATION TREE IN A NUTSHELL......................................................................................................................... 287
HOW TO RUN SEGMENTATION TREE ........................................................................................................................... 288
ANATOMY OF A SEGMENTATION TREE REPORT .......................................................................................................... 289
The Tree.................................................................................................................................................................. 289
The Table ................................................................................................................................................................ 290
TECHNICALITIES .......................................................................................................................................................... 291
Assembling input data............................................................................................................................................. 291
Known problems ..................................................................................................................................................... 292
REFERENCES................................................................................................................................................................ 292
13. PROPORTION ANALYST .................................................................... 295
PROPORTION ANALYST IN A NUTSHELL....................................................................................................................... 295
HOW TO RUN PROPORTION ANALYST ......................................................................................................................... 296
ANATOMY OF A PROPORTION ANALYST OUTPUT REPORT........................................................................................... 297
TECHNICALITIES .......................................................................................................................................................... 298
REFERENCES TO PROPORTION ANALYST ..................................................................................................................... 298
14. SAMPLE MANAGER............................................................................ 301
SAMPLE MANAGER IN A NUTSHELL............................................................................................................................. 301
HOW TO RUN SAMPLE MANAGER ............................................................................................................................... 302
HOW TO EXTRACT A RANDOM SAMPLE ....................................................................................................................... 302
ANATOMY OF A SAMPLE MANAGER OUTPUT REPORT................................................................................................. 303
TECHNICALITIES .......................................................................................................................................................... 303
REFERENCES TO SAMPLE MANAGER ........................................................................................................................... 305
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15. CROSSTAB (CONTINGENCY TABLES).............................................. 307
CROSSTAB IN A NUTSHELL .......................................................................................................................................... 307
HOW CROSSTAB WORKS ............................................................................................................................................. 308
1. Two kinds of tables ............................................................................................................................................. 308
2. Two kinds of questions........................................................................................................................................ 309
3. Code range ......................................................................................................................................................... 310
4. Data treatment .................................................................................................................................................... 310
HOW TO RUN CROSSTAB ............................................................................................................................................ 311
Data page ............................................................................................................................................................... 311
Parameters page..................................................................................................................................................... 311
Statistics page ......................................................................................................................................................... 312
OUTPUT REPORT ......................................................................................................................................................... 313
TECHNICALITIES .......................................................................................................................................................... 314
Testing proportions for significance (Z-test) .......................................................................................................... 314
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Testing tables for independence ( χ Chi squared)................................................................................................. 315
Testing variables for correlation (Pearson) ........................................................................................................... 316
REFERENCES TO CROSSTAB ........................................................................................................................................ 317
16. DESCRIPTIVE ANALYST .................................................................... 319
DESCRIPTIVE ANALYST IN A NUTSHELL ...................................................................................................................... 319
HOW TO RUN DESCRIPTIVE ANALYST......................................................................................................................... 320
Page 1: Pareto Chart.............................................................................................................................................. 320
Page 2: Descriptive Statistics ................................................................................................................................. 321
OUTPUT REPORT ......................................................................................................................................................... 322
Pareto analysis ....................................................................................................................................................... 322
Statistics.................................................................................................................................................................. 323
Box plots ................................................................................................................................................................. 323
TECHNICALITIES .......................................................................................................................................................... 324
Known problems ..................................................................................................................................................... 324
REFERENCES TO DECRIPTIVE ANALYST ...................................................................................................................... 324
17. GROUP VARIATION ANALYST.......................................................... 327
GROUP VARIATION ANALYST IN A NUTSHELL............................................................................................................. 327
HOW TO RUN GROUP VARIATION ANALYST ............................................................................................................... 328
PLANNING AND MANAGING BUSINESS TESTS .............................................................................................................. 329
Arranging data for testing ...................................................................................................................................... 329
Implementing a Marketing Testing Lab.................................................................................................................. 329
ANATOMY OF A VARIATION ANALYST OUTPUT REPORT ............................................................................................. 330
TECHNICALITIES .......................................................................................................................................................... 333
Unequal sample size ............................................................................................................................................... 333
Other ANOVA methods........................................................................................................................................... 333
REFERENCES TO GROUP VARIATION ANALYST ........................................................................................................... 334
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SECTION 3: CHARTS & MAPS ................................................................. 337
18. SMART MAPPING................................................................................ 339
SMART MAPPING IN A NUTSHELL ................................................................................................................................ 339
HOW TO RUN SMART MAPPING ................................................................................................................................... 340
HOW TO INTERPRET NORMALIZED SMART MAPPING .................................................................................................. 342
WHY AND HOW TO RE-SCALE QUADRANTS ................................................................................................................ 343
EXAMPLE OF A STRUCTURED CM IN THE OTC MARKET ............................................................................................. 344
EXAMPLE OF SALES TENDENCY ANALYSIS ................................................................................................................. 345
NOTE ON SCATTER PLOTTING...................................................................................................................................... 346
SCATTER CHART AS A FORECAST TOOL ...................................................................................................................... 346
REFERENCES TO SMART MAPPING ............................................................................................................................... 347
19. SEMANTIC DIFFERENTIAL ............................................................... 349
SEMANTIC DIFFERENTIAL CHART IN A NUTSHELL....................................................................................................... 349
HOW TO RUN SEMANTIC DIFFERENTIAL CHART ......................................................................................................... 350
TECHNICALITIES: THE SEMANTIC DIFFERENTIAL CONCEPT .......................................................................................... 350
REFERENCES TO SEMANTIC DIFFERENTIAL ................................................................................................................. 351
20. 4-DIMENSIONAL MAP ........................................................................ 353
4D MAP© IN A NUTSHELL ........................................................................................................................................... 353
HOW TO RUN 4D CHART............................................................................................................................................. 354
TECHNICALITIES .......................................................................................................................................................... 355
Anatomy of a 4D Chart........................................................................................................................................... 355
21. STACKED CHARTS ............................................................................. 357
STACKED CHARTS IN A NUTSHELL .............................................................................................................................. 357
HOW TO RUN STACKED CHARTS ................................................................................................................................. 358
ANATOMY OF A STACKED CHART ............................................................................................................................... 359
22. BENCHMARK ANALYSIS ................................................................... 361
BENCHMARK ANALYSIS IN A NUTSHELL ..................................................................................................................... 361
HOW TO RUN BENCHMARK ANALYSIS ........................................................................................................................ 362
ANATOMY OF A BENCHMARK ANALYSIS OUTPUT REPORT ......................................................................................... 363
The Benchmark Map............................................................................................................................................... 363
The Tables............................................................................................................................................................... 364
REFERENCES................................................................................................................................................................ 364
23. PROJECT MAPPING............................................................................ 367
PROJECT MAPPING IN A NUTSHELL ............................................................................................................................. 367
HOW IS PROJECT MAPPING USEFUL?........................................................................................................................... 368
MAPPING GUIDELINES ................................................................................................................................................. 368
THE WORKING ENVIRONMENT .................................................................................................................................... 369
The drawing surface ............................................................................................................................................... 369
Drop-down menu .................................................................................................................................................... 369
Toolbar menu.......................................................................................................................................................... 373
WORKING WITH PROJECT MAPPING ............................................................................................................................ 374
Enriching Maps ...................................................................................................................................................... 374
Formatting single elements..................................................................................................................................... 374
Settings page ..........................................................................................................................................................................374
Additional page ......................................................................................................................................................................376
PROJECT MAPPING OUTPUT REPORT ........................................................................................................................... 378
The Map.................................................................................................................................................................. 378
The Summary Report .............................................................................................................................................. 378
EXAMPLES OF PROJECT MAPPING................................................................................................................................ 379
REFERENCES................................................................................................................................................................ 381
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APPENDIX: DETAILED OUTPUT BY TOOL............................................ 383
PORTFOLIO ANALYSIS – BCG SHARE/GROWTH MATRIX ............................................................................................ 384
PORTFOLIO ANALYSIS – MCKINSEY ASSESSMENT ARRAY.......................................................................................... 387
BRAND MAPPING: STRATEGY (CORRESPONDENCE ANALYSIS) ................................................................................... 388
BRAND MAPPING: SUPPLEMENTARY POINTS ............................................................................................................... 389
BRAND MAPPING: MISSING DATA ............................................................................................................................... 390
BRAND SWITCH ANALYSIS .......................................................................................................................................... 391
GRAVITY ANALYSIS .................................................................................................................................................... 393
CLUSTER ANALYSIS: WARD’S METHOD ...................................................................................................................... 394
CLUSTER ANALYSIS: K-MEANS METHOD ................................................................................................................... 395
SEGMENTATION TREE.................................................................................................................................................. 396
PROFILE MANAGER ..................................................................................................................................................... 397
DESCRIPTIVE ANALYST ............................................................................................................................................... 398
SMART CHART (BUBBLES WITH LABELS) .................................................................................................................... 399
SEMANTIC DIFFERENTIAL ............................................................................................................................................ 401
4-D MAP ..................................................................................................................................................................... 402
STACKED CHARTS ....................................................................................................................................................... 403
BENCHMARK MAP ....................................................................................................................................................... 404
PROJECT (MIND) MAPPING .......................................................................................................................................... 405
FORECAST MANAGER .................................................................................................................................................. 407
CROSSTAB (CONTINGENCY TABLES) .......................................................................................................................... 411
SAMPLE MANAGER...................................................................................................................................................... 412
PROPORTION ANALYST ............................................................................................................................................... 413
VARIATION ANALYST .................................................................................................................................................. 414
QUALITY MANAGER .................................................................................................................................................... 415
DECISION TREE ........................................................................................................................................................... 417
RISK ANALYST ............................................................................................................................................................ 419
INDEX ........................................................................................................ 423
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16
www.mm4xl.com
17
www.mm4xl.com
18
Introduction to MM4XL Software
Our World
MarketingStat is a company of the virtual generation. It operates from Switzerland with a workforce
spread over Europe, North America, and Asia. MarketingStat is a privately held enterprise, funded by its
founders, and is not currently seeking investment funds.
Business consultants interested in promoting MarketingStat software and seminars, please inquire at
[email protected].
Universities, business schools and professors that would like to (i) use MM4XL in their courses, and
(ii) help us with written reference material and relevant articles, please contact [email protected].
Software distributors interested in listing MarketingStat products in their catalogues should contact
[email protected].
Single and Multi-User MM4XL licenses can be purchased online at:
http://www.shareit.com/product.html?productid=176654 .
MarketingStat GmbH (Headquarters)
Im Goldbrunnen 39
CH-4104 Oberwil
Switzerland
Phone +41 (0)61 401 6055
Fax +41 (0)61 401 6073
www.MarketingStat.com
[email protected]
Internet Sales Collector
ShareIt – element 5 AG
Vogelsanger Str. 78
50823 Cologne
Germany.
Phone +49 (0)221 240 7279
Fax +49.221 (0)240 7278
www.shareit.com
[email protected]
MarketingStat – Commercial
CH-4153 Reinach
Switzerland
Phone +41 (0)61 717 8292
Fax +41 (0)61 717 8788
[email protected]
ShareIt! Inc. USA
460 Mathews Street
Suite 1800
Greensburg, PA 15601-8059
USA
Phone +1 724 850 8186
Fax +1 724 850 8187
www.shareit.com
These are just some of the clients we proudly serve:
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19
Marketing Manager for Excel (MM4XL) is the strategic analyst every Marketing Manager wants on
their team!
MM4XL is a comprehensive analysis toolbox useful to marketers, business consultants, and
academics for improving strategic decision-making. It aims to extract more strategic information from
expensive market data by applying methods and techniques described in the relevant literature, as well as by
using innovative solutions.
MM4XL gives you unparalleled graphical and analytical power, both to support critical business decisions
and to monitor ongoing activities. And this is all in Microsoft Excel®, the most preferred working environment
for marketing departments worldwide.
Companies relying on MM4XL for business analysis report three distinct reasons why they prefer it:
Competitiveness: Managers keen on fact-and-data driven models get more information more quickly out of
business data, which translates into better-focused strategies and faster responses to competitor moves.
Productivity: Drawing maps and charts as well as running complex analyses takes only seconds with
MM4XL, and the output is already in MS Excel.
IT Resources: Last but not least, MM4XL is a comprehensive collection of tools that reduces the number of
analytical software applications run on server machines, which means greater system stability and better
resource allocation. Your IT people will appreciate this.
MM4XL Software Tools
MM4XL offers over 20 different tools, with more
on the way (MM4XL relies on an ongoing
development plan). Tools can be used in a
modular fashion or stand-alone. There are three
broad categories of tools:
(8)
Analytical (8)
Analytical
(9)
Strategic(9)
Strategic
•CrossTab
•CrossTab
•SampleManager
Manager
•Sample
•
Proportion
Manager
•Proportion Manager
•DescriptiveManager
Manager
•Descriptive
•
Cluster
Analysis
•Cluster Analysis
•
Segmentation
Tree
•Segmentation Tree
•GravityAnalyst
Analyst
•Gravity
•
Variation
Analyst
•Variation Analyst
•BCGPortfolio
PortfolioMatrix
Matrix
•BCG
•McKinseyPortfolio
PortfolioMtx
Mtx
•McKinsey
•
Brand
Switch
•Brand Switch
•BrandMapping
Mapping
•Brand
•ForecastManager
Manager
•Forecast
•
Profile
Manager
•Profile Manager
•QualityAnalyst
Analyst
•Quality
•DecisionTree
Tree
•Decision
•
Risk
Analyst
•Risk Analyst
CHARTS
&
MAPS
ANALYTICAL
Charts & Maps are tools for drawing bivariate
graphical representations that are useful when
presenting data. These tools either fill functional
gaps in Excel or add completely new functionality.
They include: Bubble Charts, Semantic
Differential and several other tools.
STRATEGIC
(6)
Charts&&Maps
Maps(6)
Charts
•SmartMapping
Mapping
•Smart
•DifferentialSemantic
Semantic
•Differential
•4DMap
Map
•4D
•
Stacked
Charts
•Stacked Charts
•BenchmarkMap
Map
•Benchmark
•Project(Mind)
(Mind)Mapping
Mapping
•Project
Analytical tools apply methods from statistics, ‘translated’ for managers. Among their many uses, these
tools can assist in analyzing datasets such as those from survey studies. Four tools compute survey sample
size, draw contingency tables, test significance of proportions, and test differences between groups. Three
other tools are useful for segmentation purposes: Cluster Analysis, Gravity Analysis, and Segmentation Tree.
Strategic tools apply concepts from management science, and are useful when building models for better
decision making. Two tools provide Product Portfolio Analysis, Brand Switch estimates loyalty levels from
sales data, Brand Mapping draws highly strategic maps applying correspondence analysis, Forecast
Manager makes short-term optimized predictions, Quality Analyst is the perfect toolbox for quality control,
Decision Tree and Risk Analyst are used for framing and analyzing issues involving uncertainty.
MM4XL includes detailed online help, and each tool has an Example sheet that can be opened directly from
the user form. For some tools, such as Forecast Manager, online help also supplies short descriptions of
commands and functions available with that tool.
Finally, MM4XL runs in five different languages: English, Spanish, French, German and Italian. Users can
switch the language from the software menu. This feature is particularly appreciated by companies with an
international workforce.
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20
Proficient with MM4XL in Five Steps
Using MM4XL is easy.
Follow this easy five-step approach and get up to speed in minutes.
Step 1
In the main toolbar click on the button Show all tools. A new toolbar is
created.
Step 2
In the new toolbar (see picture below) click on one of the buttons to
open that tool form.
1.
Tip
Rest the mouse pointer over a toolbar button to briefly display a tool
description.
Step 3
All tool forms include a listbox labeled Learning Center. Click on it to
see the list of available options. There is help material, example
sheets with data, and helpful utilities to choose from. Open the
Example sheet and familiarize yourself with the tool and the input
data.
Step 4
Click on the Cancel button to close
the tool form.
Step 5
Spend a few minutes studying the examples, and you will be ready to run each of the tools you are
interested in.
THE SCIENTIFIC APPROACH IS KEY!
When you feed MM4XL with solid data, you can get the most out of our software and, as a result, out of your
data as well. This will in turn result in enhanced competitiveness.
Sometimes, however, information is hidden in data and its value isn’t immediately apparent. Therefore, we
encourage managers to take a scientific approach to business management. Ask your marketing research
manager or data supplier about the statistical parameters of the data you use; spend time learning business
statistics and management science; let MM4XL help you make better-informed decisions.
We know that learning can be difficult when you are working full-time, but we also know of managers
succeeding, thanks in large part to scientific management. It’s up to you, and we can help!
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21
MM4XL Documentation
This MM4XL Reference Manual is your comprehensive guide to working with MM4XL software. You will find
it full of practical tips and real-life examples that will help you progress quickly in the proficient use of
MM4XL.
In addition to this book, the complete set of MM4XL documentation includes the Online Help Reference and
the Example Sheets.
Please remember to acknowledge the MM4XL source, should you quote any part of the MM4XL
reference manual in your own work or papers. Explicitly acknowledging the source is the only
allowable and legal way to make use of the text. Improper use of this copyrighted material will be
prosecuted under the appropriate law. The correct citation is:
Marketing Manager for Excel, MM4XL Software
User Guide
Copyright© by MarketingStat GmbH
Learning MM4XL Software
This Reference Manual is intended to get you up and running quickly with MM4XL. You can use the
examples in this book as a source of ideas for your own analytical work. The book is organized in standalone chapters, each covering one of MM4XL’s tools.
Working with MM4XL Software
The Online Help provides reference and how-to information for
all MM4XL tools and functions. You can search the index, and
the user-friendly HTML format enables you to jump between
topics in an intuitive manner. You can also browse the Internet
from it.
Example Sheets are provided for each of the MM4XL tools.
They show how to make selections for running the tools, and
they also show the content of the output from each tool. You
can use the data in the example sheets for learning the tools.
Open the example sheets either from the MM4XL Examples
menu as shown here or from the Learning Center listbox
available in every tool form.
Getting Help
To get help when working with MM4XL software tools, click the
Learning Center listbox to access several useful options.
Tip:
To learn from example sheets printed in a language other than English:
- Select your preferred language from the Set Language menu.
- Open a tool and launch the Example sheet from the Learning Center.
- Repeat the selection as shown in the pictures of the example file.
- Print the output to a new sheet and it will be done in your preferred language.
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22
What’s New in MM4XL
New Tools Every Few Months
MarketingStat has an ongoing development plan for MM4XL. Every few months our software is enriched with
new tools, as well as enhancements to existing tools.
At this time we introduce a new tool called Risk Analyst, useful for building models in a way that
takes into account the uncertainty involved in the events. It applies the Monte Carlo technique to
simulate the outcomes of the models. Risk Analyst provides a multitude of functions that enable you
to model in MS Excel virtually any scenario you can think of. It is fast and accurate, displaying the
results of the simulation in a preview window. A fitting tool is available to help identify appropriate distribution
functions for the user data, and Quick Help can be called from the tool to find out when to use each of the
many functions. Together with another MM4XL software tool called Decision Tree, Risk Analyst provides you
with all the resources needed to analyze even very complex business decisions. Read more about this
sensational tool in the chapter Risk Analyst.
The Brand Mapping tool has been enriched with new options to print more refined maps. Now you
can change bubble and label sizes, and you can choose whether to print map and axis titles.
Although simple, these new options can save a lot of work.
More good news is that, even after the inclusion of this new great tool, the list price of MM4XL software
stays the same. Visit www.MarketingStat.com for current pricing.
Book: Mapping Markets
MarketingStat publishes Mapping Markets for Strategic Purposes with MM4XL Software, a very useful
reference for decision-makers interested in having a deeper understanding of how to use Brand Mapping in
order to win on competitiveness. More information on this book can be found at
www.marketingstat.com/bookmapping.html.
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23
MM4XL Software Basics
How To Install
If you are unfamiliar with installing
software, DO NOT PANIC! Installing
MM4XL is simple! In Windows
Explorer,
double-click
the
file
MM4XL.exe and then follow the
instructions.
The installation facility makes it very
simple to install MM4XL. After
installation, the software can be
launched from the Start Menu or from
the desktop icons as shown in the
picture.
Security Matter
IMPORTANT NOTE! If after installing and launching you cannot see the MM4XL option in the Excel menu
bar, this is most probably due to your Excel security setting. Excel completely prevents macros from running
when set to the highest protection level.
Follow these steps (in Excel 2002) to lower the Excel protection level and run MM4XL:
1.
2.
3.
4.
Select Extra, Macros, Security from the menu.
In the form that appears, check either Medium or Low on the Security level tab.
Click on the tab Trustworthy sources and check the option Trust access to Visual Basic-Project.
Start MM4XL again, and it will work now.
Software Requirements
MM4XL is implemented in VBA. The Windows release is developed to work with MS Excel version 8.0 or
higher on PCs running Win95/98/XP or NT. It can be used without restrictions during the allowed trial time.
When your trial period is over, you are invited to register to continue enjoying the
benefits of MM4XL. To register, click the Register Now icon to enter the secure server
of our sales collector ShareIt. Or click on the blue QuickBuy button you can find on all
MM4XL tool forms.
Alternatively, point your browser to www.MarketingStat.com and enter the Buy page, or fill out and send us
the order form you can open from the MM4XL menu.
If your company needs direct invoicing, please contact:
MarketingStat GmbH
CH-4153 Reinach
Switzerland
Phone +41 (0)61 717 8292
Fax +41 (0)61 717 8788
[email protected]
Hardware Requirements
To use MM4XL you need:
•
•
•
•
An IBM®-compatible PC with an 80486sx or higher CPU (Pentium IV recommended)
A mouse device and a keyboard
A hard disk with 23MB of free space for a typical installation
MS Windows 95 or above and MS Excel 8.0 or above
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24
Setting up MM4XL on a Network
The administrator should install MM4XL on a network server or in a shared directory with Write permission,
so that MM4XL can interact with its components during operations.
Updating MM4XL
If MM4XL software is already installed on your machine, before you install a new version of MM4XL software
make sure you uninstall the previous version. You can do so using the Uninstaller utility from MM4XL's folder
in the Windows Start menu.
Note:
Certain Excel versions make copies of add-in files in a default directory, and old copies could interfere with
the latest version of MM4XL. You can remove these files using the Search utility from the Windows Start
menu. Type the string MM4XL*.xla (with the *) and get rid of all of them. Then install the latest MM4XL.
Now you are ready to work and enjoy MM4XL. Should you experience any problems, please email us at:
[email protected] and we will reply as quickly as possible.
Buy MM4XL Software
We at MarketingStat are confident that we are providing a first class product to our exclusive circle of clients,
and for this reason we allow clients to give MM4XL a full trial before registering. To continue using
MM4XL after the trial period has expired, you have to purchase a license and register your copy of MM4XL.
It is easy to buy MM4XL. The latest release is always available for download at
www.MarketingStat.com. Click on the Quickbuy button (there is also one in every MM4XL
tool form) to enter the MM4XL warehouse, and select the software package you want to buy from three
options: Full version, Educational versions, and Upgrade for existing clients.
Fill out the form that is displayed, and click on Download. Then just check your email. During the next 48
hours – usually less – you will receive your unique license number that unlocks MM4XL for unrestricted use.
If you don’t want to use your credit card over the Internet, send us an email and we will help. Fill out the
Order form that can be opened by clicking on the button Show order form from the MM4XL menu, print the
form, and send it by mail or fax to our sales office at one of these addresses:
MarketingStat GmbH
CH-4153 Reinach
Switzerland
Phone +41 (0)61 717 8292
Fax +41 (0)61 717 8788
E-Mail: [email protected]
www.mm4xl.com
ShareIT! - element 5 AG
Vogelsangerstrasse 78
50823 Cologne, Germany
Phone +49.221.240 7279
Fax: +49.221.240 7278
www.shareit.com
E-Mail: [email protected]
25
License Form
While there is only one MM4XL, there are two different license forms: Full or Educational. Functionally
they are exactly the same. However the Educational license doesn’t permit MM4XL to be used for profit
purposes, such as consulting to third parties for money.
MM4XL Full version license comes in four forms (they are all lifetime):
•
•
•
•
Single copy: 1 user only
Multi-user: several users in the same office location (prices drop significantly)
Multi-site: several users in different company locations (prices drop extremely)
Upgrade: one or several users at a reduced price
MM4XL Educational version at a lowered price:
•
•
Single copy: 1 user at a time only
Multi-user: several users in the same office location
In order to fully activate their license and avoid infringing copyright rules, Educational clients are required to
send us a copy of a document confirming their active professor or full-time student status. You can attach the
document to an email and send it to [email protected].
For current pricing of MM4XL, go to www.marketingstat.com and visit the Buy page.
License Benefits
Registered users receive the following benefits:
•
•
•
•
Lifetime copy of MM4XL software
3 months free software upgrade
6 months technical support by email or telephone
Electronic reference material
Unlocking MM4XL
When you receive your license code from MarketingStat, click
this button on the floating toolbar. In the new form, click the
Enter license number button and this window appears. Fill out the
fields and click OK. That’s it. Your copy has been unlocked and you
can now use MM4XL without restrictions, according to the license
form you registered.
Please remember: Improper use of copyrighted material may lead to
severe penalties for both you and the organization you work for.
Copyright
The MM4XL software package, together with all accompanying material, is copyright by MarketingStat
GmbH. You are entitled to share the evaluation copy of MM4XL software with your friends and
colleagues, but only in the original form as supplied by MarketingStat. This must include all original files in an
unaltered state, as released from www.MarketingStat.com. Any changes made without permission will be
pursued as appropriate.
IMPORTANT! THE SINGLE SITE LICENSE DOES NOT ENTITLE YOU TO SHARE MM4XL ON A
SERVER. To apply for a Multi-user site license, please write to [email protected]. The
unregistered copy of MM4XL works for a limited trial period only. Please do not try to use MM4XL beyond
the permitted trial period.
Continued use of MM4XL after its expiry without registering is a violation of the United States criminal code,
sections 101 through 810. This carries severe personal and corporate penalties.
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26
www.mm4xl.com
27
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28
PART 2:
MM4XL SOFTWARE TOOLS
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29
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30
Section 1: Strategic Tools
Management science concepts for better decision making.
BCG MATRIX
MCKINSEY ASSESSMENT ARRAY
BRAND SWITCH ANALYSIS
BRAND MAPPING
FORECAST MANAGER
PROFILE MANAGER
DECISION TREE
QUALITY ANALYST
RISK ANALYST
(8)
Analytical (8)
Analytical
(9)
Strategic(9)
Strategic
•CrossTab
•CrossTab
•SampleManager
Manager
•Sample
•ProportionManager
Manager
•Proportion
Manager
•Descriptive
•ClusterAnalysis
Analysis
•Cluster
•SegmentationTree
Tree
•Segmentation
•GravityAnalyst
Analyst
•Gravity
•VariationAnalyst
Analyst
•Variation
•BCGPortfolio
PortfolioMatrix
Matrix
•BCG
PortfolioMtx
Mtx
•McKinsey
•BrandSwitch
Switch
•Brand
•BrandMapping
Mapping
•Brand
•ForecastManager
Manager
•Forecast
•ProfileManager
Manager
•Profile
•QualityAnalyst
Analyst
•Quality
•DecisionTree
Tree
•Decision
•RiskAnalyst
Analyst
•Risk
CHARTS
&
MAPS
ANALYTICAL
STRATEGIC
(6)
Charts&&Maps
Maps(6)
Charts
•SmartMapping
Mapping
•Smart
Semantic
•Differential
•4DMap
Map
•4D
•StackedCharts
Charts
•Stacked
•BenchmarkMap
Map
•Benchmark
•Project(Mind)
(Mind)Mapping
Mapping
•Project
Product Portfolio Analysis: BCG Share/Growth Matrix, GE/McKinsey Array
PPA is used for assessing the competitiveness of businesses in one company’s portfolio. Certain companies look at product mix
decisions as portfolio decisions. Each product requires investment and promises a certain return. The role of management is to
determine the products that comprise the portfolio and the funds to allocate to them. In this sense, PPA becomes useful twice a year, or
more frequently if structural changes take place.
Brand Management Tools: Brand Switch, Profile Manager, Brand Mapping
Brand positioning, brand loyalty, and market share behavior are issues of strategic relevance to marketers. The tools in this collection
tackle these issues. They may give managers a competitive edge, and they will certainly prove useful in stimulating strategic thinking
within the team.
Forecast Manager
Forecasts are probabilistic statements about future events, and there are many models to select from. Forecast Manager works with
time series for short-term projections. After choosing the “right” model it selects the “right” method and sets the “correct” parameters for
an optimized fit. The bulk of the work is hidden behind a few mouse-clicks.
Quality Analyst
Statistical quality control helps companies to increase their ability to compete effectively by improving the quality of the product they take
to market. To do so, the characteristics of a sample of products or one or more processes are measured in order to make decisions
regarding their quality. MM4XL software makes available in one package all the tools needed to perform accurate, fast and visually
effective statistical quality control directly in MS Excel.
Decision Analysis: Risk Analyst & Decision Tree
Decision Analysis helps in setting up frameworks for dealing with decision problems involving risk and uncertainty. For instance, your
company calls for incremental funding and you are required to estimate potential sales for several projects and to focus on those
projects that best satisfy the growth goal. There are two aspects to be considered when approaching this challenge:
a.
the estimation of each project outcome
b.
the selection of the most appealing project(s)
The former can be handled with simulation models (use Risk Analyst). The latter can be facilitated using decision trees.
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31
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32
1. BCG Product Portfolio Analysis
BCG in a Nutshell
Building well-balanced product portfolios1 requires monitoring tools to look at the present financial and
competitive status of the SBU's2, in addition to keeping track of changes that might take place over time
among products. In this framework the Boston Consulting Group (BCG) Share/Growth Matrix is a widely
used tool. It is based on the common belief that success in business is strongly linked to cash flow3, which is
a function of market share and market growth4. While the former generates cash, the latter uses it. The
following diagram synthesizes this concept.
CASH FLOW = SUCCESS
Market Share
Market Growth
Generation
CASH
Use
Note:
An example report of this tool is available. Click on the Start button in Windows and select MM4XL –
Marketing Manager for Excel. The file can be found in the Examples folder. Alternatively, start the tool and
click the Example button.
1
All products one company offers on the market.
SBU stands for Strategic Business Unit and refers to each element of the Product Portfolio.
3
The cash flow of one product is shown as Sales minus Costs. From the financial point of view this computation can be extremely
complex, yet the general meaning is simply the subtraction of costs from revenues.
4
The market growth expressed in percentage is given as shown below:
2
⎡⎛ Market Sales 1999 ⎞ ⎤
⎟⎟ − 1⎥ ⋅ 100
⎢⎜⎜
⎣⎢⎝ Market Sales 1998 ⎠ ⎦⎥
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1. Product Portfolio Analysis
33
How To Run the BCG Portfolio Analysis
It is very easy to run the
Product
Portfolio
Analysis with Marketing
Manager.
Select
Portfolio Analysis from the
MM4XL menu, or click the button
in the floating toolbar, and the
window to the right appears.
Input the number of products you
want to analyze. If your company
markets 20 products, enter 20 in
the box beside Number of
products and a predefined report
will be automatically created. This
window lets us set two important
options to enhance the readability
of maps. Max Logarithmic
Market Share = 1000 sets the
horizontal axis of the grid at a
maximum length of 1000. All
leader products with sales higher
than three times that of their direct
competitor5 will be placed at 1000. There is no point in displaying broader measures, and in some cases,
leaders being seven, eight or ten times larger than competitors can adversely affect the whole map. The
same concept is applied to the vertical axis. Select Max market growth = 100% to set the maximum height
of the axis at 100%.
The checkbox Remove old charts is active by default, and it does what it says. Often one needs to repeat
the analysis several times due to changes in the input data. In such cases, it helps to let the tool remove old
charts.
The list box Size of the bubbles is used to enlarge or reduce the size of the bubbles of the BCG matrix.
When working with portfolios made of many products you may need to change bubble size in order to make
the matrix more readable. Accept the default value at first and see if the bubble size is acceptable.
Otherwise, run the analysis again and change the value to a better suited one.
Below is an example of the predefined input data range of the BCG Product Portfolio Analysis built in
Marketing Manager.
Tip:
Watch the Excel status bar in the lower left corner. Messages are displayed which briefly explain the kind of
5
Two products are direct competitors when they share each of the following three characteristics:
a. compete in the same market or market segment
b. offer the same technical performance
c. target the same user/buyer population
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34
operation the tool is performing at that moment.
In column A you can input any sign or value, the function is case sensitive. This is a very useful option when
running dynamic or comparative analysis. For instance, with code Yr1999 and code Yr2000 in column A you
can analyze the same portfolio at two different moments in time. Alternatively, you can code products
belonging to different categories, like in our example below, to different departments, for example. All
products sharing the same code will be displayed on the grid using the same color. Then, press Click here
for the next steps and the analysis runs.
The Product Portfolio Analysis function produces a grid and a summary report as shown below.
The summary report shows sales, market shares and market growth of products grouped in the four BCG
classes: question marks, stars, cash cows and dogs.
In column B the number of products belonging to each category are summed up. The sales of each class are
expressed in value form (column C) and as a percentage (column D) computed on total sales of the products
in the portfolio.
Note:
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35
How to Interpret the BCG Analysis
The Matrix
The portfolio matrix is built on two axes. The horizontal axis (X) tracks the Logarithmic Relative Market
Share6 and the vertical one (Y) shows the Market Growth as a percentage. The picture below summarizes
the major aspects to consider when interpreting the matrix.
1000
100
10
1
0
Notice that logarithms to base 10 are used to scale the X-axis. Full details of the logarithmic scale
computation are given in the Technicalities section. At this time, for the sake of simplicity, a logarithmic
relative market share of 1 is obtained when the sales of our product exactly match those of our direct
competitor. A logarithmic relative market share of 10 equates to our sales being twice those of our
competitor, 100 means three times and so on. When our logarithmic relative market share equals 0,1 we are
10 times smaller than our direct competitor.
The Y-axis intersects the X-axis on the value 1, all bubbles (products) placed on the right side of this value
are not market leaders7. The Y-axis, market growth, is usually set at the average level of all markets in the
portfolio. However this is not always a convenient way of computing it, so the BCG Product Portfolio tool in
MM4XL offers two alternatives: the median of all markets or a manually input value. The analyst will use the
median to get rid of very high or low growth values that can produce unreliable average figures. It is
important to define a coherent crossing value for the Y-axis, for it splits the products in fast or slow growing
markets, and this affects the way the position of single products will be interpreted and evaluated.
Both leaders and non-leaders can compete in a market with high, slow or negative growth rates. In all cases
there are implications concerning cash flow and resources allocation.
There are four different quadrants, or product profiles, displayed on a Portfolio Matrix and, according to BCG,
each should be managed observing, at least, the following rules8:
1. High Growth Low Share (question marks)
6
The Relative Market Share is computed by dividing the sales of one product in the portfolio by the sales of its largest direct competitor.
The Logarithmic Relative Market Share is simply the Relative Market Share expressed on a logarithmic scale. This helps to highlight the
decreasing effect of competitors’ power as the product's market share increases.
7
Market leader is the product collecting the highest revenue in one marketplace, in either value or units.
8
The reference is to the Product's Life Cycle theory, which identifies four phases in the life of a product: Introduction, Growth, Maturity
and Decline. In certain cases, a fifth phase called Revitalization can take place. There is a strong relationship between the position
taken by one product on the BCG Matrix and on its Life Cycle curve. Beginning from the upper quadrant on the right side of the matrix,
question marks may be reasonably associated with the introduction of the product on the market. Stars recall the growth phase, cash
cows can be in the mature stage of their life and dogs pass through the decline phase. When the relationship holds, the financial
implications explained above also hold.
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These products live in an uncertain situation. The market is dynamic but their market share is low.
Management handling these products must plan high investments to keep them competitive and cannot
expect returns, at least not in the short term. This can be the case with newly launched products9. With
established products, the divestment option can be evaluated, given the fairly unattractive position of the
question marks in the product portfolio.
2. High Growth High Share (stars)
The stars are leaders in dynamic markets. Large amounts of money must continue to be invested in them,
but they also produce cash to finance themselves. This way stars result in a slightly negative or positive
saldo. Their strategic orientation must be aggressive to constantly gain market share. These are the products
that will probably be feeding the company's portfolio in the future, and it is important to retain a certain
number of them in the current assets.
3. Low Growth High Share (cash cows)
The cows, leaders in mature markets, mainly sustain the cash needs of the portfolio. Cows do not have a
high cash requirement and generate a large positive saldo. One can expect these products to be under the
attack of smaller competitors. The reasonable strategic path for these products is to maintain their market
share.
4. Low Growth Low Share (dogs)
Products which are not leaders and compete in slow growing or recessing markets, are termed dogs. These
either need or generate cash. Dogs can definitely be unattractive and it is suggested that they be harvested.
However, not all dogs are unattractive. In the grid above, the dotted line splitting the low quadrant on the
right side of the map into two triangles, divides the very bad products (lower triangle) from the less bad ones
(upper triangle). Usually, dogs tend to gather as much cash as possible before being divested, although it
can be hard sometimes to keep their saldo positive.
What Is BCG Interpreter
BCG Interpreter, as the name implies, reads and evaluates the output of the Product Portfolio Analysis built
into MM4XL. It looks in an objective manner at the product portfolio and highlights strengths and
weaknesses. This helps managers to take corrective measures where needed, and ensures consistency in
pursuing the envisaged product portfolio policy.
Interpreter saves you time and offers solid support for users who have not yet mastered the way Portfolio
Analysis works. Managers called upon to shape the strategic route of companies will find it a valuable
support tool, also taking investment levels into account and enlarging the overall strategic picture.
Warning:
When used with dynamic portfolio analyses BCG Interpreter does not provide useful data.
How to Run BCG Interpreter
Choose BCG Portfolio Analysis from the MM4XL menu in Excel and enter the number of products to be
analyzed, as shown in the section How to Run the Product Portfolio Analysis. Click the tab Interpreter and
select the checkbox Interpret my portfolio analysis and input the two required values (see the section
Input Values for details):
•
•
Investment level
Cash flow level
You may either accept the defaults or change them to more appropriate values, as also explained in the blue
region of the picture above.
Click OK and the predefined input data range of the BCG Portfolio Analysis appears. The last column
Investment differs from the input range of the BCG analysis without Interpreter. Fill in all columns. Investment
values must be in the same unit as sales, both yours and those of your competitors. If sales are expressed in
millions, investment should also be in millions.
9
When there are several new products in the portfolio, it is recommended that the McKinsey tool, built into MM4XL, be used. This is a
limit of the BCG.
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This is all you input to run BCG Interpreter: (i) Investment and cash flow levels for the whole portfolio, (ii)
investment in value for each product.
BCG
Interpreter
returns
a
numerical summary report, three
charts, and a text report that
highlights the most relevant
aspects of the analysis.
Tip:
Divide figures in millions by 1,000
or, even better, 1,000,000. Charts
and reports will be neater.
Parameter Setting
Before you run BCG Interpreter,
define the format of the sales data
and make your present portfolio
policy clear.
Using cost price for sales rather
than retail price has a profound impact on both investment and cash flow levels. This is especially true for
investment levels, which should also be defined as accurately as possible, in order for the analysis tool to
produce reliable results.
Choose one of two alternatives for portfolio policy: Profit or Competitiveness maximization. The latter is a
long-term view and the former is short-term. In order to maximize competitiveness, investments in growing
markets should be high. This, however, implies the company has attractive products to invest on and has the
willingness and skills to establish a brand in a leading position. Maximizing profit implies lower investments,
in order to show as much cash as possible. In general, short-term policies may make sense for some
products in a mature market, such as some cows and dogs. But all cows and dogs should not necessarily
follow a short-term approach.
Tip:
Portfolios made up of many old products may be split into (i) products that require a profit maximization
approach, and (ii) products that require competitiveness maximization. Two analyses should be run and the
results interpreted conjointly.
Input Values
Investment level is a standard that changes from industry to
industry and from market to market. A value equal to 1,2
means that in order to be balanced, investments in growing
markets (stars and question marks) must be at least 20%
higher than investments in slow growing or recessive markets
(cash cows and dogs). The same concept applies to the Cash
flow level. Cash flow produced by leader products must be
higher than that produced by non-leader products. A value
equal to 2 means that leaders must produce twice the cash
flow of non-leaders. Both cash flow and investments cannot
have a value lower than 1. At least 1,2 is recommended for
investments and 2,0 for cash flow.
Tip:
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Try the default values, read the analysis, and then change the values if required.
The picture here is a legend that summarizes the concept of product portfolio evaluation built using BCG
Interpreter.
In order to set the coefficients at reasonable levels, it must be clear which investments are included in the
analysis. In general, cost of sales force, communication (advertising, promotions and public relations) and
variable costs may cover a reasonable share of the whole expenditure managed in a marketing department.
Output
Charts
BCG Interpreter produces three charts, one table of
values and a text report. The charts are placed at the
beginning of the sheet.
The bubble chart plots investments and cash flows,
both in value. The size of the bubbles is proportional to
the sales of all products belonging to one market
segment (product group).
The axes of the chart cross at the average value of both
dimensions.
The remaining two charts are self-explanatory.
Investment and cash flow values computed for the whole portfolio are displayed just above the verbal report.
In our example, investments in growing markets are 1,75 times the level of investment in non-growing
markets. This is consistent with the portfolio management theory outlined above. Cash flow of leader
products is also higher than that of non-leader ones. This is also a reasonable condition.
Tip:
To double-check our example, run the analysis again using values slightly higher than the values computed
by the software, say 1,9 and 2,3, and compare the two analyses. This may prove useful to prevent surprises
related to financial and competitiveness matters.
The BCG Interpreter report follows the BCG Summary Table.
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Verbal Report
The verbal report offers an interpretation of the portfolio as a whole, of investments, cash flow, and of each
quadrant in the share/growth grid. The illustration below shows the structure of the report.
The portfolio is evaluated in terms of investments and cash flow. MM4XL compares the user input to the
values produced by the portfolio analysis. A positive judgment is expressed if the latter are higher than the
former, otherwise, MM4XL reports on the risk. Beside each evaluation, a solution is always offered. The
same concept, evaluation and suggestion apply to both investments and cash flow.
The quadrants of the share/growth grid are evaluated in terms of number of products, market growth, and
strength of leadership. Market growth is not evaluated for non-leader quadrants (question marks and dogs).
MM4XL warns when a portfolio has few cash generators and too many cash absorbers. It also flags the
presence of slow or dynamic markets. In all cases the software elaborates and offers suggestions of how to
deal with the situation.
The evaluation of strength of leadership is based on the concept that leaders are powerful when they make
at least 1,5 times the sales of the direct competitor. MM4XL also applies the concept the other way around,
to non-leaders. In other words, to have a strong position, leaders must have a logarithmic relative market
share of at least 5. On the other side, non-leaders with a logarithmic relative market share of less than 0,5
are considered weak.
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Market Segments Summary Table
The Market Segments table follows. It shows statistics of the product groups (as defined in the column
Product Groups of the predefined data range. See the section How to Run the Product Portfolio Analysis).
An example is given below.
In the above illustration, the product group Light Duty, hence market segment, comprises 4 products, which
made sales of 2637,0. The direct competitors’ sales were 1934,0. We are leader, as shown by the relative
market share, but with a relatively small margin of safety the strength of leadership is low. The segment
grows 7.7%. We have invested 2040,9 and 510.2 on average by segment. The segment has a cash flow of
596.2, on average 149.0 for each product. Investments are about 77.4% of sales. The data above is given
for each segment that the analysis accounts for.
Note:
Take full advantage of Excel flexibility. Any parts of the analysis can be cut and pasted elsewhere.
Tip:
Run the BCG analysis twice, once with real data and once with investment, market growth and sales values
as products of educated guesses. Use the different scenarios to speculate about the future.
The output of the BCG Portfolio Analysis combined with the output of BCG Interpreter present an objective
view of a portfolio and can be used to evaluate strategic decisions.
The Portfolio Balance Concept
There are two major assumptions behind the Product
Portfolio Analysis, which help to allocate resources whilst
reducing risk:
•
•
Investment in products in growing markets must be
higher than investment in stagnant or recessive
markets.
The total cash flow of market leaders must be
higher than cash flow of non-leaders.
The following map depicts the four discussed product
typologies.
If we translate the two rules above as equations and also include the equilibrium and the opposite of each
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rule, we have six different conditions:
1. Investment(Stars + Question marks) > Investment(Cows + Dogs)
2. Investment(Stars + Question marks) = Investment(Cows + Dogs)
3. Investment(Stars + Question marks) < Investment(Cows + Dogs)
4. Cash(Stars + Cows) > Cash(Question marks + Dogs)
5. Cash(Stars + Cows) = Cash(Question marks + Dogs)
6. Cash(Stars + Cows) < Cash(Question marks + Dogs)
Combining the six outcomes gives nine possibilities when defining a portfolio, representing five major classes
of product portfolios, respectively:
A.
B.
C.
D.
E.
Strong investors with equal or low cash flow
Strong investors with high cash flow
Medium investors with cash flow in balance
Low investors with high or cash flow in balance
Low investors with low cash flow
Each of the five positions implies certain peculiarities.
1. Equilibrium
A product portfolio in equilibrium is not necessarily a
good one. The financial resources are very limited and,
should it also be the result of a mix of products
competing in growing markets, the competitive power
can be very weak and perhaps not worth the risk.
2. Profit maximization
A profit-maximizing portfolio can generate cash in the
short term, yet this is hardly a position to be held long
term. Investments are low and can be insufficient to
maintain the current market share level; however, it can
be an interesting position to hold for a short time. A
useful stop-gap while building resources to be used
against a specific target, such as a competitor or
market niche10.
B
A
D
C
E
3. Negative saldo
This is the result of an unbalanced portfolio, which will normally survive for a very short time only, unless
action is taken to reduce the investments or enlarge the cash flow.
4. Optimum
The optimal condition is given by a portfolio whose products lie in fast growing markets, investing more than
those in stagnant or recessive markets, and the cash flow of leaders is larger than for non leader products.
Portfolio Optimization
Portfolio optimization is a topic mainly handled by financial analysts. Markowitz and Sharpe have developed
models to make empirical analyses of the portfolio performance and to seek the best balance of assets in
order to maximize return and minimize risk. An interesting discussion on the components of the economic
evaluation can also be found in Wind. Although written a long time ago, Alexander and Francis present a
well-detailed review of models to optimize asset portfolios, which can be adapted to product portfolios.
10
A niche is a market segment small enough so as not to attract the attention of big players, yet large enough to be interesting to
smaller ones. Minor products can survive and grow within this sheltered space, until such time that they have no dimension large
enough to challenge stronger competitors and win extra market share.
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Technicalities
The Logarithmic Scale
The logarithmic scale of the X-axis is justified by the fact that the competitive power of one product does not
grow linearly with its sales, but rather in a logarithmic manner. For example, the following table shows the
sales of our product, held constant over time
and equal to 100, the sales of our major
competitor, increased in a linear way, the
relative market share and the logarithmic
market share. These values have been used to
draw the graph below and show the importance
of working with logarithms.
The slope of the curve of the relative market share of
our product (called Linear in the graph) slows down
almost linearly as the competitor wins share. This
means that no reference is made to the increasing
power of the competitor, given its fast growing
absolute dimension. This is wrong. Indeed, we know
that well-managed best selling products get better
prices for raw materials, large productions sink
variable costs11, large market shares attract
consumption faster than low selling products. These
and other factors can boost one company's
competitive power, yet decreasingly so.
A logarithmic curve drawn on an equally scaled axis is pictured below:
The BCG was aware of this and encapsulated the concept in the logarithmic scale of the relative market
share. Short term, the greater one product's sales, the stronger its competitive power, yet at a slower
increasing degree. The logarithmic relative market share is computed with the formula:
⎛
⎞
Our Sales
⎟⎟
Log10 ⎜⎜
⎝ Sales Competitor ⎠
Size of the circle
The diameter of the circles displayed on the Product Portfolio Analysis grid is proportional to the product
sales. The bigger one product's circle is, the larger its share of sales in the whole products' portfolio. The size
of a product's circle is given by the formula:
⎛
⎞
Pr oduct ' s Sales
⎜⎜
⎟⎟
Sales
of
Best
Selling
Pr
oduct
in
Portfolio
⎝
⎠
11
Variable costs increase as the number of units produced increases and vice versa. These can be the cost of packaging, the container,
the label, the ingredients, etc. Fixed costs are those that do not vary when production moves along certain boundaries, e.g. advertising
investments, rent, wages, electricity, etc. Fixed and variable costs together with unit price are used to compute the Break Even Point.
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References to the Product Portfolio Analysis
Joram Y. Wind
Product Policy: Concepts, Methods and Strategy
Addison Wesley, 1981
Arnoldo C. Hax and Nicolas S. Majluf
Direzione Strategica
IPSOA, 1987
Lilien, Gary L., & Rangaswamy, Arvind
Marketing Engineering
Philip Kotler
Marketing Management: Analisi, Pianificazione e Controllo
ISEDI, 1984
Mourray Bourne
Interactive Mathematics: Exponential and Logarithmic Functions
http://www.np.ac.sg/~bms/Index4.htm
Markowitz
Mean-Variance Analysis in Portfolio Choice and Capital Markets
Basil Blackwell Ltd, 1987
Sharpe
Portfolio Theory and Capital Markets
McGraw-Hill, 1970
Alexander, Gordon J. and Francis, Jack Clark
Portfolio Analysis
Prentice-Hall, 1986, 3rd edition
Barry Hedley
Strategy and the Business Portfolio
Long Range Planning, vol. 10, Feb 1977, pgg 9-15.
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2. GE/McKinsey Product Portfolio Analysis
McKinsey Analysis in a Nutshell
In the mid 1970's the management of the multinational company General Electric recognized the utility of
mapping product portfolios on a grid matrix, and asked the consulting company McKinsey to develop a tool
to overcome the limits of the BCG. The result was the Market Attractiveness / Competitive Advantage
Portfolio Analysis.
The main advantage of this tool is that it also allows for analysis of products not yet on the market. At the
same time, it is flexible for the analyst, who can choose from among several factors influencing the
competitive environment. This model is designed to maximize earnings in the near future and allocate the
company's resources in appealing markets.
There are two main groups of influencing factors:
•
•
Macro-environmental
Micro-environmental
The former are external, and the company has no control over them, e. g. political situations, pollution,
market dimension and tendency, technological evolution, and so on. The latter are internal and can be
controlled, e. g. research and development, employee training, investments, ability of management, and so
on.
The chosen factors are weighted and produce two scores for each product: one for Market Attractiveness
and one for Competitive Advantage. The scores are placed on a grid split in nine quadrants. Each quadrant
has a particular strategic meaning.
Note:
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The Factors of the Analysis
Flexibility is probably the main advantage of the GE/McKinsey portfolio matrix. In fact, the analyst is left free
to choose any factor he or she believes to be useful.
The following list of factors is available in MM4XL. Please keep the following in mind, while working with this
application. Market Attractiveness and Competitive Advantage are referred as axes. These are made up of
macro-factors, which in turn are made up of micro-factors.
Using a broad range of micro-factors has the advantage of smoothing the effect of single items, requiring very
high or low weighting. This method does require more effort, going through the complete list, but using a
shorter number of micro-factors will help to save time. The latter method does however increase the risk of
attributing too much importance to single items.
Tip:
If the bubbles are not evenly spread on your map, either you have an unbalanced product portfolio, or the
weights assigned are too high or too low. Try to be consistent when assigning weights. Avoid broad ranges
of values, unless required, perhaps to differentiate products significantly from one another. A solid
background of the company's portfolio and some practice in assigning weights will help you to run reliable
analyses. Consistency in weighting is demonstrated with the following example: when assigning weight to
the market dimension of multiple products, you could assign 100 to the product in the largest market, then
assign weights to the other products using this formula:
(market size of product X / size of largest market in portfolio) x100.
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How To Run the McKinsey Product Portfolio Analysis
Step 1
Choose McKinsey Analysis in the MM4XL
menu, or alternatively click the button in the
floating toolbar.
Step 2
Input the Number of products you are going to
analyze. Set the Size of the bubbles (first do a run
with the default value). Select the checkboxes for the
macro-factors you need, and input a weight for each
one. Weights must range between 0 and 100 and the
sum of each axis, Market Attractiveness and
Competitive Advantage, must equal 100. Click OK and
the two standard tables, shown below, will be created.
Step 3
In the template tables select the checkboxes of the
micro-factors you want to include in the analysis, and
assign a weight to each for every product. These and
the former weights are used to compute the product
coordinates on the McKinsey grid. The computation is
built by averaging macro-factors obtained as averages
of the weighted micro-factors. The weights you assign
to micro-factors must range between 0 and 100, but
unlike the previous window, their sum does not need to equal 100.
Tip:
Changing the standard labels in the top row of the Market Attractiveness table, with one unique name for
each product, automatically copies them to the Competitive Advantage table as well.
Use the row named Revenue by Product in the Market Attractiveness table to input values that will be used
to enlarge the size of the bubbles. If these are product sales, the bigger the bubble the larger its share of
sales in the whole product’s portfolio.
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You will find the bubble size very helpful to quickly identify existing relationships between the product’s
competitive position and its financial contribution.
Tip:
To enlarge the bubbles for other purposes, you could
use market shares, investments, ROI or NPV, annual
growth, price, or whatever kind of index you feel to be
appropriate.
Step 4
Once you have assigned a unique name to each
product, input revenues, selected the micro-factors and
assigned them a weight, to run the analysis simply click
the button Next placed in cell A1 above the Market
Attractiveness table. Only the checkboxes and weights
are mandatory fields.
Next
Tip:
You can define your own micro-factors by simply
replacing the predefined labels.
There you have it, running the McKinsey analysis in MM4XL is that easy!
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Note:
How To Run Dynamic Analyses
A very useful application built into the portfolio tools of MM4XL (McKinsey and BCG) is dynamic data
analysis. So far, we have described a static application, observing single products, and using a single time
period. Alternatively, we can measure the same elements at two or more given points in time and display
them on the same grid. This allows the marketing manager to observe the portfolio and its development over
time.
The dynamic nature of markets has an impact on products and therefore portfolios. Being able to look at their
past and present condition can help to anticipate changes in the future.
It is very simple to run a dynamic McKinsey analysis. Run the analysis as you have learned in the previous
section, then input weights for the same products at two different points in time.
The picture above shows the top portion of a Market Attractiveness table. Three products are listed: MultiVit,
VitC, and Minerals. Each of them has been weighted with respect to the current year and also to their
attractiveness and competitiveness in 1997. You might also want to focus on a restricted number of items (to
keep the map readable) and depict their shift over several time periods on the same grid, for instance, 1995,
1996, 1997, 1998, and 1999.
Looking beyond product analysis, remember that both static and dynamic analysis can also be applied to
marketing divisions of the same company or to local affiliates belonging to same multinational company.
Brilliant analysis is limited only by the user’s creativity.
Tip:
A reliable portfolio analysis is best achieved by employing both McKinsey and BCG tools, in order to benefit
from their strengths while reducing their weaknesses.
Output of the Analysis
MM4XL produces a map and a summary report. Read the chapter How To Interpret The Analysis for a
detailed explanation.
Tip:
You can alter the position, size, and appearance of each single element of the grid, exactly like any Excel
chart, but you cannot modify the bubbles. Should you modify the bubbles in error, use Edit Undo in the Excel
menu to restore them. Take a look at the Smart Mapping help file in MM4XL for help with editing your
charts, or refer to the Excel help (F1).
An example of the Summary Report is shown below.
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Only macro-factor values are shown in the summary report; however, by displaying the hidden rows, all
computed values for each micro-factor are shown. For instance, in the example above, rows 6 to 14 are
hidden. In a similar report, you could select row 5 and 15 with your mouse, choose Format Row Unhide in
the Excel menu, and the hidden values would be displayed. You could repeat the operation for rows 16 to 18
and for 25 to 28. All hidden rows could be shown together by selecting all rows in the range 5 to 34 and
using the unhide command.
Tip:
MM4XL stores values to draw the McKinsey map in a hidden sheet. If not required, these hidden sheets may
be deleted by choosing Format Sheet Unhide in the Excel menu and then Edit Delete Sheet.
How To Interpret the Analysis
The GE/McKinsey grid splits up into four main areas and nine
quadrants.
1. The lower right area: harvest / divest
The lower three quadrants on the right side suggest to divest
or to maximize incoming cash. Placed here are products
competing in unattractive industries, which have a weak
competitive condition, when compared to the remaining
products in the portfolio. The lower quadrant hosts the worst
items, while the other two house weak products in medium
attractive industries, and medium strong products in
unattractive markets.
2. The diagonal: selectivity
The three quadrants on the grid's diagonal (from the lower left
corner towards the upper right one) must be handled with caution. The quadrant in the middle hosts medium
competitive products in medium attractive industries. Unless the products prove to be more competitive or
the industry more attractive, the strategic interest is hardly relevant (see also the section Strategic
Implications). In the lower part of the diagonal we find products which are not at all competitive in very
attractive markets. These items can either be very attractive or unattractive for the strategic portfolio
management. In the upper part of the diagonal are plotted highly competitive products in very unattractive
industries. Although they are performing well, the market unattractiveness can put in jeopardy their existence
in the portfolio.
3. The upper left quadrant: invest & grow
This is the most interesting area of the grid. Here we find the strongest products in the portfolio competing in
very attractive industries. These are however, products not always easy to manage. They produce cash and
require high investments in order to keep growing at the same growth rate of the market they compete in.
Managers should not be attracted by their cash flow only, and must remember to feed them, thus helping
them to continue gaining market share.
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4. Neighbors of the upper left quadrant: selective growth
Both quadrants located on the right and lower side of the upper left quadrant are interesting ones. It is
suggested to manage products in both of these areas to favor their growth, while being aware that selective
decisions may need to be made. Products placed in the right quadrant are very competitive and compete in
moderately attractive industries. In the lower quadrant are placed medium strong products competing in very
attractive industries.
Strategic Implications
High
Medium
Low
There are two major assumptions
behind
the
Product
Portfolio
Analysis, which help to allocate
resources while reducing risk:
Business Attractiveness
Each quadrant of the grid suggests a
widely differing way of handling
products. Of course, given the
flexibility of this analysis tool,
different competitive environments
can suggest slight, or even drastic,
changes in the way products should
be managed. Nevertheless, sticking
strictly to some managerial paradigm
can shrink the creativity and
jeopardize the business. When
interpreting your analysis, the
following rules, as summarized
below, should be borne in mind.
Portfolio Analysis
• Push growth
• Search for leadership
• Maximize investment
• Search for growing
segments
• Heavy investments
• Keep other positions
• Defend global market
share
• Search for cashflow
• Balance investments to
defend share
• Segmentation to find
leadership
• Challenge weaknesses
• Reinforce strength
• Focus on growing
segments
• Specialization
• Selective investments
• Divest unhealthy items
• Minimum investment
• Harvest and keep ready to
divest
• Specialization
• Search for market niches
• Think of acquisitions
• Specialization
• Search for market niches
• Think of divestment
• Support management
• Plan timing for
divestments
• Attack competitors on
cash producers
High
Medium
Low
Industry Attractiveness
1. Investments on products in
growing markets must be higher than
investments in stagnant or recessive
markets.
2. The total cash flow of market leaders must be higher than cash flow of non-leaders.
Refer to the BCG help file in MM4XL to master this topic.
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References to the GE/McKinsey Product Portfolio Analysis
Lilien, Gary L., & Rangaswamy, Arvind
Hax and Majluf
Direzione Strategica
IPSOA, 1987
Philip Kotler
Marketing Management: Analisi, Pianificazione e Controllo
ISEDI, 1984
William E. Rothschild
Putting All Together: a Guide to Strategic Thinking
Amacon NY, 1976
William E. Rothschild
Strategic Alternatives: Selection, Development and Implementation
Amacon NY, 1979
Joram Y. Wind
Joram Y. Wind and Vijay Mahajan
Designing Product and Business Portfolios
Harward Business Review, vol. 59, No 1, p. 155-165
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3. Brand Mapping
Brand Mapping in a nutshell
Brand Mapping produces a picture of a given market. This picture, displayed as a map, shows which
products compete in the consumer's mind. It is used to stimulate strategic reasoning of how a product could
be positioned in order to maximize both preference and sales, for example.
Brand Mapping is a tool customized for business analysis. It uses correspondence analysis, runs fast, and
provides a detailed output report. Its map is rich in information, clear, and easy to interpret. Many business
professionals know that relationships between numbers are often far more interesting than the numbers
themselves. These people will find Brand Mapping of great value.
According to Myers (1996, pg. 255):
"Of the three approaches (author's note MDPREF, PCA, and CA), correspondence analysis is probably the most flexible and
versatile, which would account for its great popularity in marketing research today. Products/services/brands can be positioned in
terms of any type of data that might characterize it or its use, including attributes, demographics of most frequent users, attitudes of
most frequent users, usage occasion, types of distribution outlets, types of promotion, price or pricing policy, and the like."
The ultimate goal of Brand Mapping is the visualization of the latent competitive structure, which
characterizes each and every market. In this context, Brand Mapping stimulates strategic reasoning, which
means that interpreting the analysis in the light of the analyst's prior knowledge reveals strategic patterns
that others do not see.
We recommend careful reading
of this chapter and we wish you
a lot of fun and future success
using Brand Mapping.
Note:
An example report of this tool is
available. Click on the Start
button in Windows and select
MM4XL – Marketing Manager
for Excel. The file can be found
in the Examples folder.
Alternatively, start the tool and
Important
To learn how to apply the Brand Mapping tool read the book Mapping
Markets for Strategic Purposes with MM4XL Software. It is the best
resource for marketers interested in looking at competitive environments
from a highly strategic perspective.
More info: www.marketingstat.com/bookmapping.html
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3. Brand Mapping
57
How To Run Brand Mapping
To run Brand Mapping choose
Brand
Mapping
under
Strategic Tools in the MM4XL’s
menu bar. Alternatively, click the
button on the floating toolbar.
Tip:
Watch the Excel status bar in the lower
left corner. Messages are displayed
which briefly explain the kind of operation
the tool is performing at that moment.
In the first page, select one of the three
option buttons corresponding to the
analysis you want to run. If you choose
Contingency table, Brand Mapping
jumps to its final window, the control
panel. In other cases an intermediate
page appears (you see a new tab
between the Brand Mapping and Output
pages).
The Supplementary data option requires
a number in each of the two drop-down
boxes, placed in the lower right corner.
The value corresponds to the last
columns and rows of the input table. In
cases where there are no supplementary
points, simply enter zero. If you input a
zero in both boxes, Brand Mapping runs
a plain contingency table analysis. If you
are not familiar with the concept of
supplementary
points
(also
called
passive) read the section How to interpret
Brand Mapping.
The Missing data option shows an
intermediate page. This window is simply
a short explanation and no user input is
required here.
The last page tells Brand Mapping where
to get the data and how to fine-tune both
output and the analysis itself. Make an
accurate selection in this window and
your output will be much easier to read
and interpret. There are four framed
areas for user input.
1st The data.
In the first frame, The data, place the cursor in the Data table edit box and select with your mouse the
region where the data is stored. The first row and first column of this area must be text labels, so blank cells
and numerical values are not allowed. In the Output range edit box, select only the start cell, where you
want Brand Mapping to begin printing the output report. Both of these fields must be completed with a range,
in order for the analysis to run. Change text in the third edit box to assign a title to your map, this defaults to
Brand Mapping.
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2nd The bubble size.
The second frame option The bubble size
determines which values are used to compute
the bubble diameter. By default, Brand
Mapping uses the mass value. Alternatively,
the Third axis coordinates or a custom
address may be chosen.
The Third axis option uses coordinate values
when setting the bubble diameters, useful for
displaying broader data variance on a single
map. However, this visualization may be
biased by negative values, as the bubble size
is computed treating the input values as
absolute values.
The Select an address option allows users to
set the bubble diameter using a custom value
stored on the sheet. This is a very useful
option to enrich the map with external
information that may make the interpretation
easier.
The values are stored on the sheet as in the above example. The column values are stored first, and then
the row values. In our example, the range B1:B9 is entered in the edit box, either manually or using the
mouse, and Brand Mapping uses these values to set the bubble diameters.
Note:
When the number of supplementary rows is larger than the number of active rows, the
order of the labels must be reversed, so the custom row labels come first and the column
labels next.
3rd The output.
By default, Brand Mapping draws a map, and prints
contributions and squared cosines to factorial axes. Click
the respective checkbox to deactivate one or both
options. Coordinates and mass values are also printed by
default and cannot be deactivated.
When working with large data sets, it may help to reduce
the number of axes printed in the output report. Use the
option Max number of axes (0 = all) to define how many
axes you want to show. By default Brand Mapping limits the number to 4, as suggested by Benzécri (1992).
Type a zero (0) to display all axes.
Click on the button Print Options to open the form Options, which is
where you can set several print options for formatting the map.
4th The last step.
This last quadrant is only active when the option Plain contingency
table has been selected in the first window. By default, Brand Mapping
uses the Compute unequal mass option, which runs the analysis using
the raw data, exactly as input by the user. The option Set column total
= 100% transforms the original values as percentages, so that the sum
of each column (profile) is 100%. The same happens to rows if the
option Set row total = 100% is chosen. This is a useful option to reduce
the weight in orientating the map of columns and rows, which account
for a large portion of the whole data variance. Use this option, for example, to reduce the effect of leaders
with large market shares, or those with large market segments (see the section How to interpret Brand
Mapping for more details).
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3. Brand Mapping
59
The What's this buttons provides short descriptions relating to single functions.
The data input
Brand Mapping is very flexible and can handle almost any type of data table. However, the GIGO theorem
holds: Garbage In, Garbage Out. Do not forget it!
The input to Brand Mapping is a rectangular table of figures and labels, a contingency table, similar to the
one below.
Each column and row of the input table is a unique profile and Brand Mapping displays it on the map as a
bubble. Using the table above, the map output would have eight column bubbles and ten row bubbles.
Most often in marketing, the figures are preference data gathered from surveys, both ad-hoc or syndicated.
We recommend extensive use of Brand Mapping with the latter studies, in order to get the most benefit from
the expensive data, which often lies unused on a dusty shelf in a dark room. For example, the
pharmaceutical industry has a lot of data available about usage of drugs. Arrange this data in a table with the
product name as the column label, the name of the treated disease as a row label, and fill out each cell with
the number of prescriptions (preference) for each drug.
Percentages, ratings, e.g. on a scale 1-10, (Greenacre, 1984), and binary data, 1 or 0, (Hoffmann and
Franke, 1986) can also be used as input to Brand Mapping.
Tip:
Do not be afraid of using very large data tables.
Brand Mapping is actually a segmentation tool
and is of great help to identify latent structures in
complex data sets. When working with large
tables, one may need to repeat the analysis
several times, focusing more and more on the
truly relevant portion of data.
Brand Mapping's advanced features allow users to work with even more complex data tables, such as a
contingency matrix with both active and passive points. A passive point is a bubble displayed on the map,
without actually contributing to the orientation of the map itself. It can be seen as a "what if" point. This useful
feature makes Brand Mapping extremely flexible and well suited to the analysis of dynamic data sets. In the
output report, passive data items are printed with bold labels.
A dynamic data set, also longitudinal, is made up of cross-sectional data, both longitudinal and not. In other
words, take a survey today and gather the data, then repeat the same survey a while later and gather a
second set of data. This is what we call dynamic data: a set of two or more observations from the same
universe. The table above, for example, is made of two different surveys. The data in the gray area was
gathered in 2001, and data in the lower yellow one in 2002.
Section A, the gray area (as usual with labels) can be input to the Plain contingency table. Sections A and
C conjointly may be input to the Supplementary data option with four passive rows. Sections A and B
conjointly may also be input to the Supplementary data option with four passive columns. Finally, all four
quadrants together may be used with the Estimate missing data option (using the last option, quadrant B
must have blank cells). The four-quadrant matrix is useful to handle the entrance in the market of new
competitors, and it is a feature unique to Brand Mapping. These are the three basic input tables to Brand
Mapping.
The main question one should answer before starting Brand Mapping is: Should my map only display active
points, or are there useful passive points (also called supplementary points)? In other words, do I choose the
first option in the opening windows or do I choose one of the other two options?
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How To Interpret Brand Mapping
Brand Mapping produces positioning maps applying correspondence analysis, which is a broadly used
multivariate technology. Users of Brand Mapping are strongly encouraged to refer to Benzécri (1973, 1992)
and Greenacre (1984, 1993) for a comprehensive review.
How does Brand Mapping work?
According to statistics, Brand Mapping positions in a low dimensional space one bubble for each column and
each row of any rectangular table of values. The position of the bubbles in the space is derived by measuring
the variation of each profile from the average profile. The variation is measured with the Chi squared statistic
and the bubble position corresponds to a Chi squared distance.
In other words, Brand Mapping performs a basic task of great help to marketers: it pulls apart items
according to their differences, and it makes all differences visible at once, thanks to a clear and easy to
interpret output. Now, given that product positioning is largely based on segmentation and differentiation, it
goes without saying that Brand Mapping is the tool of preference for visualizing the competitive structure of
markets as perceived by customers, and also:
•
•
•
•
•
to exploit product (re)positioning concepts
to circumscribe the competitive environment and select direct competitors
to find new product opportunities (market gaps)
to evaluate new product concepts
to foster strategic reasoning
The fostering of strategic thinking is a major issue in many large companies today. Brand Mapping in many
cases can be a great starting point.
Interpreting Brand Mapping
We state here some general principles, which should be applied with caution:
•
•
•
The closer two bubbles, the higher their association.
The more one bubble moves away from the center of the map, the more one or more elements in its
profile, characterize the profile itself.
A bubble tends to be positioned in a space corresponding to the attribute category prominent in its
profile.
The route we suggest when looking at brand maps is as follows:
1. Check the amount of inertia covered by each axis and figure out how much variance exists in the
data. The lower the inertia, the smaller the variability, hence the less differentiated the profiles.
This may have strategic implications, e.g., when reasoning is applied to strategic positioning.
2. Identify any outlier points, as they can falsely affect the dimensionality of the map.
3. If needed, focus the map by rescaling the axes (simply reducing the max and min values of each
axis).
4. Plot row points and column points on two separate maps.
5. Look at the squared cosines to identify any poorly displayed bubbles.
6. Identify any evident bubble segments on the 2D and 3D space.
7. Assign a name (label) to axes and regions of the map, when possible.
8. Double-check the accuracy of the raw data.
9. Use your prior knowledge to interpret solid maps with strategic eyes.
Note:
A map is the closest picture to reality that the analysis can display in two dimensions, and it is not perfect
unless it displays 100% of data variance (inertia). The amount of variance displayed should always be kept in
mind when interpreting positions on a map, and marketers should look at inertia with interest. Indeed, inertia
gives an idea of the level of spread across bubbles, so the farther apart the bubbles lie, the broader the
market space available for new offers.
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3. Brand Mapping
61
The points above and more are discussed in the Examples section.
What is in the output?
Depending on the options selected, Brand Mapping prints by default a map and two or three tables of
figures. An explanation of how to interpret both the map and the figures follows.
The numerical output
The option that re-scales the raw data as a percentage, using
either row or column, prints a table at the top of the output
region, as shown to the right. This new table is the input to
Brand Mapping.
The next table shows the amount of inertia that each principal axis
accounts for. Brand Mapping transforms and reduces the
dimensionality of the original data set, and makes it possible to
display the largest amount of variance on a two-dimensional map.
The preceding eigenvector is always larger than the next, and the
inertia % makes these values more readily comparable. In the case
to the right, the first axis accounts for 60% of inertia, most of the
'meaning' in the distribution of points on the map. The first two axes account for 87% of total inertia, which is
a very good map to work with. Unfortunately it is not always easy to achieve such good results, and much
depends on the input data set. The larger the number of points to display, the lower the variation accounted
by the first two dimensions.
Tip:
Remove unnecessary columns and rows of data in order to improve the quality of the analysis.
The table here contains
all necessary information
to
make
a
critical
evaluation
and
an
objective interpretation of
the bubble points.
The upper part of the
table
shows
the
coefficients for the column points and the lower part shows the coefficients for the row points. Each row
describes one point.
The mass can be interpreted as a relative frequency, and the sum of all masses in each direction, rows or
columns, adds up to 1000. According to Greenacre (1993), the original coefficients produced by the CA are
weighted times 1000 by Brand Mapping, to make the report more readable. The mass of products can be
seen as the market share, although this interpretation does not work when the raw data is re-scaled as a
percentage. Re-scaling the mass may be useful to reduce the effect in orientating the map of large, quasimonopolistic market leaders.
The inertia values of one point measure its contribution to the total inertia of the low-dimensional space. The
lower the inertia the lower the variance in the data, and the higher the inertia (up to a maximum number of
axes, three in our example) the more distant are the points from the origin of the map. The column Inertia ‰
shows the relative frequency of the inertia values. In our example, Colgato absorbs 41% or 410‰ of total
inertia, and as expected on the first axis, it lies well away from the other bubbles.
Next to the inertia values are the 3C's: Coordinate, Contribution, and Squared Cosinus. All points have one
of each for each of the principal axes or eigenvectors.
The coordinates are needed to position the bubbles in the low-dimensional space, or map, and are obtained
with a process of value decomposition in basic roots for which we refer the reader to the relevant
bibliography in appendix.
The points placed on a map exert a kind of magnetic attraction of the orientation of the principal axes, which
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62
is measured by the contributions. The higher the mass of a point, the stronger its influx in orientating the
axes. In our example Colgato is the major contributor (727) to the orientation of the first and most important
axis. This impact can sometimes impair the efficacy of the visual display and may be rectified by computing
either row or column percentages.
The squared cosinus measures the correlation between point and axis. In a two-dimensional display, the
Quality of the representation of a point on the map is given by the sum of its first two squared cosines. We
deliberately chose this example to highly correlate Colgato and FreshM, respectively, with the first and
second axis. In this analysis, only the 2D quality of Good price is not well represented. The sum of all
squared cosines of one row is equal to 1000, when all axes are displayed.
The Map
Brand Mapping produces a scatter diagram and plots points in the
form of bubbles. It is the bubble distribution on the chart that gives a
meaning to the axes, and not the other way around. The axes have
no meaning unless we interpret the point distribution.
Inertia axis 1 + Inertia axis 2
The map produced with Brand Mapping is also called dual display,
as row bubbles and column bubbles are displayed in two different
low-dimensional spaces, which are then combined in order to show
all bubbles on the same map. The analysis puts data in
corresponding rows and columns. This is the reason why the
distance between one product and one diagnosis should not be interpreted, and the only meaningful element
is that of the angle created by the two bubbles. Only with one unit in one space,(e.g. products, corresponds
to one unit in the space of diagnosis) is it safe to interpret the distance between the two. The level of
association between rows and columns is computed as follows:
In the picture, the yellow bubble (product A), forms an angle with each of the three diagnosis types.
Although diagnosis one lies further from product A than any other diagnosis, the angle
⎡
⎤
formed by the two is the smallest. This implies that the association between product A θ = ⎢Tan⎛⎜ y i ⎞⎟ ⋅ 180 ⎥
⎜x ⎟ π
and diagnosis one is the highest among the three diagnoses. The angle θ in degrees
⎢⎣
⎥⎦
⎝ i⎠
of one point versus the abscissa axis is computed with:
With x and y being the first two coordinates of point i. The angle θ between a product and a diagnosis can be
computed by subtracting the angles of the points with the x-axis. There are three cases (see picture above:
θ1, θ2 and θ3):
- Case θ1:
the angle between points is acute, θ < 90°. Points are positively correlated and highlight the overrepresentation in the raw data. Leaders are usually over-represented in the market segment they dominate.
- Case θ2:
the angle between two points is more or less squared, θ » 90°. The points do not interact and show very
dissimilar profiles.
- Case θ3:
the points form an obtuse angle, θ > 90°. The points are negatively correlated, which means that a product is
under-represented (low share) in a given market segment.
The picture above lets us flag one other aspect related to the interpretation of brand maps: the further the
distance of one bubble from the origin, the more differentiated its profile from the average profile. If the
bubble is a diagnosis, this is a very notable difference, meaning that only one or few products are associated
with it. If the far spaced bubble is a product, this means it has quite a different profile from the other products.
Sometimes analysts look at wide-ranging market environments, and others tend to work with closely related
ones. It is down to the goal of the particular analysis.
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3. Brand Mapping
63
Tip:
When your analysis is done, take a minute or two to refine it. Rescale the axis to make the map more easily
read. When working with time series, connect the years with a line. Play with background colors and bring
labels with shadows and borders to the front. Insert labels with prior knowledge, such as launch dates,
company names, price levels, etc. Excel allows changing virtually each element of a map.
These are the basic tools one needs to start interpreting Brand Mapping. The topic however is much more
complex than this short summary. For this reason we encourage users of Brand Mapping to read Greenacre
(1993).
Examples
Do not let the nature of the data used in our examples put you off. We are fully aware that the field of
prescription drugs is not the most familiar environment for many of us, and this is one of the reasons that we
chose it. Without previous knowledge, the remarkable contribution of Brand Mapping in explaining
environments becomes clearer, and we hope you will fully appreciate its great support to strategic reasoning.
Example 1: plain contingency table
We analyze the market segment of antibiotics prescribed for treatment of viral and bacterial infections
occurring in the respiratory passages and lungs. The analysis will be used to identify new business
opportunities for a product already competing in this market. The same map, however, may also be used to
identify a sustainable positioning strategy for a new brand.
We use a European market where 40,000 doctors write about 45 million prescriptions to treat 300 different
diseases, with 60 anti-infective agents marketed by 35 different companies.
A table of 300 rows and 60 columns, disease by product, was used to run a first round of Brand Mapping, so
as to reduce the number of items to focus on. After 3 rounds we had reduced the original data to the table
below, which refers to products and diagnoses considered worthy of analysis.
The figures are in thousands and come from a panel of doctors who report which agent they have used to
treat which disease. Asthma, for example, was treated 372,000 times, of which 57,000 were treated with
Augme. Although one may not know the product names, the diseases should sound familiar. The white
column on the left shows that this segment accounts for 9,982,000 prescriptions of the total anti-infective
market. The white row shows the total prescriptions by product: the market shares in prescriptions. The data
in the yellow area is the input we used to run the analysis summarized in the tables and the maps below. The
data in the gray zone was removed for the reasons explained below.
Looking at the table below (coefficients refer to both the yellow and gray zones above) we can see that the
level of diversity across brands and diseases is low (sum of eigenvector values » 0,8 < 9). This means, that
in order to succeed in such an environment, brands are required to find elements of differentiation beyond
the simple technical performance. In this market it is not sufficient to say Brand X works against disease Y
because most competitors of brand X are also efficacious against the same disease. Therefore, the lower the
sum of eigenvector values, the lower the diversity across brands measured on prescribing habits, and the
higher the need for the brand to be marketed with a sharp personality.
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Of the nine principal axes, the first three explain almost 90% of the total variability in the data. This means
that 90% of the relationships
occurring in the raw data of our
example can be visualized on a
3-dimensional map, a very good
map (which can be made using
the tool 4D Map in MM4XL). The
first axis alone explains 50% of
variance, and it probably shows a
meaningful segmentation which
could be assigned a label.
Assigning labels to regions of the
map is useful for guiding the
strategic reading and reasoning.
However, the 2D row-column
association is low (.34), and one
should refrain from a direct
interpretation. Pneumonia, chronic bronchitis, and chronic sinusitis, although very small entities, had a very
strong impact in orientating the map. For this reason they have been removed and the new map, more easily
readable yet still stable, can be seen below. The coefficients that follow refer to this second map.
Tip:
The x-axis (the horizontal one) is rescaled from min -600 and max 600 to min -400 and max 400. This makes
the map more readable.
Brand Mapping produces a so-called dual display, which allows the simultaneous display of both row and
column bubbles on the same low dimensional space. When there are many bubbles on the map and when
the row-column association is low, it helps to look first at the two spaces separately, as shown below.
It is evident
that there are
some
partitions
occurring
in
both sets of
data.
Let's
start with the
diseases. On
the horizontal
axis, the most
important one,
the bubbles on
the left-hand side refer to diseases located in the throat, while the diseases on the right are located in the
lungs. One label for the x-axis could be Lower (left) and Upper (right) Respiratory Ways. The vertical split
isn't very sharp. It might be however related to the duration of the disease. On the upper side of the map
there are the acute inflammatory diseases, which tend to come and go in a short window of time, and the
more chronic or persistent diseases are on the lower side of the map.
The vertical axis appears better defined when looking at the brands only. The lower cluster of products is
comprised mainly of cephalosporines, while penicillin is found in the upper-left cluster. The former are
prescribed against more aggressive infections like those located in the lungs and the latter are mainly used
to treat acute and less aggressive bacteria, like those located in the medium respiratory ways. Labels could
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3. Brand Mapping
65
be Inflammatory Process on the upper part and Viral Infection on the lower one.
Tip:
Assigning labels and clustering bubbles is a good way to add
prior knowledge to the map and to facilitate the interpretation.
Before looking at the map from a strategic point of view it is
necessary to verify its accuracy, and this is accomplished by
looking at the coefficients that Brand Mapping prints in the
output report.
The first numbers to look at are the Squared Cosines. These
coefficients measure the level of correlation between one point
and each axis. A well-represented space has all points mainly
associated with the first three axes (this is a dimensionality that
human beings are used to dealing with). With some effort the
fourth dimension may be interpreted, yet a higher dimensionality
may result in a less understandable output.
As shown in the table below, the first four diseases plus Tonsillitis are
well displayed on our map, Throat Infection is mainly associated with the
third axis, and Infection of Respiratory Ways is associated with the fourth
axis.
The brands show an analogous situation with Zinac and Panac poorly
represented and the rest of products with a good association on the first
three axes. We should be cautious about Zimox whose very high
association with the first axis may be suspicious.
In general, this visual display seems to be accurate enough, and the high
portion of variance explained by the first two axes also suggests it.
A point strongly associated with one axis is not always the major driver of the orientation of that axis. This
may be due to a unique combination of proportions in the profile that leads the point to exert a strong or
weak impact on the orientation that the space takes. In the table above, for example, Zimox contributes
heavily to orient the first axis (645‰) and it contributes very little to the second axis. Contributions are also
useful to identify outliers. An outlier is a minor point, with high mass, placed outside of the major space,
which impacts heavily the orientation of the map. In some cases one can get rid of outliers, as we did at the
beginning of this example with the diagnoses in the gray shaded area.
The mass values can be read as market shares. In our example, given the total sum of the raw data is close
to 10000 and the mass values are expressed in thousands, there is a relationship of almost 1 to 10 between
the two. Again, our analysis is quite stable, so there are no alarming values: large products account for large
amounts of inertia. Should this not be the case the analyst has to find out the reasons why this happened
and must take into account the corresponding level of inaccuracy.
In certain cases it makes sense to look at the 3D space
in order to highlight data partitions not evident on a flat
display. In the map we have used arrows to give an idea
of the direction and depth of the position of some
bubbles on the 3rd axis. One can, however, use the tool
4D Map in MM4XL for drawing a better chart. Klacid for
instance, seems to go significantly above the plane in
the same direction as the disease Asthma. The two are
strongly associated, indeed Klacid is the most used drug
for the treatment of asthma, and these prescriptions
strongly characterize Klacid's profile. This is however
not the case for the second largest prescribed drug
against Asthma: Augme.
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66
Brand Mapping and Strategy
After accurate refinement and validation, Brand Mapping can be used for strategic purposes. Again, Brand
Mapping fosters strategic thinking, so a note on some basic marketing principles may be worth reading.
Ries and Trout (1986) wrote Marketing Warfare, a best seller inspired by
Carl von Clausewitz (1832), a Prussian soldier who wrote about the
philosophy of war. These Principles of Marketing Warfare can help the
analyst to look at the map with 'structured' eyes.
There are four groups, each of three principles:
Flanking marketing warfare
Consists of an unexpected move made in an uncontested area. In our
example this could be a new innovative product, which consolidates both
market segments (cephalosporines and penicillin) by offering a new
mechanism of action more efficacious and safer than any other treatment available today.
Guerrilla marketing warfare
Suggests focusing on a segment small enough to defend without acting like the leader, and being prepared
to get out of the business at any time. In our example this may be a me-too product (generic) that attacks
Throat Infection and holds the position as long as possible.
Defensive marketing warfare
This is only allowed for market leaders, who are also suggested to block any competitive moves, while
having the courage to attack themselves (challenge their own strategy). This may be the case of Augme that
tries to protect its Tonsillitis market.
Offensive marketing warfare
Done using as narrow a front as possible against a weakness of a larger product's strength, and the main
consideration is the strength of the leader's position. In our example none of the three leading products
Klacid, Augme, and Zimox has a sharp focus on one clear disease area. Attacking Zimox on both Bronchitis,
Klacid for example may win prescriptions and become large enough to attack Augme, the segment leader.
These principles of warfare may help when interpreting Brand Mapping, and contribute to fostering strategic
thinking. The product positioning theory is discussed under example 3.2.
Example 2: time series analysis
This example describes dimension and tendency of market segments of a large industry sector, the Over
The Counter (OTC) drugs. It is a market segmentation based on the growth trends over the last 10 years,
allowing us to identify fast growing areas which may underline macro trends among buyers.
The OTC industry of the country we
use for this example is split into 102
market segments, with some
10,000 product forms, and yearly
sales of over 20 billions US$. The
input to this analysis is a table of
103 rows by 11 columns comprising yearly sales values (in thousands) and single market segments (with
labels) as shown to the right.
In order to improve readability, the axes were rescaled to remove points lying in extreme positions. This was
simply done by activating the chart, double-clicking each axis, and typing new scale values. The red line that
connects the column bubbles was also drawn manually in Excel, using Format Data Series > Patterns >
Line.
The map below includes a great deal of information:
- Dimension and tendency of the whole industry sector (red bubbles) using a single period of the time series
(one year in our case);
- Dimension of each market segment showing the tendency of its sales curve.
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3. Brand Mapping
67
The red bubbles represent column points, or the whole industry,
and their size is proportional to the mass, therefore to the relative
size of the sales for that year. They show that the dimension of the
industry has grown since 1989 (bubble diameter), although the
growth has slowed in the past few years (growth = e.g.
sales99/sales98). The horseshoe shape represents the bold part
of the sales growth line in the chart to the right. The chart
illustrates that after moderate growth, the sales slope slowed and,
for the past two years, has turned upward again.
Interpreting the row bubble distribution on the map (market segments) is less evident than that of columns,
but it is equally interesting. It follows a similar concept where the bubble size is proportional to the mass, and
the position on the map is defined according to the sales trend of each market segment, rather than sales
growth used for the columns. The blue/yellow trend pictures are placed to correspond with the cluster of
segments showing the particular kind of sales trend, as shown in the picture.
Markets located very close to a red bubble show their peak sales in that particular year, and the farther a
market lies from the red bubbles, the flatter its sales trend. The bubbles below the line have a negative sales
trend slope and bubbles above have a positive slope. The segmentation purposes of this analysis seem to
have been achieved.
The coordinates of row bubbles on the first principal axis, the most important one encapsulating 3/4 of the
total inertia, explain the sales trend distribution. Sort the raw data using these coordinates and the market
segments will be sorted, beginning with the most upward sales slope, and ending with the most downward
one. It is amazing.
This is a very effective way of looking at large data sets, in the form of time series. Virtually every panel and
tracking study can be used as the source of time series data for Brand Mapping. Also very interesting is the
treatment of longitudinal data.
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Example 3: supplementary data
Passive (or supplementary) points are bubbles displayed on the map, which do not contribute to the overall
orientation of the map. The Supplementary data function built into Brand Mapping is useful in marketing for
the following reasons at least:
•
•
Drawing dynamic maps that show the position of competing products over time;
Combining product preference and advertising awareness in order to visualize the players and the
elements of brand image.
Both applications can be of great use when working on product positioning. Let's look at two examples.
Example 3.1: dynamic maps
Say that two surveys were taken, one in 1995 and the other one in 1998. During both surveys the same
number of patients (tracking) – though not the same individuals (panel) – were asked what drug they use for
treatment of abdominal disease(s). The answers were collated in the following table:
The respondents mentioned four major products used to treat seven common diseases in the field of ulcer
and gastritis. Both products and diseases remained the same in both surveys. The data was analyzed using
the Supplementary data function with 4 supplementary rows and 0 supplementary columns.
Tip:
Use the Estimate missing data function built into Brand Mapping when the number of columns or rows
changes between surveys.
MarketingStat opted not to print any coefficients for the supplementary points,
because their interpretation may be misleading. Only the squared cosines may be
interpreted, while exercising caution. The formula to compute the squared cosines
of one point and one axis is:
Cos 2 =
Coordinate i2
∑ Coordinate i2
The dynamic map is displayed to the
right. In 1995 the leader was clear:
Zant dominated Gastritis and Antra
controlled the richest Esophagitis and
Ulcer. Three years later both leaders
were under competitive pressure and
the products have become closer, on
both sides of the map. As stated
earlier, the closer the bubbles, the
lower the inertia, the more similar the
profiles, the stronger the need for
brand differentiation.
Marketing minded people, who focus
on macro changes occurring in
competitive environments, appreciate
dynamic maps of this kind because
such a concise picture can summarize
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3. Brand Mapping
69
a wealth of meaning, even for the most complex markets.
Analysts who want to display both supplementary rows and columns simultaneously, are advised to refer to
the literature in order to validate any 'unusual' form of data treatment.
Example 3.2: brand image maps
Active and passive data combined in the form of preference and awareness data, are particularly well suited
to the needs of managers working on product positioning and brand image.
Product positioning is based on target segmentation and brand differentiation, and according to Wind (1981)
there are seven alternative bases for positioning a product:
1. On the product features
2. On benefits, problem solution, or needs
3. For specific usage occasions
4. For user category
5. Against another product
6. Product class dissociation
7. Hybrid bases.
In order to work correctly, the positioning statement must first be written down on paper. One rule
suggests:
For [target need] the [concept]
is [most important claim]
because [single most important support]
For example:
For [gastritis sufferers] the [tablet Gastop]
is [the fastes relief against stomach burn]
because [it contains the most active H2 inhibitor]
The data for brand image analysis can be gathered with sample surveys. It is related to brand awareness,
and it should be both spontaneous and solicited. Spontaneous brand awareness is when a sample of people
answer questions like “Which brands do you know?” and “What do you recall about each brand you know?”
This is also called top of mind. On the other hand, solicited awareness is gathered when the interviewer
suggests the interviewed brand name or attributes, and asks for a rating or such like.
In our example we use unsolicited brand awareness
data gathered with a panel of doctors, who reported
their memories about the last visit of pharmaceutical
representatives promoting products for treatment of
ulcer and gastritis. The data table used as input to
Brand Mapping is shown to the right, and the map that
follows was drawn using the Supplementary data
option with zero supplementary columns, and 9
supplementary rows. It must be noted that the data
used for this example comes from two different panels,
and this is one of the strengths of Brand Mapping, which
allows for virtually any type of data to be utilized.
We have removed the row labels of the active points
(diagnoses) from the map below, to focus on the
relationship between brands and claims.
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Although the above map is of outstanding quality, the first two axes account for 98% of the total variance,
and the position of the supplementary points should be interpreted using caution. Indeed, the variance
displayed by the map refers only to the active points, so the display of the supplementary points in the 2D
space may be of reduced value to us. In our example, for instance, the claims located in the upper left region
of the map are gray because they are suspected of being poorly represented. The unusually very high or
very low coordinate values on the third principal axis (marginal location) suggest their removal from the
analysis, or at least to view them with suspicion.
The map shows an outstanding profile for Zant, who owns the eradication of the Helicobacterio Pilori (acute
angle), a form of intestinal bacteria. The battle for the mind takes place more aggressively in the left side of
the map. Agop is attacking Antra on drug efficacy, and we know from the previous analysis that it is also
succeeding.
This map shows what doctors recall that the reps said (solicited memories). If we also had data about
solicited memories, we’d have the means to validate the effectiveness of the communication effort
undertaken by the company. Communication is very expensive and if the target prospects do not recall the
product and the attributes that management considers important for success and wants them to recall, some
counter measures must be taken.
Ries and Trout (1982) wrote that positioning is the position one product takes in the target's mind. If we ask
our prospects what they know and think of certain products, we may be able to depict very stimulating
positioning maps.
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3. Brand Mapping
71
Example 4: missing data
Let's say that the table below is comprised of preference data, gathered at two different moments in time. At
the time of the first survey, three products were not yet launched: Calma, Panto, and Zurc. The launches
have impacted the market shares and now we want to map products and diagnoses shifts over time.
Brand Mapping can handle this particular case by
applying the principle of distributional equivalence, and
can safely estimate the missing values.
Arrange the data as shown to the right, with the upper
right corner left blank. Choose Estimate missing data in
the first window of Brand Mapping, not forgetting that
labels are required, and start the analysis. The lower
region of the table is treated as passive rows and the
upper one treated as active.
The estimated missing values are averages of the
available row values. Their coordinates are always in the
middle of the map and do not exert influence in orientating
the axes. Their major contribution to marketing is allowing
us to display on a single map, markets that change between surveys, either because of new competitors
entering the competitive arena, or because of new brand usage.
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References to the Brand Mapping Analysis
Benzécri, Jean-Paul
L'Analyse de Données, Tome 2: L'Analyse des Correspondances
Dunod, 1973
Benzécri, Jean-Paul
Correspondence Analysis Handbook
Marcel Dekker Inc., 1992
von Clausewitz, Carl
Vom Krieg
Penguin Classics, 1982
Cooper, Lee G., Inoue, Akihiro
Building Market Structures From Consumer Preferences
Journal of Marketing Research, XXIII, August 1996
Douglas, Carroll, J., Green, Paul E. and Schaffer, Catherine M.
Interpoint Distance Comparison in Correspondence Analysis
Journal of Marketing Research, XXIII, August 1986
Interpoint Distance Comparison in Correspondence Analysis: A Clarification
Journal of Marketing Research, XXVI, November 1987
Reply to Greenacre's Commentary on the Carroll-Green-Schaffer Scaling of Two-Way Correspondence
Analysis Solutions
Journal of Marketing Research, August 1989
Greenacre, Michael J.
Theory and application of Correspondence Analysis
Academic Press, 1984
The Carroll-Green-Schaffer Scaling in Correspondence Analysis: A Theorethical and Empirical Appraisal
Journal of Marketing Research, August 1989
Correspondence Analysis in Practice
Academic Press, 1993
Greenacre, Michael J, Hastie, Trevor
The Geometric Interpretation of Correspondence Analysis
Journal of the American Statistical Association, June 1987, Vol. 82, No. 382
van der Heijden, Peter G.M., de Leeuw, Jan
Correspondence Analysis Used Complementary to Loglinear Analysis
Psychometrika, 50, December
Hoffman, Donna L., Franke, George R.
Correspondence Analysis: Graphical Representation of Categorical Data in Marketing Research
Journal of Marketing Research, XXIII, August 1986.
Lebart, Ludovic, & Morineau, Alain, and Warwick, Kenneth M.
Multivariate Desriptive Statistical Analysis: Correspondence Analysis and Related Techniques for Large Data
Matrices
NY, John Wiley and Sons, Inc., (1984)
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3. Brand Mapping
73
Lilien, Gary L., Rangaswamy, Arvind
MarketingStat
Mapping Markets for Strategic Purposes with MM4XL Software
MarketingStat, November 2004
Michelaud, Françoise-Xavier
Correspondence Analysis
Ramses Abul Naga's Advanced Econometrics Workshop at HEC, 1996
Myers, James H.
Segmentation and Positioning for Strategic Marketing Decisions
American Marketing Association, 1996
Pearson, Egon Sharpe and Hartley, H. O.
Biometrika tables for Statisticians
Cambridge University Press, 1972
Ries, Al, Trout, Jack
Positioning: The Battle For Your Mind
Warner Books, 1982
Marketing Warfare
Mc Graw Hill, 1986
Focus
Harper Collins, 1996
Tenenhaus, Michel, Young, Forrest W.
An Analysis and Synthesis of Multiple Correspondence Analysis, Optimal Scaling, Dual Scaling,
Homogeneity Analysis and Other Methods for Quantifying Categorical Multivariate Data
Psychometrika, 50, March
Weller, Susan C., Romney, A. Kimball
Metric Scaling Correspondence Analysis
Sage University Paper, 1990
Wind, Joram Y.
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4. Brand Switch Analyst
Brand Switch Analyst in a Nutshell
Brand Switch Analyst analyzes brand switch behavior, which is the tendency of consumers to change
preference between comparable products. This is vital information for fostering strategic thinking in
managers aware of the importance of customer retention.
It is very easy to use Brand Switch Analyst. The only
data needed is the sales of several competitors for two
or more time periods. The output consists of figures
and charts that, for each product, show the amount of
sales (market share) won from or lost to competitors.
Switch rates can highlight weaknesses in the preference dynamics of competing brands, which in turn makes
it possible to allocate marketing resources in a more targeted way and, hopefully, to increase success.
Brand Switch Analyst can also be used as a forecasting tool for projecting market shares and trends up to
their steady point, which is the point in time when no more changes occur.
Finally, you can also run dynamic switch analysis, which is the analysis of switch values for one product at
different points in time.
Note:
Why should I use Brand Switch Analyst?
Professor Kotler said:
“Marketing executives must watch their market shares just as much as their profits. Present customers can
never be taken for granted”.
Although written in 1963, this statement is still of great relevance, and in part it has also inspired the
development of Brand Switch Analyst. Market share is seen as a major means of determining competitive
position and the following three factors determine its structure:
• The
• The
• The
management's ability to retain present customers, also called Retention Rate or Brand Loyalty Index.
management's ability to draw customers away from competitors, that is the Switching-in Rate.
tendency for a brand to lose customers, that is the Switching-out Rate.
Brand Switch Analyst makes accurate estimates of switch and retention rates, which otherwise would be
estimated using expensive marketing research surveys. It is a tool that can be used for challenging business
axioms and to reinvigorate strategic discussion within teams. It allows you to look at data from a different
perspective when segmenting customer preferences and competing products. It is also useful for developing
functional know-how, for instance, for marketers interested in quantitative techniques.
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How to Run Brand Switch Analyst
There is one main window where the analysis is fine-tuned and then everything runs automatically.
Click the tool button in the floating toolbar to start Brand Switch Analyst.
Data Input
As input data to Brand Switch Analyst, we recommend using either sales data (in value or units), or market
shares for several competing brands, over a time horizon as broad as possible. The input data matrix looks
like the one below.
Tip:
operation the tool is performing at that moment.
Let us use an example. Suppose in a town of 1,000 people there are
only three bakeries: Center Bread, Warm Bread, and Every Bread. The
management of Center Bread seeks insight into the shift of clients
among the three bakeries. Their sales values for 10 months are shown
to the right. (We are using a short series of data to keep the example
brief, but remember that longer series are better.) The data in the
colored region of the table to the right is the input range to Brand
Switch Analyst.
Tip:
Select a cell with your mouse first and then call Brand Switch Analyst, which is designed to automatically
recognize the pre-selected area as the data output range. From here, you only need to select the input
range.
• The first row and the first column of any table are automatically recognized as labels.
• The data range does not accept non-numeric or missing values (use zeros for the latter case).
User Interface
The picture shows the user interface to Brand
Switch Analyst. Everything is kept very simple.
The Data range field is where you select the input
data values, the colored region in the matrix of our
example. The Output cell is the upper left cell of the
range where printing of the analysis output begins.
Use Job title to assign a title to your analysis. The
title is then used in the maps and at the top of the
report. The Maps, Reports, and Solver tabs enable
you to define several options related to the output
and the algorithm.
Tip:
Place the mouse pointer over the labels of the
Brand Switch Analyst dialog box, and a short
description is displayed for a few seconds.
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Reports user selections
The Reports panel shows controls related to Market share and Solver. Check the box Brand switch rates in
value if you want to translate the switch percentages into values (see also the Brand Switch Matrix
chapter). The checkbox Forecast t+1 in % prints one line of values below the Market share matrix (see the
picture in the Data Output section). The forecast projects market shares by applying Markov processes.
Simply selecting and copying can project later values. See below for more about forecasting.
Note:
Brand Switch Analyst applies quadratic programming and Markov processes. The latter is a concept from
mathematics that has received much attention, for its ability to describe brand-switching phenomena and to
predict market share at some future date. The method goes back to the early 1900’s, and its first application
was for predicting the movement of gas particles in a closed chamber. Since then, many other applications
have followed and in the 1960's, marketing came to focus its attention on Markov processes. Today, thanks
to Excel and Solver, it has been possible to automate the complex quadratic programming algorithm behind
Brand Switch Analyst.
The Solver checkboxes are used for printing standard Solver reports. For more details about these reports
you should refer to the Solver User Manual. Each report is printed on a new sheet. Be aware that selecting
these checkboxes may produce a considerable number of new sheets because the optimization algorithm
used to solve the quadratic programming model behind the estimation of switch values starts Solver
recursively. This means that for each optimization a new model is tested and a new series of Answer,
Sensitivity, and Limits reports is printed. With all three options checked, a model that re-iterates five times
produces 15 new sheets.
Solver user selections
The page to the right shows controls related to the
programming model. On the left side the Solver
parameters are the same as those used in the
original Solver user dialog. You should refer to the
Solver User Manual for more details about these
values. Precision and Tolerance do not share the
meaning one would intuitively attribute to them. Read
the Solver manual for further details, however you
should not worry too much about these values. The
default values set by Brand Switch Analyst are viable
for most problems.
Should your model require more time (Max time) or Iterations, Solver will prompt for your answer. Click
either Continue or Stop when the pop-up window below is displayed. It does not matter to Brand Switch
Analyst, which will reach an optimal solution, if you so choose.
Select the first radio button in the Algorithm re-iterations
pane if you want to find an optimal solution to your model.
Otherwise tell Brand Switch Analyst how many times to
repeat the optimization algorithm. This last option may help
you to cut the time needed to reach an acceptable solution.
Tip:
Watch the Excel status bar in the lower left corner.
Messages are displayed which briefly explain the kind
of operation the tool is performing at that moment.
The Add New constraint button is not active. This
function button has been added by MarketingStat for
future development. This utility will allow the setting of
additional rules for the quadratic model, but we await
the comments of our customers before implementing
this new function.
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Maps user selections
The window displayed above shows the user interface and hosts controls related to the charts (maps) in
printed output.
In the upper frame, check Print all switch maps if you want to print one map for each product in your
analysis model. For instance, a seven-product input range produces seven charts similar to the one below.
In this same frame, checking Change color by
map assigns a different background color to
each chart. The option Group maps
consolidates all charts in one single (grouped)
picture, while the Cascade maps option places
ungrouped charts in a cascade form.
Tip:
Select the consolidated maps with your right
mouse button, then select Grouping and
Ungroup. The maps will then appear as standalone, normal Excel charts editable in the usual
way. An alternative method is also available. Select all pictures (charts and shapes) that you want to
consolidate using Shift+click, then right-click on the selected pictures, and select Grouping and Group.
Consolidated pictures can be moved around MSOffice applications more easily than single shapes.
Alternatively, you may only want to Map a single product. Click the
Map one product only button to display the window pictured to the
right. Select the product you want to draw one single map for and
several options in the Maps multipage will automatically be
deactivated. Check the Print all switch maps box to reactivate them.
Tip:
Use the Map one product only option to prevent Excel from eating up your system resources when printing
many graphics. See Known Problems below for additional information.
The lower frame of the Maps page hosts controls related to map labels. Input the
Font size that you want to use in the map. This option is useful when handling
crowded maps.
Show labels as allows you to customize the values placed in the map. The picture
to the right shows all available alternatives. The default value is (To-From), which
shows the difference between sales lost to one competitor, less the sales won from
that same competitor, for the product at the top of the chart.
The Hide intermediary sheets checkbox can be used to shield the data needed to draw the maps, which
are printed on a separate sheet.
Data Output
Brand Switch Analyst returns the output shown to the right for the
input data, including:
1. Market shares for all items in the analysis
2. Market share forecast for each brand at time t+1 (user option)
3. Switch-in, switch-out, and retention rates as a percentage
4. Switch-in, switch-out, and retention rates in raw value as input
(user option)
5. Solver reports: answer, sensitivity, and limits (user option)
6. One or more maps that illustrate the switch dynamic between brands (user option)
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80
The market share is the ratio (Brand Sales / Total Market Sales). Center Bread in January 2003, for instance,
posts sales for 88.986 and the total market is worth 156.879, so its market share equals 56.7%.
The last row of the market share table can show the market share forecast for each brand at time t+1. The
forecast values are computed multiplying the last row of the input data matrix times the matrix of switch
rates.
Tip:
Need a forecast for more than one period? Select the forecast row with the mouse as shown above and draw
down the lower right, small, black box shown by the arrow. This is forecasting with a 1st order Markov
process.
We suggest you read the recommended literature before using Markov processes when projecting sales.
Indeed, our model produces a first order Markov process, and you may want to know more about higher
order Markov processes, which in fact may project more accurate values. Microsoft Excel makes available all
functions that you need for producing accurate results based on switch rates. The MMULT() function is used
to multiply vectors, and it is all you need to produce higher order Markov forecasts. Read also the section
Technicalities for more details.
Brand Switch Matrix
We would like to draw your attention to the use of Brand Switch Analyst for the analysis of consumers’ brand
switch behavior. Any brand switch matrix is made up of three elements:
1. Column values (Switch-From rates)
2. Row values (Switch-To rates)
3. Diagonal value (Retention index or Brand Loyalty index)
Interpreting these values in the light of the manager's prior knowledge of the market, may suggest useful
hints and foster strategic thinking. Reading the numbers is easy, but it is the underlying picture that can
make the difference.
2. Column values (switch-to)
Show the portion of sales that switch
from rows to columns. Warm Bread, f.i.,
receives 14.9% of the sales of Center
Bread and 70.1% of the sales of Every
Bread. Column totals in percentage are
not meaningful.
Anatomy of a Brand Switch Matrix
1. Matrix size (nxn)
It is always equal to the square
of the number of products. 14 is
the max number of products
you can input, due to a limit in
the number of unknown
variables Solver can handle.
Brand Switch Matrix (%)
MS% Switched To (col):
Center
Warm
Every
Bread
Bread
Bread
14.9%
0.0%
Center Bread
85.1%
26.3%
41.1%
Warm Bread
32.5%
0.0%
70.1%
Every Bread
29.9%
Number of iterations needed to reach an optimal solution: 3
5. Number of iterations
Show the number of times that Brand
Switch started Solver in order to reach an
optimal solution. Alternatively, it shows the
number of iterations set by the user.
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Market
Share
100%
100%
100%
4. Diagonal values
(Retention)
Show the portion of sales
retained by each product.
Every Bread for instance
retains only 29.9% of its
total market share. The
other 70.1% switches to its
competitors. These values
3. Row values (switch-from)
Show the portion of sales that moves from row
products to competitors. Center Bread, f.i.,
loses 14.9% of its sales to Warm Bread. No
switch toward Every Bread has been detected.
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The matrix below shows the Brand Switch Matrix in value. The figure 12079 in the first row equals 14.9% of
Center Bread's sales in Oct03 (re: switch matrix in %), and so on. It is now possible to compute meaningful
column totals, which can be used for computing the difference between row and column totals. The new
value corresponds to the net difference between the sales each product gains and the sales it loses. Center
Bread, for example, is estimated to lose 11, say dollars, in the next period, while Warm Bread will gain 945$.
The matrix cells detail where the money is coming from and going to.
In the data output table above the overall total equals the size of the market in Okt03 (Oct.03).
Anatomy of a Brand Switch Map
Brand switch maps describe every detail reported in the Brand Switch Matrix and more. They are normal
Excel charts and can be handled as usual in the Microsoft environment.
3. Label meaning
Depending on the selection in the user interface, labels show product
name and figures related to switch-in and -out rates and to the net
balance in value of the two.
To and From labels are intended as share of sales going To or coming
From the upper product.
2. Upper product
It may be either one row product (sales from) or a
column one (sales to) depending on the label
selection in the Maps multipage.
M ap 6 o f 7
Brand Sw itch
4. Background color
It can change from map to
map. Check the option
‘Change color by map’ in
the Maps multipage.
P rc t 6
( T o - F ro m ) :
- 4 .4 0 8
P rc t 5
(To -Fro m):
-2.226
P rc t 7
(To -Fro m):
-1.486
P rc t 4
(To -Fro m):
-0.341
7. Bubble size
It is relative, according to the market
leader of the last time period.
Size = Product sales / Market leader
sales.
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P rc t 3
(To -Fro m):
0.657
P rc t 2
(To -Fro m):
0.752
P rc t 1
(To -Fro m):
-2.105
6. Bubble border
Yellow for green bubbles.
Dark blue for red bubbles.
Border colors help splitting
winners and losers even when
the chart is printed on paper
(black and white).
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Dynamic Brand Switch Analysis
In the Brand Switch tool window select a valid
data range on the sheet, click the button
Dynamic Loyalty Analysis in the page Maps
and the form to the right appears. Select the
product you want to run the dynamic analysis
for, select the Starting period, select one or
more of the checkboxes available and click the
OK button.
When the dynamic analysis of loyalty is
requested the tool computes, for the selected
product, the three main switch behaviour
indices (switch-in, switch-out and loyalty) for
each period, beginning from the one chosen in
the list box Starting period and ending with
the latest period available.
The output shows the trend for the three switch values for one product. This is very valuable information for
managers, for instance, when monitoring the effectiveness of promotional actions on brand loyalty, or when
seeking market space at the expense of competitors.
Dynamic Analysis Report
The table below refers to the input data of the sheet you can open clicking on the Example button from the
Brand Switch tool form. A dynamic analysis was run for the brand Lucky Strike starting with Year 1939 and
ending in Year 1943.
In the Total column the upper half
of the table shows the same
values that can be found in the
range C28:C32 of the sheet
“MM4XL - Brand Switch Analysis”
of the example file for the Brand
Switch tool. These are the input
values for the brand Lucky Strike
in the period 1939-1943. Each
input value has been broken into
the three components of switch
behavior (switch-in, switch-out and
loyalty), and the results are shown in one row. Values in green are switches in favor of the analyzed brand,
values in red are unfavorable switches, and loyalty rates are shown between the red and green values in
black.
Lucky Strike increased brand loyalty from 28.9% to 33.6% in the period 1939-1943. It had a positive,
decreasing relationship to Camel, from which it drew around 5% sales every term, and it had a negative,
increasing relationship to Chesterfield, to which Lucky Strike lost around 5% sales every term. The column G
Switch In-Out shows the saldo of the incoming and outgoing sales, and its development is negative indeed,
which stands for a progressive loss of competitive power.
The lower half of the table shows statistics concerning the values in the top half. Saldo equals the difference
between term 1943 and term 1939. The remaining statistics refer to the values in their same column in the
upper half of the table, and their basic nature should not
require further explanation. Just in case, details concerning
descriptive statistics can be found in the chapter for the tool
Descriptive Analyst.
The values in the table above can be printed in percent as
well. We have omitted the data for the sake of brevity.
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Percent values should be treated with caution. They refer to the user input data, so two identical percentages
from different products will have, most probably, very different values in the original unit.
The table Correlations of Switch Values, as the name says, shows the measures of association of switch
values between brands. The measure ranges from 1 (strong positive association) to -1 (strong negative
association). In our case, three correlation indices can be computed. The -92.4% refers to the correlation of
values in the range B27:B31 and those in the range D27:D31. The index tells us that there is a negative
association between switch values from Camel and the portion of loyal sales for Lucky Strike. Given loyalty
increases for Lucky, we deduct switch from Camel to Lucky is slowing down.
Loyalty Rate vs Switch Rate: LUCKY STRIKE
0.8%
34.0%
0.7%
33.0%
33.6%
0.6%
33.5%
0.5%
0.4%
32.0%
31.6%
31.0%
0.2%
0.1%
30.2%
30.0%
0.0%
0.0%
29.0%
28.9%
-0.2%
28.0%
The Dynamic Analysis tool prints two more charts as
well: one showing the correlation values and one
showing the tendency of switch values. They are quite
intuitive and can be seen in the accompanying example
sheet.
-0.4%
27.0%
26.0%
-0.4%
Switch in Minus Switch Out
35.0%
Loyalty Value
The chart Loyalty Rates versus Switch Rates is
useful for grasping at a glance the tendency for one
brand. The blue line shows the Loyalty rate and it is
plotted on the left axis. The pink line shows the values
in the range G27:G31 of the table above, which is the
overall sum of switch activities, ending up negative in
our case. Adding this to the fact that loyalty levels tend
to flatten, we can conclude that Lucky Strike was going
through a tough time.
-0.6%
Year 1939
Year 1940
Lucky Strike
Year 1941
Year 1942
Year 1943
Switch In(new) - Out(disloyal)
Analysis Case: Hair Loss
One question managers are often called to answer is whether to put more effort into retaining existing
customers, or to concentrate on winning new ones. There is no ready answer to the dilemma, yet Brand
Switch Analyst can add some interesting insights in market analysis, which could help to reinforce the logic
behind business decisions.
Hair Loss EU Market
This example refers to an existing European market, although
product names have been changed for our purposes. The
products we mention are in direct competition and their switch
matrix gives interesting results that highlight the concept of
customer retention. Management has asked: “How can we
prevent the loss of market share in this declining market?”
The chart to the right shows the market share curves for the five
products used to treat alopecia (hair loss).
One is in liquid form and the remainder are capsules. The treatment length varies from one to three months,
prices are all quite similar, and all products are sold mainly through pharmacies. Keep2, the market leader,
holds some 50% of market share. A marketing research study
has shown that unsatisfied consumers do not jump from product
to product, but stop the treatment and start again using a
different product between three and six months later.
In such situations, a brand loyalty strategy is preferable to that of
winning customers from competing products. This concept is
also reinforced by the values in the Brand Switch Matrix.
Tip:
When you break down brands into single references, make sure Brand Switch Analyst works with direct
competitors so as to reduce, as much as possible, the 'noise' that affects the analysis. Direct competitors are
products that share all three characteristics of competition: they (i) offer the same technical performance, (ii)
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compete in the same market segment, and (iii) talk to the same target group.
Keep1, Keep2, and Keep3 claim to stop hair loss. Liquid claims to favor hair growth, and Fall claims to
prevent hair loss. From the consumer point of view there is a lot of hope when buying this sort of product,
although they also know that the probability of success is low. However, being sold through pharmacies,
although without prescription, may confer on these products a sense of believability, so many with the need
try these remedies. Intuitively, based on what has been written so far, one could expect customers:
i) to try one treatment and stop (non customers);
ii) to repeat the same treatment (loyal);
iii) to repeat, but with a new treatment (disloyal).
These products are the
way in to the market
There is not really much to do in the first case,
unless one really provides a treatment that
works. The second instance is captured in the
diagonal values of the brand switch matrix, and
the third case equals 1 minus the loyalty rate of
one's brand.
Keep2 and Keep3 show very high loyalty rates.
The former is market leader with more than 50%
market share; the latter is 2 years old and
controls 15% market share. Liquid has lost 25
points of share in the past 10 years and for the
past 2 has been below 5%. Keep1 was leader
10 years ago with 50% share and since then it
has declined regularly; nowadays it is down to
15%. For 10 years Fall has floated between 1525% share.
K2
K3
+27
Fall
These products show a
positive net change, yet they
are 2 ways out to the market.
+3
+10
K1
+42
Liquid
Now, the question Keep2's management is asking is “How can we prevent the loss of market share in this
declining market?” The picture above, based on the data from the switch matrix, may add some insight to the
decision process. The bubble size relates to the present market share; the arrows show the overall product
gain and its origin.
The market seems to move downwards. It looks as if users try the product and do not find it useful, so move
to an alternative product, whose claim is stronger than the first tried. If this does not work either, they leave
the market. The competition is clearly focused on communication (benefit, support and tone). Keep2 has a
high profile and therefore captures most new users. Its retention rate, however, is becoming weaker than in
the past. The declining market is perhaps also playing a role in accelerating this trend.
It seems from the picture above that Keep2's management should target Fall in order to maintain their
market share. Every term they lose around 5% share to Fall and gain 3.5% from it with a net loss of -1.5%.
Given that Keep2 retains around 95% share, targeting Fall could make available another 8.5%, which could
turn Keep2 into a winner again.
Analogous reasoning could be applied from the point of view of any other competitor in this market and the
conclusions might be completely different. What is important and common to any scenario though, is the
ability of the analyst to see the latent structure in the data, which is the soul of the data. It is the most
extreme and meaningful synthesis of the information that can be extracted from the data set that each
analyst should struggle for.
We hope this brief example has shown why we believe Brand Switch Analyst is a great tool for fostering
strategic thinking in business decision-makers. It is however only when analysts use their prior knowledge of
the market that Brand Switch Analyst produces the most interesting results.
Other Applications of Brand Switch Rates
Apart from the estimation of brand switch rates and forecasting, there are plenty of other applications where
the use of quadratic programming and Markov chains have been reported. Among others:
1. The application for the evaluation of different business plans is reported in Wroe & Adlerson.
2. Kotler shows how to use it for drawing what it calls the Competitive Marketing-Mix Model. He shows how
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multiplying the Marketing Response Vector by the Marketing-Mix Matrix produces the brand purchase
probability vector.
3. In operations management Markov chains and processes are used in a quite broad number of instances,
such as in logistics, production, packaging, call plans (reps), and more. Most of the sources cited in our
bibliography deal with this sort of problems.
Finally, we suggest using Brand Loyalty indices as a means of comparison for products belonging to the
same portfolio (same company). Plotting the Brand Loyalty values against brand investments may offer an
interesting perspective of the overall product portfolio competitiveness. In general, products holding large
market share have higher retention rates. Therefore, looking at the retention rates is a means of comparing
the ability of a firm to gain competitiveness in different market segments.
Tip:
Do you want to measure the market elasticity of adoption for a new brand? Run two brand switch analyses:
the first with the real data and the second adding a column of zeros to the first matrix. Then, multiply the
switch matrix by itself as many times as the switch values of the fictitious brand do not go back to zero.
Repeat the analysis for several markets, plot on a chart the loyalty rates (diagonal), and find out which
market is tougher for new competitors to penetrate.
Technicalities
For the technicians who like to look into the black box, here is a description of the model behind Brand
Switch Analyst. For a detailed reference read Theil and Rey and the bibliographic references listed later in
this chapter.
The Quadratic Programming Model
Let P be the matrix of transition probabilities (switch rates) to be estimated, with 0<= pij <= 1, Theil and Rey
methodology is to minimize the sum of the squared residuals subject to the constraints set to the pij. In
general, let D be any nxn symmetric and positive definite matrix. We can estimate transition probabilities
solving the following quadratic problem:
Minimize:
∑ et +1Det +1 − ∑t (xt P − xt +1)D (xt P − xt +1)
'
'
'
'
'
'
t
Subject to:
Brand Switch Analyst solves the model iteratively, and it can also search for an optimal solution. It first
transforms the input data in relative frequencies, then it sets the transition probabilities pij to unknowns and
Solver minimizes the equation above.
The criticisms of this model are mainly concerned with the assumptions that:
i) the market stays the same over time, its size does not vary;
ii) all consumers are supposed to buy every time;
iii) it considers a fixed quantity is bought by each customer.
We believe the simplification of the model can be seen as the cost of saving the money over a representative
marketing research study. Brand Switch Analyst is a loyal reproduction of the method first introduced by
Theil and Rey in the journal Management Science.
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MMULT
With the brand switch matrix available you can use
Excel's built-in function MMULT() for:
1. computing higher order Markov processes;
2. projecting future market shares (Refer to the Excel
online help for details. See also the chapter on the
tool Profile Manager).
MMULT returns the matrix product of two arrays. An array can be a vector of data placed on one single row
or column range. Multiple arrays take the form of a matrix. Multiplying the (multiple vector) full matrix of
switch rates by the (single row vector) last row of available sales values, MMULT returns the projected sales
values at time t+1, as when you print the forecast from the Brand Switch user interface.
Squaring the switch matrix produces the probability of retention, gain, and loss of share at time t+2 without
re-computing the switch matrix. This is also called a second order Markov process. Back to forecasting,
Okt03 (Oct.03) is the last available data and forecast at t+1 means November03. By squaring the switch
matrix (second order Markov process) and multiplying it by the sales forecast t+1 you produce an estimate of
market shares at time t+2 (Dec03). The matrix above corresponds to the square of the switch matrix of our
Bakeries example. A third-order matrix is found by multiplying the row vector times the second order matrix,
and so on.
Known problems
When using Brand Switch Analyst there are two technical limitations you should be aware of.
First, as already mentioned, the standard Solver version included in any copy of Excel allows the use of 200
unknown variables or less. Therefore, the maximum number of products that can be analyzed with the
standard Solver is 14, as the estimation model uses 14x14 (196) unknown
variables in order to be solved, which is the closest number to 200.
Second, if you get the error message shown to the right, do not panic. It is
neither your fault nor the software. Certain Excel versions do not return
memory resources back to the system after producing large volumes of
charts. The only way to get them back is by restarting Windows. Microsoft
claims to have fixed this problem with Excel 2000.
Tip:
Use the Map One Product Only to prevent Excel from eating up your system resources. This way Excel
does not collapse.
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References to the Brand Switch Analysis
Wroe Alderson and Paul E. Green, 1964.
Planning and Problem Solving in Marketing.
R. D. Irwin, Illinois.
Frontline Systems, Inc., 2000.
Solver User Guide.
Frank Harary and Benjamin Lipstein
The Dynamics of Brand Loyalty: A Markovian Approach.
Operation Research, Vol. 10 (Jan.-Feb., 1962) pp. 20-21.
Ira Horowitz, 1970.
Decision Making and the Theory of the Firm.
Holt, Rinehart and Winston, New York.
Jacob Jacoby and Robert W. Chestnut, 1978.
Brand Loyalty and Management.
John Wiley & Sons, New York.
Philip Kotler
The Use of Mathematical Models in Marketing.
Journal of Marketing, Vol. 27 (October, 1963), p33.
Philip Kotler, 1971.
Marketing Decision Making.
Holt, Rinehart and Winston, New York.
A. Madansky, 1969.
Least Squares Estimation in Finite Markov Processes.
Psychometrika, Vol. 24 (1959), pp 137-144.
Microsoft Excel 97.
User Manual.
Philippe Naert and Peter Leeflang, 1978.
Building Implementable Marketing Models.
Martinus Nijhoff Social Sciences Division, Boston.
Lester G. Telser, 1963.
Least-Squares Estimates of Transition Probabilities.
Measurement in Economics, Stanford University.
H. Theil and Guido Rey, 1966.
A Quadratic Programming Approach to the Estimation of Transition Probabilities.
Management Science, Vol. 12, No. 9, May 1966.
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5. Profile Manager
Profile Manager in a Nutshell
Professor Kotler suggests that marketing managers should evaluate models drawn with the same modelling
technique applied by Profile Manager when they want to make explicit the individual effect variables exert on
brand switching behaviour.
The typical application of Profile Manager is when planning new product development (NPD). Marketing
research suppliers often suggest running Conjoint Analysis for highlighting the combination of, say, product
attributes that maximize customer preference. When, however, one cannot afford the investment for a new
study or, even better, if one has dated data, which may still hold, running Profile Manager could supply an
understanding of the behaviour of market shares according to the preference of customers that can help
choosing among alternative concepts, such as new products, new claims, new target audiences, and more.
Sensitivity Analysis: Product A, Change in
Market Share
20.0%
Adv
Quality
20.0%
Pack
Store display
Shelf space
Price
Premium
Price deal
18.0%
15.0%
8.0%
8.0%
6.0%
5.0%
18.5% 23.5% 28.5% 33.5% 38.5% 43.5%
Attribute effect on market share
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How To Run Profile Manager
Profile Manager is a simple to run but extremely useful tool. Among it’s many applications, it can be used to
draw what-if market scenarios.
Click the tool button in the floating toolbar to start Profile Manager. The window shown below
appears. This is where you define the basics of the analysis you want to run, then click OK. That’s
it.
Note:
An example report of this tool is available. Click on the
Start button in Windows and select MM4XL –
Marketing Manager for Excel. The file can be found in
the Examples folder. Alternatively, start the tool and
In the upper field, Input range, select with the mouse
the area on the sheet where the data concerning the
profiles to be investigated are stored. We selected the
range B2:E10 (see the table in the section Anatomy of
a Profile Manager Report later in this chapter), which
entails 4 profiles: Product A, B, C, and D. Then we
selected the range F2:F10 as the Response vector
(this must be a single column of data); the range
A2:A10 as Item labels; and finally, the Output range
where Profile Manager can start printing the report of
the analysis. Read more in the Technicalities section
about variables used for the analysis.
After you have told Profile Manager where to find the
data, use the Print Data pane to select the data to
print. The box to the left shows the labels of the data
set selected in the Input range. Select an entry and click the Add>> button to move the item to the box to the
right.
For all items listed in the right pane, Profile Manager prints a report comprising the selected sections. The
checkboxes are all quite self explanatory. Labels in first row is selected by default and it means text is
displayed instead of numbers in the first row of the Input range. Select Remove old charts when running
multiple fine-tuning analyses with the same data set, to automatically get rid of old plots. The sensitivity
analysis includes both a table and a chart. Select both Sensitivity analysis and Sensitivity chart if you
want to inquire how single variables impacted the profile’s market share. Estimated share chart prints a bar
chart with the estimated market shares (what Kotler calls brand probability purchase vector) and Profile
chart prints a semantic differential chart, like the chart you can draw with the Semantic Differential tool.
Use the Learning Center in the lower left corner of the form to open the MM4XL online Reference Manual,
the Example sheet with test data, and other helpful utilities.
Click OK and Profile Manager will print the output report.
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Anatomy of a Profile Manager Report
The full report Profile Manager can print contains 3 main parts: estimated shares, profile chart, and the
sensitivity analysis.
Input data
The table below shows the input data to Profile Manager required for running the analysis. It includes:
•
•
•
variable labels (cells A2:A10),
input data (cells B2:E10),
and the marketing response vector (F2:F10).
The first two parts, labels and data, make up the profile(s). They can be gathered in a variety of ways,
ranging from sample surveys to desk research and competitive intelligence. The third part, the marketing
response vector, is the result of a survey or of educated guessing. Educated guessing is often done at the
early stage of concept development, for instance, for a new product launch or just a new product feature.
One can simply list their best guesses about the relative importance each of the items takes in the profile,
and run several scenarios to work with. We suggest caution, however, when doing this.
The profiles are expressed in eight variables (rows), most
of which have different scales of measurement. The higher
the frequency, the higher the relative attractiveness of that
attribute.
Professor Kotler calls this matrix the competitive marketing
mix matrix.It is used for summarizing the average market
perception of the analyzed brands measured along several
dimensions of competition. On the other side, continues
Kotler, the Marketing Response Vector in column F stands
for the average relative importance consumers (or your gut feeling) attribute to each of the dimensions. In the
data above, for instance, the sample of surveyed consumers attributed the lowest importance to getting a
good price deal when buying the product category (5%), and they attributed the highest rating (20%) to
Quality and Adv. The sum of the response vector is 1 and the list of variables used for the analysis varies
from business to business.
Profile Manager can analyze up to 36 different row items.
The Charts
The two charts below are drawn as a result of the analysis, if you choose to do so. The one on the right, the
Estimated share chart, is a common bar chart one can make in Excel. It shows the market share values
reached running the analysis with the data shown above. The chart on the left, the Profile chart, is a chart
one can make in Excel with MM4XL only. Use the tool Semantic Differential if you wish to draw one. With
Profile Manager this chart is used for comparing the product profiles all together. In our example, the data of
product A, for instance, is in the range B2:B10 of the data set above.
Profile chart
Price deal
Estimated share
24%
24%
25%
27%
Price
19% 22%
28% 31%
27%
Premium
25%
26%
Pack
25%
25%
Quality
Shelf space
21%23%25%
Adv
18%
Store display
31%
29%
21%
14%
27.6%
28%
23.5%
24%
36%
24%
22%
25.6%
36%
23.3%
23%
22%
25%
21%
10%
15%
20%
Product A
Product C
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25%
30%
35%
40%
Product A
Product B
Product C
Product D
Product B
Product D
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93
Reading the two charts, the marketing manager can get an understanding of what attributes are driving the
success or failure of the analyzed product profiles.
Sensitivity Analysis
When the options Sensitivity analysis and Sensitivity chart are selected in the tool form, Profile Manager
estimates to what extent each attribute impacts share. Profile Manager returns a table and a chart like the
two below for each product the user opts to make a sensitivity analysis for.
The tornado chart refers to the data in the table, and it shows the spread and the strength of the impact of
each attribute on the market share of one single profile.
Market Share
20.0%
Adv
Quality
20.0%
Pack
Store display
Sensitivity Analysis: Product Product A
Market share
Min
Max
Max-Min
Price deal
26.2%
31.2%
5.0%
Premium
26.1%
32.1%
6.0%
Price
25.6%
33.6%
8.0%
Shelf space
26.5%
34.5%
8.0%
Store display
23.9%
38.9%
15.0%
Pack
23.1%
41.1%
18.0%
21.5%
41.5%
20.0%
Quality
Adv
20.5%
40.5%
20.0%
Shelf space
Price
Premium
Price deal
18.0%
15.0%
8.0%
8.0%
6.0%
5.0%
18.5% 23.5% 28.5% 33.5% 38.5% 43.5%
Attribute effect on market share
More details on how market share and sensitivity analysis are computed can be found in the section
Technicalities.
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94
Technicalities
The model
Professor Kotler suggests that marketing managers evaluate models drawn with the same modelling
technique applied by Profile Manager when they want to make explicit the individual effect variables exert on
brand switching behaviour.
Professor Kotler assumes the characteristics of different brands are summarized, at time t, in a competitive
marketing mix matrix similar to the one we use in the section Anatomy of a Report. The measures of relative
attractiveness of each brand on one dimension are shown in the rows. The higher a row value the better that
brand performs on that variable. If we were working with price, the highest relative attractiveness would be
attributed to the lowest price.
Kotler calls brand probability purchase vector the market shares estimated with the model, which are
obtained by multiplying the competitive marketing mix matrix and the marketing response vector. The
resulting vector will add up to one and its outcome is influenced by (1) the relative attractiveness of the
attributes and (2) the weight customers attach to each brand characteristic. Profile Manager uses the formula
MMULT() for multiplying matrixes in Excel.
Among its limitations, this model is linear and does not allow modelling interaction effects among variables.
One of the benefits Kotler mentions is that it helps to find better ways to scale relative awareness and
attitudes toward brand differences.
Sensitivity Analysis: Product Product A
The sensitivity analysis is run altering iteratively the content of the input
data. Each input value of the matrix is set first to zero and then to 1, while
other row values are rescaled accordingly. The shares obtained with the
fictitious parameters are displayed in the columns Min and Max of the
table to the right, and the column Max – Min of the matrix shows the
width of the impact each variable exerts on the estimated share.
Price deal
Premium
Price
Shelf space
Store display
Pack
Quality
Adv
Min
26.2%
26.1%
25.6%
26.5%
23.9%
23.1%
21.5%
20.5%
Market share
Max
Max-Min
31.2%
5.0%
32.1%
6.0%
33.6%
8.0%
34.5%
8.0%
38.9%
15.0%
41.1%
18.0%
41.5%
20.0%
40.5%
20.0%
Known problems
If while using MM4XL you get the error message shown to the right, do not
panic. It is neither your fault nor the software. Certain Excel versions do not
return memory resources back to the system after producing large volumes of
References
Philip Kotler
Marketing Decision Making. A Model Building Approach.(pgg 508-510)
Holt, Rinehart and Winston, Inc. 1971.
Microsoft Excel. User Manual.
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6. Forecast Manager
Forecast Manager in a Nutshell
MM4XL Forecast Manager runs 14 of the most common and effective short-term forecasting methods. It can
also model time series in terms of special events such as promotional actions.
Thanks to Solver, Forecast Manager is enriched with the power of linear optimization, which means reaching
the best solution for every fitted curve. Each method is run in seconds, hundreds or even thousands of times,
every time trying new parameters. The curve that best fits the data is then shown in a succinct but detailed
report rich in charts, coefficients, and indices that highlight the information needed by the forecasting
manager to make the best decision.
Forecast Manager has been written in accordance with current MBA textbooks. It is accurate, cost-effective,
and easy to learn. Last but not least, all computations are shown by means of common Excel formula – we
opened the Black-Box for you.
Forecast Chart - Series: Appliance Shipments
450
430
Input - Forecast
410
390
370
350
330
310
290
270
Forecast
-5%
Forecast t+3
Time 59
Time 57
Time 55
Time 53
Time 51
Time 49
Time 47
Time 45
Time 43
Time 41
Time 39
Time 37
Time 35
Time 31
Time 29
Time 27
Time 25
Time 33
Observed
Forecast t+1
Best Fit:
Brown's Linear Exponential Smoothing
MSE: 118.111
MAPE: 2.8%
MAD: 9.155
R-squared: 87.9%
Theil's U: 0.254
Durbin-Watson: 0.112
Time 23
Time 21
Time 19
Time 17
Time 15
Time 13
Time 9
Time 11
Time 7
Time 5
Time 3
Time 1
250
+5%
Note:
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6. Forecast Manager
97
How To Run Forecast Manager
Click the tool button in the floating toolbar to start Forecast Manager.
There are four pages where you can change settings: Input Data is used to assign a report title and
define the input data range; Data Attributes is where you can define output layout and details for the
forecasting algorithms; Method Gallery is the place to select the fit methods you want to run; and Special
Events is the page where you shape the way Forecast Manager handles special events such as promotional
activities.
Note:
When active, the checkbox Activate help online shows brief explanations of available functions. Click on
the label that turns your mouse cursor to a question mark and a short explanation of that function will be
displayed in the online help area of the form.
Page 1: Input Data
In Input Data you can assign a title to the output report. The Input data range is the place where the data to
be fitted are stored. This must be one or more columns, each of at least 5 numerical values larger than zero.
Note:
If there are zeros in your input data replace them with very small values such as 0,000001, otherwise
MM4XL will warn of wrong input data. This is due to the optimization algorithm defined with formulae on the
sheet, which does not permit using zeros in some cases.
The Output range can be either one single cell or multiple ones. In either case the output will start printing at
the top left cell in the range. The Data labels range works the same way as the Input range, but it allows for
entering text as well as numbers, which will be used as row labels for your forecast. For example, you can
use time labels such as Mar01, Apr01, and so on.
Note:
In the output report, dates may accidentally be changed to numbers as a result of Excel’s format settings. If
necessary, change the Excel formatting settings in Extra, Options.
The Forecast horizon spin button defines how many time periods ahead to project after the last known
value. When forecasting short-term, horizons beyond 12 periods are seen as medium-term rather than short.
In order to produce useful results, a 1:2 limit has been set on the forecast horizon, so for example if you are
using a series of 20 periods you can project up to 10 periods ahead.
If your data contains column labels in the first row, select labels in first row on the right side of the window.
These labels are used for distinguishing between series when running a multi-series forecast. Check the
Show hidden sheet option if you want to see the sheet where MM4XL stores the data used to produce the
forecast for each selected method. This is also the place where you can “open the black-box” and see what
formulae were used with each forecasting method. Remove formula is the option you select for replacing
formulae with numbers in the hidden sheet.
Tip:
Formulae cost resources, so when doing multi-series (batch) forecasts, select the Remove formula option
and Forecast Manager will run faster.
In the field Special events select with the mouse the range where the text labels used for identifying the kind
of special event affecting time periods are stored. This range must be the same size as the Input data range,
but in this case blank cells are allowed and are even required for time periods when no event is being
assumed.
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List of constraints on Input Data page:
Option
Constraint
Input range
- Min 5 rows of values
- No zeros, blank cells, or text strings
Data label range
- Same size as input range
- No blank cells
Special events range
- Same size as input range
Forecast horizon
- Larger than zero
- Max horizon < (number of input periods / 2)
Input range
- Max 230 columns of data
- Max number of rows limited by Excel only
Page 2: Data Attributes
Clicking on the Data Attributes tab opens the panel below. The Quality of Forecast pane is important
because it defines the Measure of best fit, the parameter Forecast Manager uses for ranking the quality of
fitted curves. There are 5 different measures of fit to choose from: MAD, MAPE, RMSE, MSE, and R
squared. You will find more about reliability measures later in the Technicalities section. For now, it is worth
saying that these coefficients determine the discrepancy between actual and fitted values. The best curve is
chosen from among the hundreds or thousands of curves Forecast Manager tests.
The Moving periods drop down box is used for running the three moving average methods available.
Each of the buttons in the Cockpit pane
opens a new page where you can refine
your forecast. Use the Select all and
Deselect all radio buttons to select or
clear all options available under each
button.
The Reports button displays controls for
printing the Forecast chart with actual
and fitted curves placed between the
boundaries of a confidence interval (CI).
Fitted values lying outside the boundary
are highlighted on the chart with either a
green (above CI) or red marker (below
CI). The Full accuracy report prints for
each selected model all the coefficients
computed for measuring the quality of fit.
Besides the 5 measures of fit mentioned
above, Theil’s U and Durbin-Watson
indices are also shown. The Confidence
interval can be set at the desired percentage level between 1% and 100%
(of each forecasted value). The Special events chart shows the forecast
error between limit boundaries set by default at 1 and 2 standard
deviations. Values crossing the limit are highlighted as being affected by
some sort of “special effect” presumably produced by marketing activities,
such as promotional campaigns, for instance.
The Seasonal Cycle button allows modeling of seasonal cycles. When
the Print seasonal indices checkbox is selected, the seasonal
coefficients computed on the actual values are printed on the sheet. The
selection in the picture to the left indicates a quarterly series (4 seasonal
periods) beginning with the first quarter.
The Indices button displays an
option called Reliability & accuracy measures that prints a
summary table showing all major coefficients needed for evaluating
the quality of fit. Besides the coefficients introduced above, turningwww.mm4xl.com
6. Forecast Manager
99
points are counted, both missed and false signals, and the consistency of performance is measured in
terms of values below and above the confidence interval.
The Error button opens the frame to the right. The Error summary
checkbox prints a table showing, for each item in the series, errors in
terms of value, percent, and cumulative percent. The Cusum chart
option, whose default limits are set at 2SD (2 standard deviations),
prints a chart for monitoring the correct functioning of the forecast
algorithm. You can change it to 1 or 3 standard deviations.
The Solver button displays a panel for setting the Solver parameters.
Generally, you should leave these parameters at their default settings.
Change them only if you are an experienced Solver user. The default
settings handle most optimization models. If Solver cannot reach a solution
based on the default parameters, you are prompted to proceed or stop the
optimization algorithm. The algorithm, however, stops for one iteration only.
Given that it takes several iterations to reach an optimal solution, Solver
may well start again even after you select to stop.
List of constraints on Data Attributes page:
Option
Constraint
Moving periods
- Min = (number of rows / 2)
Special event chart
- Starts checking from period 6 on
Consistency of performance
- Available only when Confidence interval option in Reports is active
Page 3: Method Gallery
The third tab in the opening window, Method Gallery, is where you select the forecast method(s) to be run.
There are 4 groups of methods to choose from:
A.
B.
C.
D.
Methods for series without trend and without seasonality
Methods for series without trend and with seasonality
Methods for series with trend and without seasonality
Methods for series with both trend and seasonality
Each button opens a new window. Use the Select all and Deselect all radio buttons to select or clear all
options available under each button. Here is a complete list of the methods available:
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100
Details about each forecast method can be found in later sections of this chapter.
Page 4: Special Events
Finally, the Special Events tab is where
you can define occasional events, such
as promotional actions or any other
event that may cause a temporary
change in the sales level of the curve
you analyze.
If you clear the Measure special events
checkbox, all controls on the page are
deactivated.
You cannot analyze special events
without selecting at least one forecast
period to apply the coefficient(s). The
time period(s) accounting for special
events can be selected with the drop
down list Forecast period and the list
Kind of event specifies what sort of
event you are forecasting. A promotional
campaign of a direct competitor may
produce a negative effect on your sales
and vice versa. Labels in this list are
read from the Special events range in
the Input data page.
The Smoothing method tells Forecast
Manager how to remove the effect of special events from the input data. There
are four available options, as shown to the right. Quadratic trend is the default
selection. The Linear trend method replaces values in the fitted line affected by
special events with values obtained by means of a linear regression equation
such as the one below (see math notation in section Technicalities):
Yˆt = β 0 + β 1 xt
The variable x refers to time and the beta coefficients are found with a linear regression. The Quadratic trend
method applies the same concept as the linear one, but, of course, the equation above is modified to include
a third term for time squared. The Preceding value method replaces an affected value with the first
unaffected value preceding it. The Average method replaces values affected by special events with a
mathematical average of all terms preceding the value to be smoothed.
The two Remove>> buttons delete the selected entry in their respective lists.
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6. Forecast Manager
101
The Coefficient listbox shows five options that tell the software how to estimate
the effect of future special events of the same nature as those listed in the Kind
of event pane. Average values is the default coefficient, and it estimates the
value of special events by averaging all special event effects belonging to the
same event category. For instance, Forecast Manager estimated the following
three percentage effects for an event category named “Promo -15%”: +12.3%, +
9.7% + 13.9%. In this case, 11.9% is the average value used for encapsulating
in the forecast the value of the special event effects of kind Promo -15%. Last
value uses as coefficient for one event category the %-effect of the last special event found in the input data
for the same event category. First value uses as coefficient for one event category the %-effect of the first
special event found in the input data for the same event category. Largest value uses as coefficient for one
event category the largest %-effect of all effects for the same event category. Finally, Smallest value uses as
coefficient for one event category the smallest %-effect of all effects for the same event category.
Note:
The picture shows an example of input selection. Selecting range A1:A15 runs
a single series forecast while selecting range A1:C15 runs a multi-series
(batch) forecast.
Output Report
A full output report generated by Forecast Manager includes the following:
1. Report heading
2. Best fitted model
3. Accuracy and Seasonality tables
4. Control charts
5. Special events
You can choose whether to print the last three reports, and part of the second report is also user defined.
The default setting prints the most commonly used elements of each of the four groups.
Tip:
Most labels in the reports are explained using comments. When you see a red triangle (cell comment) in the
upper right corner of a cell, hover the cursor over that cell and a short explanation of the label is displayed.
The output report is primarily concerned only with the best-fitted curve. To view the details (formulae) of each
fitted model, select the option Show hidden sheet to display the sheet that hosts all intermediate
computations needed for fitting the models. A hidden sheet can be unhidden from the Excel menu by clicking
Format>Sheet>Unhide and selecting the appropriate sheet.
For educational purposes, Forecast Manager has been written in a way that makes no mystery of what
happens in the background.
Note:
In the upper region of the hidden sheet there are indices. Most of these are computed with array formulae. If
you are not familiar with this very useful sort of formula read the Excel help file (press F1) and remember that
array formulae are entered with the keys Shift+Ctrl+Enter rather then simply Enter. Array formulae can be
recognized by the braces brackets { } that contain the formula (still written with the sign = in front of it).
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102
Anatomy of a Forecast Manager Output Report
What you see in an output report of Forecast Manager reflects only part of the work the software did. This
section describes the output you see: the final report. The hidden report is explained in the example sheet
Forecast.xls that you can open from the Start menu in Windows.
1. Report heading
This section summarizes the user input selections. It briefly describes the actual and fitted curve, and lists
the name of the best-fitted model and its coefficients. The Technicalities section in this chapter gives details
about items that might not be well known, such as the Coefficient of variation in the table below.
2. Best fitted model
Forecast Report
For each item in the actual time series, this section
shows the corresponding forecasted value, its error,
and the confidence interval. The confidence interval
would be more correctly called the coefficient of
Consistency of Performance, as shown in the
Reliability & Accuracy Measures table in section 3.
This is the level at which forecast managers want to
proof how many fitted values lie above and below the
critical boundaries.
The standard labels printed by default when no label
range is selected are shown in column A below. They
can be replaced with your own labels.
Series name:
Job date (d/m/y):
Input range:
Observations:
Forecast horizon:
Error measure:
Seasonality:
Statistics
Min
Mean
Median
Std Dev
Max
Coefficient of variation
Best Fit Parameters
Method:
Alpha:
Beta:
Gamma:
Appliance Shipments
15.12.2002
Forecast.xls - Input - $A$1:$A$61
60 periods
4 periods
MSE
4 periods
Observed
269.5
339.5
341.9
31.5
400.8
9.28%
Fitted
276.8
341.7
344.9
29.6
393.7
8.68%
Error
-9.5
0.1
-0.3
3.3
10.6
Error%
-2.97%
3.55%
0.799
---
There are
hidden rows
here.
Tip:
To hide or unhide rows, select the row before and after the hidden one(s), such as row 30 and row 78 in the
picture above, and click on Format>Row>Hide/Unhide.
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6. Forecast Manager
103
3. Accuracy & Seasonality tables
Reliability & accuracy measures
MAD:
MAPE:
RMSE:
MSE:
R squared:
Theil's U:
Durbin-Watson:
Turning-point performance
False signals
Missed signals
Consistency of performance (+/-5)
Values below conf. interval
Values above conf. interval
There are two types of accuracy report. The Reliability & accuracy
measures table shows coefficients relating to the best-fitted model only.
The Full accuracy report shows the same coefficients for all fitted
models. The table below refers to a forecasting exercise run using all
available models.
2.517
0.7%
3.260
10.627
98.8%
0.079
2.010
10
12
6
100.0%
0
0
Full accuracy report
Forecast model
Holt's double exponential smoothing
Triple Exponential Smoothing
Weighted moving average
Exponential smoothing
Holt-Winter's additive seasonality
Holt-Winter's multiplicative seasonality
Stationary data additive
Stationary data multiplicative
Double moving average
Moving average
Seasonal regression
Quadratic trend
Linear trend
R
DurbinTheil's U:
squared:
Watson:
Rank #
MAD:
MAPE:
RMSE:
MSE:
1
2
3
4
5
6
7
8
9
10
11
12
13
14
2.517
2.531
2.807
3.204
3.229
3.614
3.676
3.686
3.766
5.880
5.937
8.902
8.959
9.155
0.7%
0.8%
0.8%
0.9%
1.0%
1.1%
1.1%
1.1%
1.1%
1.7%
1.8%
2.7%
2.7%
2.8%
3.260
3.288
3.643
4.224
4.226
4.763
4.946
5.283
5.419
7.150
7.258
10.049
10.072
10.868
10.627
10.811
13.272
17.845
17.862
22.683
24.461
27.912
29.367
51.126
52.674
100.986
101.447
118.111
98.8%
98.8%
98.5%
98.4%
98.6%
97.1%
96.9%
97.1%
97.0%
95.6%
95.8%
89.7%
89.6%
87.9%
0.079
0.077
0.088
0.106
0.099
0.123
0.128
0.134
0.138
0.186
0.181
0.233
0.234
0.254
2.010
1.848
1.718
0.722
0.712
1.474
1.420
0.984
0.990
0.198
0.233
0.143
0.137
0.112
Detailed information about each coefficient can be found in the Technicalities section later in this chapter.
Tip:
When you see a red triangle (cell comment) in the upper right corner of a label cell, hover the cursor over
that cell and a short description of the label is displayed.
The Seasonality table shows indices computed by averaging all actual
values corresponding to each period of the seasonality cycle. In the
example to the right we see a series made up of quarterly actual
values, and therefore four indices. The first one was calculated by
averaging all time periods with a seasonal cycle equal to one, and so
on.
Seasonality table
Seasonal time 1
Seasonal time 2
Seasonal time 3
Seasonal time 4
Value
336.3
338.2
340.4
343.1
Index
99.1%
99.6%
100.3%
101.0%
4. Control charts
Forecast Manager prints three different charts:
•
•
•
Forecast chart
Cumulative sum control chart (CuSum)
Special events chart
The Forecast chart (see the example below) shows how well the best curve fits the actual data. You can
see the forecasted values and can choose to display the confidence interval above and the below fitted
values. The accuracy coefficients are shown in the form of a legend. This chart is useful for presentations, for
a quick view of the best fit. But it does not supply much information about how well the model worked,
although all fit coefficients as well as both Theil’s U (goodness of fit) and Durbin-Watson coefficient
(autocorrelation of error terms) are available.
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104
450
430
Input - Forecast
410
390
370
350
330
310
290
270
Forecast
-5%
Forecast t+3
Time 59
Time 57
Time 55
Time 53
Time 51
Time 49
Time 47
Time 45
Time 43
Time 41
Time 39
Time 37
Time 35
Observed
Forecast t+1
Best Fit:
MSE: 118.111
MAPE: 2.8%
MAD: 9.155
R-squared: 87.9%
Theil's U: 0.254
Durbin-Watson: 0.112
Time 33
Time 31
Time 29
Time 27
Time 25
Time 23
Time 21
Time 19
Time 17
Time 15
Time 13
Time 9
Time 11
Time 7
Time 5
Time 3
Time 1
250
+5%
The Cumulative Sum chart, often called the CuSum chart, is used for diagnosing the functioning of
forecasting models. The whole concept is based on the fact that forecasting errors must be randomly
generated as long as the model predicts correctly, which is not accurately. Random terms show a normal
distribution with an average equal to zero and standard deviation equal to σ t . In the case of systematic
errors, the blue line (cumulative error) in the
chart below would cross one of the red
boundaries. This would indicate incorrect
functioning of the model, suggesting that the
model parameters should be adjusted. The
boundaries are typically set at two standard
deviations of the cumulative error term
above and below the zero line, which is also
the default value Forecast Manager uses.
Read Lewandowski (pg 155) for references
to this topic.
Cumulative Sum Control Chart (CuSum) - Series: Appliance Shipments
60
Cumulative Forecast Error
Upper Limit +2 SD
40
20
0
-20
-40
Lower Limit -2 SD
-60
1
3
5
7
9
11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59
Time
The Special Events chart is similar to the CuSum chart. The difference is that it works with the error term
not cumulated and the chart is used to highlight periods that exhibit an abnormal error size, either larger or
smaller than expected. The expected boundaries are set by means of standard deviation computed on the
error terms. Read Bail and Peppers (pg 131) for references to this topic.
Forecast errors lying outside two standard deviations are identified as abnormal and are highlighted with
either a red (lost) or green (won) marker. The forecasted amount above or below the limit is then computed
and displayed in a label in original units and percentage.
Special events summary:
- Favorable: 1.0% or 2.9
- Adverse: -0.5% or -1.7
- Total: 0.4% or 1.2
Special Events Analysis - Series: Appliance Shipments
Favorable Events
4.0%
Won: 1.0%
or 2.9
% Forecast Error
3.0%
2.0%
ULim +2SD
1.0%
ULim +1SD
0.0%
-1.0%
LLim -1SD
-2.0%
LLim -2SD
-3.0%
Lost: 0.5%
or 1.7
-4.0%
1
3
5
7
9
11
Adverse
Events
13
15
17
19
21
23
25
27
29
31
33
35
37
39
41
43
45
47
49
51
53
55
57
59
Time
In the chart above there are two abnormal quantities. The one at time 7 is positive, and it brought 2.9 units or
0.9% more sales than expected. If we were running a promotional action this might have been the result of
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6. Forecast Manager
105
that action. On the other side, the red marker highlights a larger than expected loss at time 19. The legend in
the upper right corner of the chart summarizes all favorable and adverse events.
Tip:
Abnormal quantities measured at the beginning of the time series, as in our example, can be attributed to the
adapting effect of the algorithm to the actual values. We therefore suggest that, whenever possible, you use
time series that do not exhibit such movements at the beginning of the series.
Finally, another graphical control chart worth mentioning here, although it is not implemented in MM4XL, is
the Turning-Point diagram. A turning-point happens when the slope of the actual curve changes direction.
The Reliability & Accuracy Measures table reports on turning-point performance. The Appliance Shipments
series example above, for instance, exhibits 10 turning-points, and the model did not match 6 of them
(Missed signals). On the other side, the model predicted 12 changes in direction which actually did not
happen (False signals).
Turning-points are often more important to managers than the trend itself. Indeed, forecasting accurately
when a change in slope is going to happen may help you save or make more money. There are four basic
turning possibilities, as shown in the following table:
ACTUAL
No Turning-point
Turning-point
The number of False Signals is found with: E =
T1
FORECAST
No TP
TP
NN
NT
TN
TT
NT
NT + TT
The number of Missing Signals is found with: E =
T2
TN
TN + TT
Note:
Turning-point performance in the Reliability & Accuracy Measures table starts counting fitted values from the
third value plus the number of moving periods on. This is a condition required by some models we coded.
A sample Turning-Point diagram is shown below, together with an explanation of each portion of the
diagram. The coordinates needed for plotting the points on the chart can be found with the formula:
Predicted (horizontal axis):
∆Yt = Yt − Yt −1
Actual (vertical axis):
∆Yt = Yt − Yt −1
Turning-Point Analysis
IIIB – Overestimate
of positive change
Predicted Change (∆Y)
IIA – Overestimate of
negative change
Line
of
Perfect
Forecast
IIB – Underestimate
of negative change
IV – Turning Point Error
Prediction of upturn that
did not occur; or failure to
predict a downturn.
Actual Change (∆Y)
Predicted (Mov Avg 3)
I – Turning Point Error
Prediction of downturn
that did not occur; or
failure to predict an
upturn.
IIIA – Underestimate
of positive change
Actual
Panels I and IV host the 12 false signals reported in the Reliability & Accuracy Measures table. Read Bail
and Peppers for references to this topic.
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106
5. Special Events
Time series forecasting models enable you to project values into the future according to a given array of
existing actual data. These models, however, do not allow you to integrate periferal information that would
bring the forecasting exercise closer to reality. For example, if our company wants to implement a
promotional campaign to increase consumption, this may lead consumers to react in one of three different
ways:
1. They may prefer our product due to the temporary benefit during the campaign, but would not
otherwise have used it (preference of non-users);
2. They may tend to buy more product than usual due to the appealing offer, which implies an
increased stock level (buyers increased stock);
3. Some buyers anticipate their purchase in order to profit from the special offer, which again implies an
increased stock level.
Therefore, special events may be characterized by two phases:
1. An increase in sales during the campaign;
2. A decrease in sales in the following periods.
Special Event: Sales Tendency
Sales
After
Campaign
During
Campaign
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Tim e
The target reaction to a promotional campaign depends on three main factors:
1. Nature of the campaign. It may be a price reduction, an increase in quantity, a free gift, etc.
2. Intensity of the event(s). A temporary reduction in price of 5% generates different reactions than a
reduction of 10%.
3. Coverage of the campaign. A quick local campaign may produce different results than a prolonged
national campaign.
In general, to produce effective results with a promotional action, the campaign should be short enough to
push the reaction of consumers. Too long a campaign mitigates the effect of the temporary benefit and
results tend to lose their appeal.
The Special events summary table below was created with Forecast Manager. The first column lists the time
periods when the user flagged the occurrence of special events (with the special events range on the Input
Data page). The second column displays the label the user assigned to each event. The Smoothed value is
found with one of the formulae described under Special Events in the Technicalities section. The Event
effect is found by subtracting the smoothed value from the actual value. Finally, the Event coefficient is
found using one of the methods described under Special Events in the Technicalities section. Read
Lewandowski (pg 196) for more details.
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6. Forecast Manager
107
The Event coefficients, one for each kind of event, are then applied to the forecast value using the formula
below and at the desired forecast periods as required by the user:
Yˆt + n = Yˆt + n ⋅ (1 + Ci )
There are other sources of abnormality that can impair the forecasting exercise:
•
•
•
Changes in the series characteristics, such as average, trend, seasonality, etc.
Transitory exceptional events, such as holidays, strikes, etc.
Permanent exceptional events, such as exit or entry of a major competitor, political and regulatory
changes, etc.
From case to case you may find that the features offered by Forecast Manager for handling special events
will also apply when working with other sources of abnormality.
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108
Technicalities
This section deals with the most technical issues related to forecasting and to Forecast Manager.
Forecasting? Never heard of it.
A forecast is a probabilistic statement concerning future events. Forecasting methods can be divied into
qualitative, quantitative, and hybrid techniques. Bails and Peppers (1993) include in the qualitative category
(also sometimes called judgmental, non-statistical, or non-scientific methods) the Delphi method, marketing
research, panel consensus, historical analogy, naïve extrapolation, sales force composite forecasting, and
the jury of executive opinion. Forecast Manager focuses on the quantitative category of methods, the
statistical approach. Although qualitative methods are invaluable, they are the result of years of experience in
the field and can hardly be reproduced with a standard layout. Most expert forecasters have started with
quantitative models and then developed qualitative models over time to overcome limitations in the
quantitative approach. The combined modeling of statistics and soft knowledge led to the development of
what are called hybrid models which, when equipped with simulation technologies, can be potent tools for
projecting into the long term.
Quantitative techniques can be divided into autoregressive and regression models. Forecast Manager
applies both, with emphasis on the former. Regression models, also called causal models, require a set of
independent variables (cause) to be used in order to fit a dependent variable (effect). Autoregressive models
embrace a long list of methods, including moving averages, smoothing techniques, adaptive filtering, time
series decomposition, trend extrapolation, and Box-Jenkins.
We do not advocate one method over another. The best method depends on the characteristics of the time
series you are working= with. This is why we recommend using tools such as Forecast Manager that
automatically try several models to find the best fitting curve.
Tip:
Most naïve regression models can be run with the Analysis Toolpak available in Excel. Check under
Tools>AddIns to see if it is installed. You can open it from Tools>Data Analysis.
Forecasting Technique Selection
The selection of the appropriate forecasting technique depends on several critical factors, some of which are
more common then others. In our experience, three factors are worth considering here: forecast horizon,
data pattern, and level of accuracy.
Forecast horizon
This is the number of periods the forecast should go into the future after the last known value. Typically,
decision-makers are interested in one of the following:
•
•
•
Short-term forecast = one to six periods.
Intermediate-term = seven to 12 periods.
Long-term = beyond 12 periods.
The long-term forecast tends to relate to trend factors (e.g. product demand, market size, industry structure,
etc.). The short-term is tied to seasonality and cyclical variations. In general, long-term horizon forecasts find
causal methods (regression) more valuable and autoregressive methods become less valuable. In the shortterm, however, when dealing with stable series (that exhibit few turning-points), autoregressive methods can
be very useful.
Level of accuracy
This is dependent on the project for which the forecast is being made. In some cases, a rough approximation
of the trend pattern may be enough for the end user. When a high level of accuracy is required, Forecast
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6. Forecast Manager
109
Manager makes available all the indices and charts needed to judge whether the model is accurate enough,
or whether a better one can be devised from among the 14 available models.
Tip:
After a visual inspection of all fitted curves, you may find that other models predicted the latest part of your
input data better than the best curve chosen automatically. In this case, recompute the fit measures in the
hidden sheet by reducing the number of rows in the formulae. This will confirm whether a model other than
the selected one should be used.
The accuracy of forecast can be inspected visually or tested by means of statistical measures. In both cases
the process is based on the analysis of the error associated with each forecasted item, and its ultimate goal
is to test how well one model forecasts (fits the actual curve).
The forecast error is computed with the formula:
et = Yt − Yˆt
The smaller the error term et the better the forecast.
Y represents the actual sales level and Yˆ the
forecasted one. However, one model can forecast better under certain circumstances and less well under
others. Therefore, it is highly recommended to test the quality of forecast by means of several measures and
to compare forecasts obtained with different models.
Graphical methods inspect the
reliability of forecasts quickly and
accurately, and they help to identify
systematic error patterns produced
by the model.
41 0
41 0
M o del 1
390
390
370
370
350
350
330
330
31 0
31 0
290
290
A ct ual d at a
Linear t rend
270
The pictures to the right show how
the same data were fitted with
different models. Sometimes one
cannot identify by simple visual
inspection which model is best, so
plotting error terms helps to discern
among the various methods. When
the model forecasts accurately the
error terms are randomly scattered
around the zero error-line.
250
41 0
A ct ual d at a
270
M o ving averag e - 3
250
41 0
M o del 3
390
390
370
370
350
350
330
330
31 0
31 0
290
M o del 4
290
A ct ual d at a
270
M o del 2
A ct ual d at a
B ro w n's Linear Exp Sm
250
270
Ho lt 's d o ub le exp sm
250
The three most common ways for inspecting forecast reliability by means of graphical methods are:
•
•
•
Plotting cumulative error terms (called CuSum chart in Forecast Manager).
Plotting error terms (called Special Events chart in Forecast Manager).
Using turning-point diagrams.
Data pattern
Trend and seasonality are the two core elements of any shortterm forecasting exercise made by means of autoregressive
models. Both elements can be found or not in a time series.
When they are present, also separately, they take either an
additive or a multiplicative form. Additive trend or seasonality is
one that increases over time at a regular rate (panels A and B in
the picture to the right). On the other side, a multiplicative trend
or seasonality increases at a faster rate than in the past (panels
C and D).
A
B
C
D
In general, regression models can replicate any pattern, given that the forecast manager can identify,
measure, and gather the relevant independent variables that explain the model. When forecasting shortterm, the autoregressive and regression models available in Forecast Manager offer a valuable solution to fit
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110
any curve form resembling the curves shown above. However, unstable series that show a high number of
turning-points may produce weak results.
Forecast Manager: Opening the black box
Forecast Manager is designed to be as transparent as possible, so that you can see what happens to treated
data. This also satisfies the information requirements of the educational community. All formulae used in the
models can be accessed on sheet, but you can select the Remove formulae option to replace them with
numbers, which has the advantage of burning fewer system resources than formulae.
Forecast Manager can run up to 14 models in four categories, as shown below. In addition, the treatment of
special events may be considered as a fifteenth model.
SEASONALITY
NO
YES
NO
• Linear trend
• Exponential smoothing *
• Moving average
• Stationary data additive seasonality *
• Stationary data multiplicative seasonality *
YES
•
•
•
•
•
•
• Holt-Winter’s additive seasonality *
• Holt-Winter’s multiplicative seasonality *
• Seasonal regression
T
R
E
N
D
Brown’s linear exponential smoothing *
Holt’s double exponential smoothing *
Quadratic trend
Weighted moving average *
Triple exponential smoothing *
* Model finds optimized unknown values using Solver.
Forecast Manager creates a new worksheet in the output workbook where it stores all intermediate data
needed to produce the final report content. This sheet contains five main sections, as shown below:
Series1
Input
Data
…..
Series n
Input
Data
Coefficients
Model(s)
Chart data
Forecast(s)
Coefficients
Model(s)
Chart data
Forecast(s)
Forecast Manager can analyze multiple time series at once. The data of the first series treated for fit starts in
cell A1. In the first 12 rows of the sheet the coefficients used to identify the best fit are placed. Below them,
on the left side of the sheet the input data as supplied by the user are shown. On the right side, all
intermediate computations for each model are shown. In the furthest right portion of the sheet data used for
drawing control charts are stored. Finally, below each model the forecasted value(s) are displayed. The
same structure is repeated, below the output of the first series, for batch forecast analysis of multiple time
series.
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6. Forecast Manager
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In the first row of each time series analysis the best-fit coefficient of each model – the coefficient the user
chose for identifying the best model – is shown. This is an important section, for Solver uses it when
optimizing models that use unknown values. These models are marked with an asterisk in the table above.
How to find optimized unknowns
Forecast Manager assigns to each forecasting method a portion of the hidden sheet, and it handles each as
a separate model, to use Solver to find optimized unknown values when required. Read the notes in the
example file Forecast.xls for an explanation of how to set up optimization models using Solver.
An optimized unknown is one that best satisfies the
constraints of the chosen measure of fit accuracy. If you
were to select the best fitted model using MSE, the
optimum unknown would be the one that produces the
lowest MSE value. When the unknown value lies between
0 and 1 and we test values at intervals of 0.001 it may
take 1000 trials to find the optimal value. Two unknowns
may require exploring 1,000,000 values. We stress the
‘may’ because often finding the first minimum value is not
enough to reach the optimal solution. Indeed, in real life it
is seldom the case when working with uni-modal
equations, and multi-modal functions require repeating the
optimization process to make sure of reaching the lowest value. The picture above shows this concept
graphically.
Forecast Manager automatically runs the optimization algorithm until the measure of accuracy satisfies its
constraints, e.g. minimum value for MSE or maximum value for R squared.
In the literature there are references to ‘autoadaptive optimization’. This is a special case of optimization
where the unknown variables are allowed to change between time periods. We found this methodology to be
viable for fitting the series but not for forecasting. In fact, the estimation process for forecasts did not produce
robust enough outcome results due to the approximation of unknown values.
Lewandowski (1974) offers a detailed explanation of the concept of optimized unknown parameters. Besides
the linear optimization method we apply, he also describes Friedman’s and Gradient methods.
General formulae: Models with unknowns
The models in the following table require the solving of single and nested equations that make use of
unknown values. This is a task that can be performed with Solver, the standard equation solver supplied with
Excel.
Notation:
Yi = Actual data
Yî = Fitted data
Yi = Average of actual data
Ei = Yi − Yî = Residual = Error term
(
)
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112
Forecasting model
No Trend No Seasonality
General fit
Unknown value
Exponential smoothing
Yˆt +1 = Yˆt + α Yt − Yˆt
(
)
α (alpha)
0 ≤α ≤1
Source: Ragsdale
No Trend Yes Seasonality
Stationary data additive
seasonality
Yˆt + n = Et + St + n − p
Source: Ragsdale
St = β (Yt − Et ) + (1 − β )St − p
Stationary data
multiplicative seasonality
Yˆt + n = Et ⋅ St + n − p
Source: Ragsdale
Weighted moving average
α (alpha)
0 ≤α ≤1
β (beta)
0 ≤ β ≤1
Et = α (Yt − S t − p ) + (1 − α )Et −1
α (alpha)
0 ≤α ≤1
β (beta)
0 ≤ β ≤1
⎛ Y ⎞
Et = α ⎜ t ⎟ + (1 − α )Et −1
⎜S ⎟
⎝ t− p ⎠
⎛ Yt ⎞
St = β ⎜⎜ ⎟⎟ + (1 − β )St − p
⎝ Et ⎠
W (weight)
0 ≤ wi ≤ 1
Yˆt +1 = w1Yt + w2Yt −1 + wk Yt − k +1
Source: Ragsdale
k
∑w
i =1
i
=1
Yes Trend No Seasonality
Brown’s linear exponential
smoothing
Yˆt + n = at + bt n
Source: Ragsdale
⎛ α ⎞ 1
2
bt = ⎜
⎟(St − St )
⎝1− α ⎠
St1 = αYt + (1 − α )St1−1
at = 2 S − S
1
t
α (alpha)
0 ≤α ≤1
β (beta)
0 ≤ β ≤1
2
t
St2 = αSt1 + (1 − α )St2−1
Holt’s double exponential
smoothing
Source: Bails
Triple exponential
smoothing
Source: Bails
Yˆt + n = Et + nTt
Et = αYt + (1 − α )(Et −1 + Tt −1 )
Tt = β (Et − Et −1 ) + (1 − β )Yt −1
α (alpha)
0 ≤α ≤1
β (beta)
0 ≤ β ≤1
1
Yˆt +1 = at + bt n + ct n 2
2
at = 3St1 − 3St2 + St3
α (alpha)
0 ≤α ≤1
⎛ α
⎞
⎟ (6 − 5α )St1 − (10 − 8α )St2 + (4 − 3α )St3
bt = ⎜⎜
2 ⎟
⎝ 2(1 − α ) ⎠
{
⎛ α ⎞ 1
2
3
ct = ⎜
⎟ St − St + S t
⎝1− α ⎠
St1 = αYt + (1 − α )St1−1
2
(
}
)
St2 = αSt1 + (1 − α )St2−1
St3 = αSt2 + (1 − α )St3−1
Yes Trend Yes Seasonality
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6. Forecast Manager
113
Holt-Winter’s additive
seasonality
Yˆt + n = Et + nTt + St + n − p
Source: Ragsdale
Tt = β (Et − Et −1 ) + (1 − β )Tt −1
St = γ (Yt − Et ) + (1 − γ )St − p
Holt-Winter’s multiplicative
seasonality
Yˆt + n = (Et + nTt )St + n − p
Source: Ragsdale
α (alpha)
0 ≤α ≤1
β (beta)
0 ≤ β ≤1
γ (gamma)
0 ≤ γ ≤1
Et = α (Yt − St − p ) + (1 − α )(Et −1 + Tt −1 )
α (alpha)
0 ≤α ≤1
β (beta)
0 ≤ β ≤1
γ (gamma)
0 ≤ γ ≤1
⎛ Y ⎞
Et = α ⎜ t ⎟ + (1 − α )(Et −1 + Tt −1 )
⎜S ⎟
⎝ t− p ⎠
Tt = β (Et − Et −1 ) + (1 − β )Tt −1
⎛Y
St = γ ⎜⎜ t
⎝ Et
⎞
⎟⎟ + (1 − γ )St − p
⎠
General formulae: Models without unknowns
Forecasting model
No Trend No Seasonality
General Fit
Variables
Linear trend
Yˆt = β 0 + β1 X 1t
β i = Beta coefficients found with linear
Y + Yt −1 + Yt − k +1
Yˆt +1 = t
k
k = Number of moving periods.
Yˆt = β 0 + β1 X 1t + β 2 X 2 t
β i = Beta coefficients found with
Yˆt + n = Et + nTt
Et = 2 M t − Dt
2(M t − Dt )
Tt =
(k − 1)
Y + Yt −1 + ... + Yt − k +1
Mt = t
k
M t + M t −1 + ... + M t − k +1
Dt =
k
n = Number of forecast periods.
k = Number of moving periods.
regression.
X 1 = Independent variable: time.
Source: Ragsdale
Moving average
Source: Ragsdale
Yes Trend No Seasonality
Quadratic trend
multiple regression.
X 2 = Dependent variable: time2.
Source: Ragsdale
Source: Ragsdale
Yes Trend Yes Seasonality
Seasonal regression
Source: Ragsdale
(
)
Yˆt = β 0 + β1 X 1t + β 2 X 2 t ⋅ Cst
β i = Beta coefficients found with
multiple regression.
X 2 = Dependent variable: time2.
C s = Seasonal coefficients.
t
Seasonal coefficients
Seasonal coefficients determine the average percentage by which seasonal periods differ from one another.
If we have a quarterly time series with a common 4-period seasonal cycle, the first seasonal coefficient
relates to the period Jan-Mar and expresses the average amount of percentage sales of all the periods JanMar in the time series. In Excel seasonal coefficients can be found with the formula:
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114
=SUMIF(range, criteria, sum_range) / COUNTIF(range, criteria)
In the formula above, the values contained in Sum_range are obtained as shown below and are used for
deriving average percentages. This is the method suggested in Ragsdale (2001).
Ct =
Yt
β 0 + β1 X 1 + β 2 X 2
t
t
Report heading
The report heading shows the basic user selection, some general statistic values about the observed (actual)
and fitted data, and which method was found to best fit the actual series. Most data in the heading is selfexplanatory. The Coefficient of variation, however, is worth mentioning here.
Index
Coefficient of variation
Source: Jarrett.
Formula
Cv =
Meaning
σi
⋅ 100
µi
σ = Standard deviation.
µ = Mean.
Yields the magnitude of the range within which values of the
analyzed and fitted time series can be found.
Reliability & accuracy measures
Forecast Manager can print several indices that are useful for evaluating the accuracy of curve fit, the overall
fit reliability, and the consistency of the quality of fitted values.
Accuracy is measured with the following indices:
Index
MAD
Mean Absolute Deviation
Formula
Meaning
Assigns equal weight to all errors, so it is easy to compare, but
it is difficult to interpret its scale of measurement.
It fails to take under- and over-representation into account.
Meaning: the smaller the more accurate the fit.
N
MAD =
∑E
t
t =1
N
Source: Ragsdale
MAPE
Mean Absolute % Deviation
Source: Ragsdale
MSE
Mean Square Error
N
MAPE = 100%
MSE = ∑
Like MAD but in percentage, so it overcomes the scale of
measurement problem. Meaning: the smaller the more
accurate the fit.
Et
∑Y
t =1
t
N
(Y − Yˆ )
Minimizes the occurrence of a major error. But penalizes
techniques that produce only a small number of large errors,
perhaps at start. Meaning: the smaller the more accurate the
fit.
2
i
i
N
i
Source: Ragsdale
RMSE
Root Mean Square Error
Source: Ragsdale
R Squared
Coefficient of Determination
Like MSE. Is sometimes preferred to MSE because it is easier
to interpret, for it has the same unit of measurement as the
actual series. Meaning: the smaller the more accurate the fit.
N
∑E
t =1
RMSE =
N
∑ (Y
n
R2 = 1−
Source: Jarrett
2
t
i =1
n
i
∑ (Y
i =1
i
− Yî
)
Represents the part of actual data explained with the fitted
data. This is also the square of the correlation between actual
and fitted data. Meaning: the larger the more accurate the fit.
0 ≤ R2 ≤ 1
2
−Y )
2
Overall reliability is measured with the following indices:
Index
U-statistics
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Formula
Meaning
If the method forecasts perfectly then U=0.
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115
Source: Jarrett
U=
If generating erroneous forecasting U=1.
0 ≤U ≤1
MSE
S y2 + S y2ˆ
S y2 = Variance actual series
S ŷ2 = Variance fitted series
Durbin-Watson coefficient
∑ (E − E )
∑E
DW tests the correlation of residuals (error terms).
If DW > U, conclude Ho.
If DW < L, conclude Ha.
Ho: error terms are independent.
Ha: error terms are correlated.
U = Upper level and L = Lower level can be found in DW
tables. Sample size, significance level, and number of
independent variables are needed to locate the appropriate
values.
2
DW =
Source: Jarrett
t −1
t
2
t
Consistency of fitting performance is measured with the following indices:
Index
Formula
Turning-Point Performance
False Signals: E =
T1
Source: Bails
Consistency of Performance
Meaning
NT
NT + TT
Missing Signals: E =
T2
TN
TN + TT
A turning-point is a change in the direction of either the curve
of actual data or of predicted values.
False signals occur when a change in the direction of the fitted
data is not due to a change in the direction of the actual data.
Missed signals occur when a change in the direction of the
actual data is not paired with a change in the direction of the
fitted data.
Level set by the user and comprised in the
range 0-100% of fitted data.
Counts the number of fitted values lying above and below the
boundary level set by the user, typically 1-10% of fitted values.
Index
Formula
Meaning
Cumulative Sum Chart
(CuSum)
∑ ≤0 ± 2σ
Source: Jarrett
Control Charts
t
e
t
Source: Lewandowski
Shows the cumulative error term within an upper and a lower
boundary.
σ e = standard deviation of residuals
t = corresponding time period.
Limit = 0 ± 2σ e
Shows the percentage residual curve between upper and lower
limits.
The leading concept behind the chart is that residuals are
normally distributed, so error terms lying above the 2 standard
deviation limit can be seen as abnormal. The cause of
abnormality can be found, for instance, in promotional actions
run by your company or a competitor.
Index
Formula
Meaning
Smoothing Method
S i = Yi − y s
y s = Smoothed value.
Removes exceeding sales from actual data by applying one of
4 methods.
Quadratic trend, Linear trend, and Average methods are
computed on all actual data preceding the value to be
smoothed.
The Preceding value method replaces actual data with the first
preceding actual value not affected by special effect.
Special Events Chart
Source: Lewandowski
Special Events
Source: Lewandowski
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116
Coefficients
Yˆt + n = Yˆt + n ⋅ (1 + C i )
C i is computed in one of 5 ways: Average, Last value, First
value, Largest value, and Smallest value. See section Special
Events for details.
Source: Lewandowski
Known problems
References to Forecast Manager
Bails, Dale G., and Peppers, Larry C.
Business Fluctuations. Forecasting Techniques and Applications.
Prentice-Hall International Editions, 1993
J, Durbin, and Watson, G. S.
Testing for Serial Correlation in Least Square Regression.
Biometrika, 38 (1951), 159-77.
Garwin, W., W. Crandall, J. John, and R. Spellman
Application of Linear Programming in the Oil Industry
Management Science 3 (1957): 407-430.
Hamilton, James D.
Time Series Analysis
Princeton University Press
Jarrett, Jeffrey.
Business Forecasting Methods.
Basil Blackwell, Ltd. 1987.
Lewandowski, Rudolf.
Prognose und Informationssysteme und Ihre Anwendungen.
Walter de Gruyter & Co., Berlin, 1974.
Luenberger, D.
Investment Science
Oxford University Press, 1997
Ragsdale, Cliff T.
Spreadsheet Modeling and Decision Analysis.
South-Western, Thomson Learning, 2001.
Schnarrs, S, and J. Bavuso
Extrapolation Models on Very Short-Term Forecasts
Journal of Business Research 14 (1986): 27-36
Winston, Wayne, L., and Albright, S. Christian
Practical Management Science.
Duxbury, 2001.
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118
7. Quality Manager
Quality Manager in a Nutshell
Statistical quality control (SQC) can help companies increase their ability to compete effectively by improving
the quality of the output they bring to the market. To do so, SQC measures the characteristics of a sample of
products or one or more processes in order to make decisions regarding their quality. The most popular SQC
techniques are available in the MM4XL tool Quality Manager.
There are two groups of analytical methods in SQC:
•
•
Statistical process control (SPC)
Acceptance sampling (AS)
SPC is a decision-making tool useful for ensuring that processes perform within limits. When a process goes
beyond set limits, SPC helps to identify when the change happens, and the manager can assess whether
the change is good or bad. If the change is bad, action should be taken to remove the cause. If the change is
good, the occurrence of the cause should be made common practice.
There are two kinds of measures in SPC:
•
•
Attributes characteristics: monitored with P, NP, C and U charts
Variable characteristics: monitored with Xbar-Sigma and Xbar-Range charts
When the characteristics of the sample do not meet the specifications it means the process is not in control.
A technique called process capability analysis helps to relate control limits to specification limits and find out
whether the process is performing as planned or not.
AS helps to ensure that the material a company receives and delivers is acceptable. There are three main
tools used in AS:
•
•
•
Operating characteristics curve (OCC)
Hypergeometric operating characteristics curve (HOCC)
Average outgoing quality (AOQ)
MM4XL software makes available in one package all the tools needed to perform accurate, fast and visually
effective statistical quality control directly in MS Excel.
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7. Quality Manager
119
Introduction to Quality Manager
Quality Manager is a very flexible MM4XL tool that draws the most common and useful Statistical Quality
Control (SQC) charts. Learn how to use each of the quality control charts available in Quality Manager by
reading the material in this chapter. There are 10 options to choose from:
SPC, attribute charts
• C chart
• U chart
• P chart with fixed and variable lot size
• NP chart
SPC, variable charts
• X-bar and Range (X-R)
• X-bar and Sigma (X-S)
Process capability
• Process capability analysis
Acceptance sampling
• Operating characteristics curve (OCC)
• Hypergeometric operating characteristics curve (HOCC)
• Average outgoing quality (AOQ)
The continued application of Quality Manager can bring tangible benefits in four areas:
•
•
•
•
The quality of processes improves due to the removal of the sources of nonconformity.
Productivity rises due to a better functioning of processes.
Costs decrease due to a better use of resources.
Competitiveness increases due to increased efficiency in the company.
Quality Manager works in a preview mode, which means that every analysis is shown online and the user
chooses whether to print hardcopy. It can also work in batch mode, where a large database of several
variables can be selected at once, and then a number of different charts can be previewed and printed, so
that the user avoids having to run each analysis separately.
How to use Quality Manager
In the MM4XL floating toolbar, click on the button shown to the left and the tool opens.
Alternatively, select Quality Manager from the main MM4XL drop down menu. The first window that
opens is shown below. It enables you to select the range of data to be analyzed. If the data range is
selected before opening the tool, the input field in the window automatically shows the range selection. If
you click the Next button without making a range selection on the sheet, Quality Manager works in
reduced mode, and only some charting options are available. The checkbox Use automatic update is
useful when working with large data series, such as hundreds of items, which can keep Quality Manager
busy for long a time in order to show the results. When this checkbox is unchecked you have to click the
Recalculate button in the second window to update results. Click Next to move to the second window.
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120
Quality Manager allows you to select several variables at once in the input range. Then, in the second
window, you can select one variable at a time and draw the appropriate control chart. To select multiple
variables from the picture below, for instance, position the mouse in cell A1, click and hold down the left
mouse button, then drag to cell H35 and release the mouse button.
The second window is where most of the work is done. Depending on the selected chart type, this window
may look slightly different from the sample below. Most options, however, work similarly for most charts. A
detailed explanation concerning use and interpretation of each chart type available in Quality Manager can
be found in the relevant sections of this chapter. The sample below provides an explanation of the elements
of the window.
Labels auto detection
Quick help online answers
basic questions
Results are shown live in the form
Data simulation for
comparison.
Auto detection of input
data by rows or col’s.
Items out of control are
identified and highlighted
Several chart types:
- X-Range & X-Sigma
- C, U, nP and P
- OCC, HOCC, AOQ
- Process capability
Online information
on input data and
control limits.
Each tool requires
data in an own form
Tools have own
parameters.
The Learning Center
links to reference
material for each
MM4XL tool and to
useful websites.
Quick help
online
Manual
recalculation
Go to printing
The input data is tested for normality
against the normal curve (red line)
When the analysis is done and you wish to print the results on the sheet, click the Next button to display the
third and last window, shown below. We strongly suggest that you try the options in the Learning Center.
That is where you will find help with the tool you are using and, more generally, with the whole MM4XL
software. The Learning Center also provides a number of links useful to marketers.
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7. Quality Manager
121
By default the tool places the results for the selected chart type in a New sheet. Select the option Output
range and select a place in the sheet where you want to print results if you do not want to add a new
worksheet (Excel sheet) to the workbook (Excel file). The labels describe the functioning of most features in
the window above. Note that the option Close this dialog when done is unchecked by default. Check it if
you want to close Quality Manager after a report has been printed; otherwise click on the Back button to
return to the previous window and run a new analysis. When unchecked, the option Display lines prints
charts in output that exhibit item points not connected with a line, as shown in the chart below, where the
green diamonds show the simulated data and the blue squares refer to the user input data.
Average number of
defects
U-chart
Simulatio n Data
User Data
0.2
0.1
0.1
0.0
0.0
0.0
9.0
18.0
27.0
36.0
45.0
Lot
A verage number o f defects
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Xbarbar
LCLxbar
UCLxbar
122
Introduction to Quality Control
In a world crowded with products of every kind and with customers’ demands, we need to pay attention to
improving what is already available as opposed to developing new things. Improvement in line with customer
needs and wishes requires a profound understanding of the competing environment and of the competitive
ability of companies. The ability to compete can be thought of as a chain of processes that take an input, add
value to it, and produce an output.
Often, due to a stereotyped way of thinking, when we talk of processes we tend to think of a production line.
But what about sales and management processes? For instance, the time an order takes to be processed,
the number of orders flowing in every day, the length of time to answer customer inquiries, the trend in gross
profit over time, the trend of return on sales, the response to direct marketing campaigns, the calls to 0800
phone numbers, and the interviews of a panel or tracking survey. These are just a few of the situations that
business decision-makers can understand as a sequence of events that taken together form a process.
Large processes can be broken down into components, which enables identification of the details that are
causing the process to fail or succeed. The concept of improvement, or change for the better, is key to
quality, and it has been effectively summarized in the now popular Japanese term Kaizen, which means
“continuous improvement involving everyone in the organization”.
Within this context, statistical quality control can help companies to increase their ability to compete
effectively by improving the quality of the output they offer in the market.
What is statistical quality control (SQC)?
Statistical quality control (SQC) applies statistical analysis to ensure that the output, products, and services
of a company satisfy the needs of the customers. The characteristics of a sample of products or one or more
processes are measured in order to make decisions regarding their quality. There are two groups of
analytical methods in SQC:
•
•
SPC is a decision-making tool useful for ensuring that processes perform within limits. When a process goes
beyond set limits, SPC helps to identify when the change occurs and the manager can assess whether the
change is good or bad. If the change is bad, action should be taken to remove the cause. If the change is
good, the occurrence of the cause should be made common practice.
Effective SPC requires selecting characteristics useful for measuring the process, and gathering accurate
measurements. There are two kinds of measures:
•
•
Attribute characteristics are measured with counts, for instance, the number of visiting customers or
incoming calls.
Variable, or continuous, characteristics can take any number and are typically measured with
devices, for instance, the weight of packaged goods or the time it takes to process an order.
Attribute characteristics can be monitored with:
•
•
P charts and NP charts. Useful when dealing with lots, for instance, boxes containing 24 packs each
or 250 bottles of shampoo made during each production cycle.
C charts and U charts. Useful when dealing with single units, such as the number of errors on a
single newspaper page or the number of customers receiving the wrong items in their orders.
Variable characteristics are monitored with:
•
•
X-bar and Sigma (X-S). Two charts used to detect changes in the average or in the amount of
variation in the process.
X-bar and Range (X-R). Used in place of the X-S charts when the sample size is smaller than 6.
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7. Quality Manager
123
When the characteristics of the sample do not meet the specifications it means the process is not in control.
A technique called process capability analysis helps relate control limits to specification limits and find out
whether the process is performing as planned or not.
AS helps ensure that the material a company receives and delivers is acceptable. The acceptance is stated
according to the inspection of one or more samples taken from one or more lots. Unacceptable samples
require action. In the case of incoming goods, the merchandise can be sent back to the supplier. Outgoing
services and products, on the other hand, call for the removal of the cause of rejection. Care must be taken
that each lot contains the output of one single process only for a specific period of time. Mixing up lots and
periods of measurement could prevent the analyst from identifying the source of the problem and correcting
the malfunction. Samples must be drawn randomly.
Three main tools are used in AS:
•
•
•
Operating characteristics curve (OCC). Given a certain acceptance level, the OCC plots the
probability of accepting a lot versus different levels of quality.
Hypergeometric operating characteristics curve (HOCC), like OCC but for small lot sizes.
Average outgoing quality (AOQ), is a chart showing the product of incoming quality times the
probability of acceptance.
An alternative to AS is the inspection of 100% of all items in all lots, but this may be economically unfeasible.
Variation, source of improvement
Every process is a function of five elements: material, methods, machines, environment, and people.
Variation exists in each element and, when all are combined, generates variation in a process. Variation is
divided into two groups of causes: common and special. Common variation is due to chronic causes built into
the process, and it is always there. Special variation arises due to acute influences that are not commonly
part of the process. The Kaizen concept of improvement aims to eliminate both common and special causes
of variation. Toyota and Motorola, among many other companies, apply the Kaizen concept.
In a process, however, it is not always immediately apparent what the variation arises from. A description of
the variables measuring the process may shed some light, and basic statistics such as mean, median, mode,
range and standard deviation are commonly used to describe the distribution of measurement.
Frequency
Count Exp.
16.0
14.0
12.0
10.0
8.0
6.0
4.0
2.0
0.0
Min 303
384 Max
18.6
1 Standard
deviation
Mode 366
Median 364
Average 360
Range 81
As shown in the chart above, these descriptive statistics help to indicate whether a process is producing a
stable, normally distributed output, or whether it has changed to an unstable condition. When the process
fails to work correctly, however, this information alone does not help to find out when the change occurred.
Fortunately, the quality control charts (QCC) used in SPC can fill this gap.
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For more information about descriptive statistics, read also the material concerning the tool Descriptive
Analyst available with MM4XL software. Besides a number of useful indices, the tool draws box-plot charts
and makes the Pareto analysis (ABC curve) often used to describe variables. This makes it useful for
investigating processes further.
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SPC, Attribute Charts
C chart
The C-chart measures the number of nonconformities in a single item. Nonconformities are results of a
process that depart from the expected norm. For instance, newspaper pages are supposed to be free of
errors, so errors (defects) are the nonconformities in the page. The number of customers receiving wrong
items in their order are also nonconformities, as are the number of daily purchases with a coupon in a
supermarket or any other data series measuring incompliance with counts at different moments in time.
User selections
The picture below shows a C-chart drawn with MM4XL’s Quality Manager tool. After selecting a Chart type,
as shown in the picture, if you have selected a range with more than one variable (column) in input, choose
the variable for Num defective to analyze, otherwise, the tool will automatically show the data of the only
input series available. If an input range was not selected in the first window, the C-chart will not be available
in the list of chart types and the right side of the window below will be blank. Click on Next to go to the
window where you select options for printing the results on sheet.
Technical notes
The control concept of the C-chart is based on a low presence of nonconformities with a high probability of
occurrence, and such processes behave according to the Poisson probability distribution function. When the
checkbox Simulate data in the window above is selected, Quality Manager shows a series of Poisson
random numbers (thin green line) before the user input data (thick blue line). The simulated data helps you to
understand whether the process is following a stable pattern or not. Unstable processes need to be
stabilized in order to be correctly analyzed with control charts. If the shape of the user data is remarkably
different from that of the simulated data, one can reasonably conclude that the user data may be influenced
by some kind of external force. That is, the impact on the input data should be removed and a new analysis
should be run.
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In order to detect a change, the input data is shown in a chart within boundaries as in the picture above. The
control limits are placed at three standard deviations (see field Z in the second window) above and below the
average (Cbar) of nonconformities. Measurements falling outside control limits indicate a change in the
process.
UCL = Cbar + 3σ
Cbar = Σci/n
ci = Nonconformity
σ = √Cbar
n = Sample size
LCL = Cbar - 3σ
Using the C-chart to detect a change in a process is like saying that as long as results lie within the three
standard deviations from the mean the process is seen as working correctly. In this situation it is advisable to
work with data series comprising 20 to 40 base measurements useful to calibrate the chart. A too-short
series may depart seriously from the shape of the Poisson distribution and, therefore, produce an unreliable
control chart.
The LCL cannot go below the zero. When an item goes beyond the UCL the chart has found a change. The
change can be bad or good according to the measurement data. For instance, if the data refer to errors in
the orders delivered to clients, the change is bad and the source of change should be identified and removed
from the process. If the data refer to orders placed in a direct marketing campaign, the change is good and
the source producing the change should be made common practice in the process. Items beyond limits are
highlighted with a red, round marker, as shown in the window on the previous page.
Input data
The input data for the C-chart requires one single column of counts. The picture below shows a suitable data
series in the range A1:A51 (note the hidden rows). These can be negative nonconformities, such as defects
occurring every hour, or they can be positive nonconformities, such as daily sales from a direct marketing
campaign.
Tip:
In order to speed up the tool, uncheck the Simulate data option when working with long data
series.
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127
Output results
The C-chart can show in output two charts and three tables according to the user selection in the third
window (see the section Introduction to Quality Manager). The first table, shown below, contains indexes
describing the input data in terms of:
•
•
•
•
•
Size of the variable: Max, Min, Sum, Range and Counts
Central tendency: Average, Median, Mode and Standard deviation (of a variable)
Chart limits: Upper Control Limit (UCL), Cbar, Lower Control Limit (LCL), Sigma
Z stands for the number of standard deviations where the control limits should be placed
Sigma is the standard deviation of a subgroup
For the sake of brevity, the second table is not shown here. In five columns it shows the details of the chart
limits by item. In the picture below, the small, red triangle in the upper right corner of the first column label is
a Comment which displays a short message. A number of comments are created by Quality Manager. Place
the mouse pointer on the red triangle to display the message.
The C Control Chart in the picture below refers to an input variable (thick blue line) presenting one
observation outside the UCL while all other points lie within limits. The thin green line on the left refers to
simulated random data that Quality Manager produced, in this case, according to the Poisson distribution.
Comparing the random data to the user input data can help you get a visual understanding of the departure
of the input data from normality. In this case, both simulated and user data take a shape that does not show
any particular sign of an existing trend. Therefore, we could believe the input data is stable and can be used
for the purpose of control. The peak outside of the limit may be due to random variation. Should the peak
exceed the control limit remarkably, you need to explain the reasons for departure and try to stabilize the
process, removing the noise. For a better way to assess normality, read also the material on the Process
Capability tool available in Quality Manager.
C Control Chart
Simulated Data
User data
Defect count
3.6
2.6
1.6
0.6
-0.4
0.0
19.0
38.0
57.0
76.0
95.0
Units:
Defect co unt
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Xbarbar
LCLxbar
UCLxbar
128
The third table is made of four columns relating to the data for the histogram chart. The Levels column
refers to the intervals classes. n shows the counts for each class, and Count Exp reports the expected
number of items in each class for a normally distributed variable.
The histogram in the picture below shows two series:
•
•
The blue bars refer to the observed frequency of count classes in the input data, and come from
column n. The first bar, for instance, tells us that there are 25 zeros, or sampled items without
nonconformities. The second bar shows 16 counts for ones in the data (although the axis value
below the second bar is 1.3 due to a rounding effect). And so on for all bars.
The bell-shaped red line shows the expected normal curve for a variable with the same range as
the input data. It is created with the values from column Count Exp, and it helps to verify with a
quick visual inspection whether the input data follow a normal distribution or not. C-charts, however,
follow the Poisson distribution in that they tend to approximate normality only with a large number of
observations.
Histogram of Inspected
12
10
8
6
4
2
0
1.0
2.2
3.4
4.7
5.9
7.1
8.3
9.6
10.8
12.0
Counts
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U chart
The U-chart works the same way as the C-chart, but is used to control nonconformities in lots rather than in
single units. For instance, the daily number of errors in a whole newspaper, the weekly number of orders
won with cold calls, the monthly number of transactions in a store, and so on.
User selections
The picture below shows a U-chart drawn with MM4XL’s Quality Manager tool. After selecting Chart type, as
shown in the picture, if you have selected a range with more than one variable (column) in input, choose the
variables for Num inspected and Num defective to analyze, otherwise the tool will automatically show the
data of the first two input series available. If an input range was not selected in the first window, the U-chart
will not be available in the list of chart types and the right side of the window below will be blank. Click on
Next to go to the window where you select options for printing the results on sheet.
Technical notes
The control concept of the U-chart is the same as for the C-chart. Read also the material in this chapter
concerning the C-chart in order to get a clear view of how the U-chart works and what assumptions it sets.
The control limits are placed at three standard deviations (see field Z ) in the window above and below the
average (Ubar) of nonconformities. Measurements falling outside control limits indicate a change in the
process. Items beyond limits are highlighted with a red, round marker, as shown in the window above.
UCL = Ubar + 3σ
Ubar = Σui/ni
ui = % Nonconformity in a lot
σ = √Ubar/ni
ni = Inspected in a lot
LCL = Ubar - 3σ
Input data
The input data for the U-chart requires two columns of counts. The picture below shows a suitable data
series in the range A1:B26 (note the hidden rows). These can be negative or positive nonconformities
(defects) in lots of a given sizes.
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Tip:
In order to speed up the tool, uncheck the option Simulate data when working with long data
series.
Output results
The U-chart can show in output two charts and three tables according to the user selection in the third
window (see the section Introduction to Quality Manager). The first table, shown below, contains indexes
describing the input data in terms of:
•
•
•
•
•
Chart limits: Upper Control Limit (UCL), Ubar, Lower Control Limit (LCL), Sigma and Range
For the sake of brevity, the second table is not shown here. In 8 columns it shows the details of the chart
a Comment which displays a short message. A number of comments are created by Quality Manager. Place
the mouse pointer on the red triangle to display the message. The column Fr/def stands for the fraction of
defectives. Sigma stands for the standard deviation, and is found with =SQRT(Ubar/Num inspected).
The U Control Chart in the picture below refers to an input variable (thick blue line) presenting one
observation outside of the UCL while all other points lie within limits. The thin green line on the left refers to
simulated random data produced by Quality Manager, in this case, according to the Poisson distribution.
Comparing the random data to the user input data can help you get a visual understanding of the departure
of the input data from normality. In this case, both simulated and user data take a shape that does not show
any particular sign of an existing trend. Should the peak exceed the control limit again, you should explain
the reasons for departure and consider whether to stabilize the process, removing the noise, if any. For a
better way to assess normality, read also the material on the Process Capability tool available in Quality
Manager.
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131
Average defects
U-chart
1.7
1.5
1.3
1.1
0.9
0.7
0.5
0.3
0.1
-0.2
Simulated Data
0.0
9.0
User data
18.0
27.0
36.0
45.0
Lot size
A verage defects
Xbarbar
LCLxbar
UCLxbar
The third table is made of four columns relating to the data for drawing the histogram chart. The Levels
column refers to the intervals classes. n, the column on the right, shows the counts for each class. Column
Count Exp reports the expected number of items in each class for a normally distributed variable.
•
•
The blue bars refer to the observed frequency of count classes in the input data. The first bar, for
instance, tells us that there are two items with one nonconformity. The second bar shows one count
for two nonconformities in the data, and so on. The axis value below the second bar is 2.2 due to a
rounding effect. To remove the decimal place, select the horizontal axis with the mouse, double-click
on it, and on the Figures page of the window that opens, set the Decimal places option to zero.
the input data, and it helps to verify with a quick visual inspection whether the input data follow a
normal distribution or not. U-charts, however, follow the Poisson distribution in that they tend to
approximate normality only with a large number of observations.
12
Histogram of Inspected
10
8
6
4
2
0
Co unts
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P chart with fixed and variable lot size
The P-chart is perhaps the most used control chart for attribute data. It can measure the number of
nonconformities in lots of fixed or variable size. Nonconformities are results of a process that depart from
normality. In the case of lots of fixed size, negative nonconformities could measure, for example, out of every
100 incoming calls the number waiting longer than 45 seconds for an operator to pick them. On the other
hand, positive nonconformities could measure such things as the daily number of orders resulting from total
cold calls.
The picture below shows a P-chart drawn with MM4XL’s Quality Manager tool. Select one of two P Chart
types. The variable lot type requires you to then select two variables for Num inspected and Num
defective. The fixed lot type requires one variable only for Num defective. If an input range was not
selected in the first window, the P-charts will not be available in the list of chart types and the right side of the
window below will be blank. Click on Next to go to the window where you select options for printing the
results on sheet.
Technical notes
The control concept of the P-chart is based on the Binomial probability distribution function. When the
checkbox Simulate data in the window above is checked, Quality Manager shows a series of Binomial
random numbers (thin green line) before the user input data (thick blue line). The simulated data help you to
understand whether the process is following a stable pattern or not. Unstable processes need to be
stabilized in order to be correctly analyzed with control charts. If the shape of the user data is remarkably
different from that of the simulated data, one can reasonably conclude that the user data could be influenced
by some kind of external force. That is, the impact on the input data should be removed and a new analysis
should be run.
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133
In order to detect a change, the input data is shown in a chart within boundaries as in the picture above. The
control limits are placed at three standard deviations (see field Z in the window) above and below the
average (Pbar) of nonconformities. Measurements falling outside control limits indicate a change in the
process.
The limits for the P-chart with fixed lot are set as follows:
UCL = Pbar + 3σ
Pbar = Σpi/n
pi = % Nonconformity
σ = √Pbar(1-Pbar)/n
n = Lot size
LCL = Pbar - 3σ
The limits for the P-chart with variable lot are set as follows:
UCL = Pbar + 3σ
Pbar = Σpi/ni
pi = % Nonconformity
σ = √Pbar(1-Pbar)/ni
ni = Lot size
LCL = Pbar - 3σ
Using P-charts to detect change in a process is like saying that as long as results lie within the three
standard deviations from the mean the process is seen as working correctly. To calibrate the chart it is
advisable to work with data series comprising 20 to 40 base measurements. Too short a series may depart
seriously from the shape of the Binomial distribution and, therefore, produce unreliable control charts.
When an item goes beyond control limits the chart has identified a change. The change can be bad or good
according to the measurement data. Returning to the opening examples, an increase in calls waiting longer
than 45 seconds to be picked up by an operator is a bad change, and the process needs to be adjusted to
continue working as planned. On the other hand, an increase in orders on cold calls is a good change, and
the source of variation should be clearly identified in order to make the change common practice in the
process. Items beyond limits are highlighted with a red, round marker, as shown in the window above.
Input data for the fixed lot
The input data for the P-chart with fixed lot requires only one column of counts. The picture below shows a
suitable data series in the range A1:A35 (note the hidden rows). These can be negative or positive
nonconformities.
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Output results for the fixed lot
The P-chart with fixed lot can show in output two charts and three tables according to the user selection in
the third window (see the section Introduction to Quality Manager). The first table, in the picture below,
contains indexes that describe the input and simulated data in terms of:
•
•
•
•
•
Chart limits: Upper Control Limit (UCL), Pbar, Lower Control Limit (LCL)
For the sake of brevity, the second table is not shown here. In six columns it shows the details of the chart
a Comment that displays a short message. A number of comments are created by Quality Manager. Place
the mouse pointer on the red triangle to display the message. The column Fr/def stands for the fraction of
defectives.
The P-Chart with fixed lot size in the picture below refers to an input variable (thick blue line) without
observations outside of control limits. The thin green line on the left side refers to simulated random data
produced by Quality Manager, in this example, according to the Binomial distribution. Comparing the random
data to the user input data can help you get a visual understanding of the departure of the input data from
normality. In this case, both simulated and user data take a shape that does not indicate any particular sign
of an existing trend. Therefore, we could conclude that the input data is stable and can be used for the
purpose of control. For a better way to assess normality, read the material on the Process Capability tool
available in Quality Manager.
Fraction defective
P-chart w ith fixed lot size
0.1
Simulated Data
User data
0.1
0.1
0.0
0.0
0.0
0.0
0.0
12.0
24.0
36.0
48.0
60.0
Lot number
Fractio n defective
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Xbarbar
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LCLxbar
UCLxbar
135
Input data for the variable lot
The input data for the P-chart with variable lot requires two columns of counts. The picture below shows a
suitable data series in the range B6:C31 (note the hidden rows). These can be negative or positive
nonconformities.
Output results for the variable lot
The printout of the P-chart with variable lot size looks exactly like that of the P-chart with fixed lot with the
exception that the chart shows variant control limits (dotted lines) rather than straight lines:
P-chart w ith variable lot size
Simulated Data
Fraction defective
0.2
User data
0.1
0.1
0.0
0.0
0.0
9.0
18.0
27.0
36.0
45.0
Lot number
Fractio n defective
Xbarbar
LCLxbar
UCLxbar
•
•
The blue bars refer to the observed frequency of count classes in the input data. The first bar, for
instance, tells us that there is one count for items equal to or smaller than 25 in the data. The second
bar shows three counts for items larger than 25 and smaller than 52.8. And so on for all bars.
the input data, and helps to verify with a quick visual inspection whether the input data follow a
normal distribution or not. P-charts, however, follow the Binomial distribution in that they tend to
Tip:
When working with P and nP charts, sometimes it is necessary to adjust the Pbar value in order to
align the central line (Pbar) of simulated and user data. When the two lines lie roughly at the same
level one can safely assume the simulated data reflect the shape of the data input by the user. For
P charts, the P-bar value is shown in the lower right area of the window among the statistics. An
estimate of the nP-bar can be found by first running a P chart with fixed lot and then applying the Pbar to the NP chart.
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nP chart
The nP-chart works the same way as the P-chart (read the corresponding section as well), but it is used to
control nonconformities in lots of fixed size only, and it plots the number of nonconformities rather than the
proportion of nonconformities. Plotting the number rather than the proportion of defectives makes the nPchart simpler to use than the P-chart. However, the nP-chart can only plot data from fixed size lots, which is
a substantial limitation to its application, and for this reason the P-chart is more widely applied than the nPchart.
Tip:
Read also the material in this chapter concerning P-charts in order to get a clear view of how the nPchart works and what assumptions it sets.
User selections
The picture below shows an nP-chart drawn with MM4XL’s Quality Manager tool. After selecting the Chart
type, f you have selected a range with more than one variable (column) in input, choose the variable to
analyze for Num defective, otherwise, the tool will automatically show the data of the first series available. If
an input range was not selected in the first window, the nP-chart will not be available in the list of chart types
and the right side of the window below will be blank. Click on Next to go to the window where you select
options for printing the results on sheet.
Technical notes
The control limits are placed at three standard deviations (see field Z in the window) above and below the
average (nPbar) of nonconformities. Measurements falling outside control limits indicate a change in the
process.
UCL = nPbar + 3σ
nPbar = Σpi/n
pi = Nonconformity
σ = √nPbar(1-nPbar)/n
n = Lot size
LCL = nPbar - 3σ
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Input data
The input data for the nP-chart requires one column of counts. The picture below shows a suitable data
series in the range A1:A35 (note the hidden rows). These can be negative or positive nonconformities.
Simulation data
When checked, the feature Simulate comparison data in the second window displays a new data series on
the left side of the Attribute charts called Simulated data. These are points produced according to the
distribution function characterizing the chart, for instance Binomial for nP-charts, and they are useful for
confirming through a visual inspection the stability of the user input data. If the shape of the user data is
remarkably different from that of the simulated data one can reasonably conclude that the user data could be
influenced by some kind of external force. That is, the impact on the input data should be removed and a
new analysis should be run.
Tip:
In order to speed up the tool, uncheck the simulation option when working with long data series.
Output results
The nP-chart can generate as output two charts and two tables, depending on the user selection in the third
window (see the section Introduction to Quality Manager). The first table, in the picture below, contains
indexes that describe the input data in terms of:
•
•
•
•
•
Chart limits: Upper Control Limit (UCL), Pbar, Lower Control Limit (LCL)
Z stands for the number of standard deviations where control limits should be placed
a Comment that displays a short message. A number of comments are created by Quality Manager. Place
the mouse pointer on the red triangle to display the message.
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138
The nP-Chart in the picture below refers to an input variable (thick blue line) presenting one observation
outside of the UCL while all other points lie within limits. The thin green line on the left side refers to
simulated random data produced by Quality Manager, in our example, according to the Binomial probability
distribution function. Comparing the random data to the user input data can help you get a visual
understanding of the departure of the input data from normality. In our example, both simulated and user
data take a shape that does not indicate any particular sign of an existing trend. Therefore, we could
conclude that the input data is stable and can be used for the purpose of control. For a better way to assess
normality read the material on the Process Capability tool available in Quality Manager.
NP-chart
12.8
Simulated Data
User data
10.8
np
8.8
6.8
4.8
2.8
0.8
-1.2
0.0
12.0
24.0
36.0
48.0
60.0
Lot number
np
Xbarbar
LCLxbar
UCLxbar
•
•
The bars refer to the observed frequency of count classes in the input data. The first bar, for
instance, tells us that there are two counts for zeros in the data. The second bar shows four counts
for ones. And so on for all bars.
The bell-shaped line shows the expected normal curve for a variable with the same range as the
input data, and helps to verify with a quick visual inspection whether the input data follow a normal
distribution or not. nP-charts, however, follow the Binomial distribution in that they tend to
Tip:
When working with P and nP charts, sometimes it is necessary to adjust the Pbar value in order to
align the central line (Pbar) of simulated and user data. When the two lines lie roughly at the same
level one can safely assume the simulated data reflect the shape of the data input by the user. For
P charts, the P-bar value is shown in the lower right area of the window among the statistics. An
estimate of the nP-bar can be found by first running a P chart with fixed lot, and then applying the
P-bar to the nP chart.
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139
SPC, Variable Charts
Xbar and Range charts (X-R)
These two charts monitor the location and the variation of a process, respectively. The Xbar chart shows
how the process changes according to a central measure of dispersion, the average, and the Range chart
shows when the variation of the process changes. For example, they could be used to monitor whether a
satisfactory cleanliness level is maintained in five restaurants of the same chain throughout the day, or to
monitor the sales trend of a product for four sales representatives, or to monitor visits to a website with and
without pay-per-click advertising. These charts, however, should be used only when the rate of data
collection is slow. In all other cases, the X-Sigma charts with larger samples are preferrable because the
sigma value is more accurate than the range value, due to the fact that the latter is found using only two
values of a sample, the largest and smallest one, while sigma uses all values in the range.
The picture below shows X-R charts drawn with MM4XL’s Quality Manager tool. If an input range was not
selected in the first window, the X-R charts will not be available in the list of chart types and the right side of
the window below will be blank. After the desired chart type is selected, the charts will display in the right
side of the window as shown below. The result can, of course, be printed in a worksheet.
Technical notes
The control concept of the X-R charts is based on the following assumptions:
•
•
•
•
•
The input data has at least two observations in each sample.
The size of the samples is equal for all groups.
The data are normally distributed or approximate normality. This implies that the data is collected in
a short time and there are enough measurements. A common rule of thumb suggests using at least
20 samples and 100 points. If this doesn’t approximate normality you should increase the sample
size (use the Process Capability tool to verify whether a process approximates normality). When the
sample size exceeds five units some authors suggest using the X-Sigma charts instead of the XRange charts.
All groups have equal weight.
Observations are collected independently, in order to avoid using autocorrelated data.
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•
For the Range chart only, between-group (sample) variation must be due to special causes, which
implies a correct functioning of the process.
Unstable (or out of control) processes run outside of control limits and/or present random patterns of
variation, which must be stabilized in order to be correctly analyzed with control charts. Stabilizing a
process may require collecting new data.
In order to detect a change, the average and the range of the input data are shown in two charts within
boundaries as in the picture below. In both charts control limits are placed three standard deviations above
and below the central line. Measurements falling outside control limits indicate a change in the process. In
practice, 99.7% of normally distributed observations fall within the three standard deviation boundaries, and
there are only 27 chances in every 10,000 that it falls outside. Therefore, it is reasonable to conclude that
observations outside of the limits show nonconformity in the process, and the analyst should explain why this
occurred.
Xbar-chart
UCL = Xbarbar+A2*Rbar
Xbarbar = ΣXbar/k
LCL = Xbarbar-A2*Rbar
Range-chart
UCL = D4 * Rbar
Rbar
Xbar = ΣXi/n
R = Max(n) – Min(n)
Rbar = ΣRi/k
n = Observations
k = num. of groups
A2 = Constant
D4 = Constant
D3 = Constant
LCL = D3 * Rbar
When an item goes beyond limits a change has occurred. The change can be bad or good depending on the
measurement data. For instance, if the data refer to sales levels falling below the central line, this represents
negative performance. When outside the LCL the change is bad and the source of change should be
identified and removed from the process. Above the central line the change is good and the source of the
change should be made common practice in the process.
In general, the rules governing the normal distribution can be used to interpret control charts:
•
•
•
•
Randomness of data
Symmetry of the distribution
99.7% of the observations lie within the three standard deviations
95.5% of the observations lie within the two standard deviations
Other rules of thumb to identify variation in the data suggest paying attention to data showing:
•
•
Seven successive observations on one side of the central line (there is a probability equal to 0.57 or
0.78% of finding such a distribution, and it is reasonable to believe it may be due to a process out of
control)
Seven successive observations either increasing or decreasing
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141
•
Two successive points placed very close to one of the limits (the probability of two successive
normally distributed points lying between two and three standard deviations on one side of the
central bar is 0.05%)
Input data
The input data for the X-R charts require two or more columns of data. The picture below shows a suitable
input data in the range B1:F26 (note the hidden rows).
Output results
The output from the X-R charts is made up of two charts and two tables, in accordance with the user
selection in the third Quality Manager window (see Introduction to Quality Manager). The first table, shown
below, contains basic indexes describing the process. Xdbar is the overall process mean computed on all
observations. Rbar is the average Range value of ranges for all groups of observations. StDevBar is the
average standard deviation value of standard deviations for all groups of observations.
limits by item. The second to fifth columns are used to draw the Range chart and the remaining columns are
used to draw the Xbar chart.
The X-Range Chart shown below refers to an input variable with all observations within confidence limits.
Although there has been a slight change in the range chart between the seventh and eleventh sample, this
has not altered the system. Also the five sequential points in the lower half starting at sample 20 tend to
verify that the process is stable and can be used for the purpose of control.
Subgroup range
Range Control Chart
45.0
35.0
25.0
15.0
5.0
-5.0 1.0
6.0
11.0
16.0
21.0
Subgroup Number
UCLxbar
LCLxbar
Range
Xbarbar
The Xbar Chart below confirms a change in average for sample number 10, and also shows a slight
negative bump for samples 19-21.
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Subgroup Average
Xbar Control Chart
157.2
152.2
147.2
142.2
137.2
132.2
127.2
1.0
6.0
11.0
16.0
21.0
Subgroup Number
UCLxbar
LCLxbar
A verage
Xbarbar
A joint reading of the two charts helps us to monitor that a given process performs as expected. This implies
a thorough knowledge of the process in analysis, in order to explain any cause of variation detected by the
charts.
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Xbar and Sigma charts (X-S)
These two charts are used instead of the Xbar and Range chart when the sample size is larger than five
units, which assumes that the rate of data production is high and it is not a problem to produce more data for
better sample stability. The main difference is that the Range chart is replaced by the Sigma chart, which is
more accurate because the range value is found using only two values of a sample, the largest and smallest
one, while sigma uses all values in the range.
The Xbar chart indicates changes in the process average compared to the average during the base period.
The sigma chart shows changes in the variation of the process (sigma) comparing the variation of subgroups
to a base period. You should read also the material in this chapter concerning the Xbar and Range charts, in
order to get a clear view of how the Xbar and Sigma charts work and the assumptions they set.
The picture below shows X-S charts drawn with MM4XL’s Quality Manager tool. If an input range was not
selected in the first window, the X charts will not be available in the list of chart types and the right side of the
window below will be blank. After the desired Chart type is selected the charts will display in the right side of
the window as shown below. The result can, of course, be printed in a worksheet.
Technical notes
In order to detect a change, the average and the range of the input data are shown in two charts within
boundaries as shown below.
Xbar-chart
UCL = Xbarbar+A3*Sbar
Xbarbar = ΣXbar/k
LCL = Xbarbar-A3*Sbar
Sigma-chart
UCL = B4 * Sbar
Sbar
Xbar = ΣXi/n
S = √Σ(ni-Xbar)2/(n-1)
Sbar = ΣSi/k
n = Observations
k = num. of groups
A3 = Constant
B3 = Constant
B4 = Constant
LCL = B3 * Sbar
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Input data
When working with X-S charts, follow the same instructions as for X-R charts. The only difference is that X-S
charts should use six or more columns of data for each sample. The picture below shows suitable input data
in the range B1:K26 (note the hidden rows).
Output results
The output results of X-S charts are interpreted in the same way as already explained for X-R charts.
The output from the X-S charts is made up of two charts and two tables, in accordance with the user
selection in the third Quality Manager window (see Introduction to Quality Manager). The first table, shown
below, contains two indexes. Xdbar is the overall process mean computed on all observations. StDevBar is
the average standard deviation value of standard deviations for all groups of observations.
For the sake of brevity, the second table is not shown here. In nine columns it shows the details of the chart
limits by item. The second, fourth, fifth and sixth columns from the picture below are used to draw the Xbar
chart, while columns 3, 7, 8 and 9 are used to draw the Range chart.
The Xbar Chart in the picture below refers to an input variable with all observations within confidence limits.
The input data does not exhibit any trend, so we assume it is stable and can be used for the purpose of
control.
Subgroup Average
Xbar Control Chart
109.5
104.5
99.5
94.5
89.5
1.0
6.0
11.0
16.0
21.0
Subgroup Number
UCLxbar
LCLxbar
Subgro up A verage
Xbarbar
The X-Sigma Chart below shows a change in average for samples number 4, 9 and 10, and it also shows a
slight negative bump for sample 23. Again, no noteworthy changes are detected, for all observations lie
within limits. However, this cyclic tendency to peak closer and closer to the UCL should be explained and, if
necessary, removed from the process.
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Sigm a Control Chart
Subgroup standard
deviation
17.3
15.3
13.3
11.3
9.3
7.3
5.3
3.3
1.3
1.0
6.0
11.0
16.0
21.0
Subgroup Number
UCLxbar
LCLxbar
Subgro up StDev
Xbarbar
The joint reading of the two charts helps us to monitor that a given process performs as expected. This
implies a thorough knowledge of the process in analysis in order to explain any cause of variation detected
by the charts.
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Process capability analysis
Capability is the ability of a process to perform a task. A process capability (PC) study assesses whether the
process is working correctly. That is: (1) the process is stable, and (2) the input data is normally distributed.
Unstable processes are influenced by external nonrandom forces, and they have to be stabilized in order to
perform meaningful PC analyses. Stabilizing a process may require collecting new data and/or enlarging the
sample size.
The picture below shows the PC analysis drawn with MM4XL’s Quality Manager tool. After the desired Chart
type is selected the charts are displayed in the right side of the window as shown. The result can, of course,
be printed in a worksheet.
The objective of a capability study is to evaluate the relationship between the output produced by a process
and the limits set by the analyst. Output falling outside the limits is nonconforming to the planned functioning
of the process. There are two kinds of limits:
•
•
Specification limits (LSL and USL) are typically set by users such as engineers, managers, etc. For
instance, one could set the limits for the number of visits one sales representative is supposed to
make in a given period of time to 75 and 200.
Natural tolerance limits (LNTL and UNTL) are based on the process capability and are computed
using mean and standard deviation.
Input data
The input data for Process Capability analysis requires one or more columns of either counts or continuous
values, as shown for the SQC charts (C, U, P and nP). Both tables below, for instance, are suited for PC
analysis.
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Output results
Output from the Process Capability analysis is made up of two charts and two tables in accordance with the
user selection in the third window (see the section Introduction to Quality Manager). The first table, in the
picture below, shows indexes describing the process capability.
Process capability is measured with indexes. An index is a relative relationship. When it falls outside limits
the process requires the attention of the analyst. Three common kinds of indexes are used to measure
process capability:
•
•
Cp measures the relative distance of the sample mean from the target mean. CpL and CpU
measure the distance of the sample mean from the lower and upper specification limits. A CpL and
CpU greater than one means that natural tolerance limits are greater than specification limits, which
means that the specification limits are requiring a precision beyond the capability of the process. On
the other hand, when they do not exceed specification limits the chance of producing
nonconformities is low.
Two more process capability indexes are called Cr and Cpk. The first is the inverse of Cp,
measuring the percentage of the specification band used up by the process, and it should be as
close to zero as possible in order to improve the processes. Cpk is a more accurate measure than
Cp when the process is not centered because it compares both halves before and after the mean to
the lower and upper specification limit, respectively.
The formulae of the process capability indices are as follows.
Index
CpU
Cp
CpL
Cr
Cpk
Formula
Description
Max − Avg
3 ⋅σ
Max − Min
6 ⋅σ
Min − Avg
3 ⋅σ
⎛
⎞
⎜1 − Cp ⎟
⎝
⎠
i
Upper capability index
i
Potential capability
i
Lower capability index
i
i
i
i
i
i
⎛
⎞
Min ⎜⎝Cpl ; Cpu ⎟⎠
Capability ratio
Demonstrated excellence
For the sake of brevity, the second table is not shown here. In nine columns it shows the details of the chart
limits by item. The Cumulative Frequency and Cumulative Normal are the columns used to draw the
Cumulative chart, shown below. Interval (equal to the process average +/- z standard deviations),
Frequency and Count Expected are used to draw the histogram chart.
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•
•
The bars refer to the observed frequency of count classes in the input data.
The bell-shaped line shows the expected normal curve for a variable with the same range as the
input data, and helps to verify with a quick visual inspection whether the input data follow a normal
distribution or not.
Kolmogorov-Smirnov test
The Kolmogorov-Smirnov is a popular test for goodness-of-fit of normally distributed variables. It returns a
value (D) that, compared to critical values of D for the K-S one-sample test, tells us whether the analyzed
data follows a normal process or not. Quality Manager performs the whole job and returns one of five selfexplaining labels. In the table above we read Little doubt, which means, as the label suggests, that there is
little doubt that the data analyzed are normally distributed. The same conclusion can be also reached with a
visual inspection of the Cumulative chart where it is clear that the shape of the input data of Cumulative
Frequencies (blue line) follows a normal pattern as the Cumulative Normal curve (pink one) suggests. The
other labels that Quality Manager returns in answer to the K-S test are N/A when the test cannot be
successfully run, Very unlikely, Low chances, Concern and Reasonable to believe.
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Acceptance Sampling
Operating characteristics curve (OCC, for large lots)
The OC analysis of sample plans helps to provide the desired consumer and producer risk. Consumer risk is
the risk of accepting low quality lots, also called Type I risk (α). Producer risk is the risk of rejecting good
quality lots, also called Type II risk (β). The OCC plots the probability of acceptance for different levels of
quality, and the objective is to be able to accept lots according to the desired acceptance quality level (AQL)
95% of the time.
The picture below shows an OC analysis drawn with MM4XL’s Quality Manager tool. The result can, of
course, be printed in a worksheet.
The OCC behaves in compliance with the rules governing the Binomial probability distribution function. It
requires large samples and assumes a low probability of occurrence for nonconformities, it works with
attribute measures, and it assumes only two possible outcomes, such as good-bad, on-off, etc. A chart of the
Binomial distribution is shown in the material concerning P-charts in this chapter.
Input data
The input data for the OCC does not require a worksheet range selection. Instead the user must enter the
following values in the tool window:
•
•
•
•
•
Sample size is the number of items in a lot.
Low, is the lower bound of the x-axis (horizontal), cell A10 in the first table of the Output Results
section.
High, is the upper bound of the x-axis, cell A29 in the first table of the Output Results section.
Number of classes, e.g. rows 10-29 in the first table of the Output Results section.
Number of columns. These are the lines in the charts. The first column (line) is equal to the
probability of finding zero defectives in the lot; the second column is equal to one defective in the lot
and so on. The number of columns should be lower than the sample size plus one, because there
cannot be more defectives than the total items in the sample.
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Output results
Output from the OCC is made up of two charts and two tables in accordance with the user’s selection in the
third window.
The table below shows the Acceptance curve, which is the probability of accepting a lot according to different
levels of error (columns from zero to four). We read, for instance, 64% in cell D14. This means that if 4% (cell
A14) of items in the lot are defective there is a probability equal to 64% that the lot will be accepted as a
good one according to our hypothesis in cell D9 that only two items are defective. The information in the
table is summarized in the chart Probability of Acceptance.
Excel formula for Acceptance
=BINOMIAL(B9;[sample size];A10)
The table below shows the probability of rejecting an acceptable lot, which is found by subtracting the
probability of acceptance (see the table above) from one. The information in the table is summarized in the
chart Probability of Rejection.
Excel formula for Rejection
=1-BINOMIAL(I9;[sample size];H10)
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Hypergeometric operating characteristics curve (HOCC, for small lots)
The HOCC is used instead of the OCC when the number of lots is small. In the literature it is sometimes
recommended that you use the OCC when the sample size exceeds 10% of the lot size. Other authors
suggest using the HOCC for samples smaller than 20% of the lot size.
The picture below shows an HOCC drawn with MM4XL’s Quality Manager tool. The result can, of course, be
printed in a worksheet.
The HOCC behaves in compliance with the rules governing the Hypergeometric probability distribution
function. It can work with small samples, it requires attribute measures, and it assumes only two possible
outcomes, such as good-bad, on-off, etc. The following is a chart of the Hypergeometric distribution.
Input data
The input data for the HOCC does not require a worksheet range selection. Instead the user must enter the
•
•
•
•
Lot size is the number of items in a lot.
Low, is the lower bound of the x-axis (horizontal), cell C39 in the first table of the Output Results
section.
High, is the upper bound of the x-axis, cell C61 in the first table of the Output Results section.
Increment, is the number of defectives in a lot, range C39:C61 in the first table of the Output Results
section. The value must be smaller than that of the Lot size.
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•
Number of columns. These are the lines in the charts. The first column (line) is equal to the
probability of finding zero defectives in the lot; the second column is equal to one defective in the lot
and so on. The number of columns should be lower than the sample size plus one, because there
cannot be more defectives than the total items in the sample.
Output results
The HOCC curve works the same way as the OCC, with the difference that the first column of the tables
refers to the number of defective items rather than to the percentage. One table and one chart refer to the
probability of acceptance of samples.
Excel formula for Acceptance
=HYPERGEO(D39;[sample size];C39;[lot size])
The table below shows the probability of rejecting an acceptable lot, found by subtracting the probability of
acceptance (see the table above) from one. The information in the table is summarized in the chart
Probability of Rejection.
Excel formula for Rejection
=1-HYPERGEO(D39;[sample size];C39;[lot size])
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Average outgoing quality (AOQ)
Outgoing quality (OQ) is the quality of a lot after it has been inspected, and it is a function of incoming quality
and the sampling plan. Incoming quality is the quality of material when it comes into the plant. Low incoming
quality will never produce perfect outgoing quality. However, an accurate sampling plan may help to increase
the level of outgoing quality when the incoming quality is low. The AOQ is found by multiplying the incoming
quality by the probability of acceptance.
The picture below shows an AOQ analysis drawn with MM4XL’s Quality Manager tool. The result can, of
course, be printed in a worksheet.
Input data
The input data for the AOQ does not require a worksheet range selection. Instead the user must enter the
•
•
•
•
•
Sample size is the number of items in a lot.
Low, is the lower bound of the x-axis (horizontal), cell C39 in the table of the Output Results section.
High, is the upper bound of the x-axis, cell C58 in the table of the Output Results section.
Number of classes, e.g. rows 39-58 in the tables of the Output Results section.
Number of columns. These are the lines in the charts.
Output results
The diagonal line in the chart below shows the maximum possible outgoing quality, and the curves show the
outgoing quality level for different levels of defectives in the sample. For instance, 58% stands for the level of
outgoing quality when the incoming quality is roughly 60%. This means that incoming quality equals outgoing
quality, so that management could decide to maintain the status quo or improve outgoing quality.
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Average Outgoing Quality
80%
Outgoing Quality
60%
58%
41%
40%
27%
20%
16%
7%
0%
0.0
0.2
0.4
0.6
0.8
Incoming Quality
The information in the chart is detailed in the following table that accompanies the AOQ analysis.
Average Outgoing Quality
Diagonal
Increment
Curves
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Formula
=Max([col]39:[col]58)
=[previous class]+Increment
=(High-Low)/Num. of Classes
= BINOMIAL(D38;[sample size];C39)
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Technicalities
Input requirements
Valid user data selections require at least five cells of values. When this minimum is not reached, Quality
Manager allows you to use only the Acceptance Sampling family of tools. These are: Operating
characteristics curve (OCC, for large lots), Hypergeometric operating characteristics curve (HOCC, for small
lots), Average outgoing quality (AOQ).
Blank and missing input
Quality Manager automatically sets blank and missing values to zero values. This may affect the end results
of your analysis.
Constants
X charts made with Quality Manager use constant values in accordance with the guidelines suggested in the
Manual on Presentation of Data and Control Chart Analysis published by ASTM (table 16, page 77, 7th
edition).
Large input series
Very large input series, say over 500 data points on a Pentium 4 PC, may impose a long waiting time before
the results can be shown in the preview window. The waiting time may be even longer when simulated data
are produced. To shorten this time you can uncheck the option Automatic update of charts in the first window
of Quality Manager. The Recalculate button in the second window will then allow you to update the preview
after your selection is made.
At the lower left side of the window, the status bar displays the rank number of the data point loading. This
feature runs too fast to be seen with short data series.
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References
Michael R. Beauregard, Raymond J. Mikaluk, Barbara A. Olson
A Practical Guide to Statistical Quality Improvement
Van Nostrand Reinhold, New York, 1992
Committee E-11 on Quality and Statistics
Manual on Presentation of Data and Control Chart Analysis
ASTM International, 2002
Gopal K. Kanji
100 Statistical Tests
Sage Publications, 1993
Douglas C. Montgomery
Introduction to Statistical Quality Control
John Wiley & Sons, New York, 1991
Walter A. Shewhart
Statistical Methods From the Viewpoint of Quality Control
Edward Deming Editor, 1939
G. Barrie Wetherill, Don W. Brown
Statistical Process Control
Chapman and Hall, London, 1991
Steven M. Zimmermann, Marjorie L. Icenogle
Statistical Quality Control Using Excel
American Society for Quality (ASQ), Milwaukee, WI, 1999
W. Edwards Deming
Quality Productivity and Competitive Position
Massachusetts Institute of Technology, 1982
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8. Risk Analyst
Risk Analyst in a Nutshell
Risk Analyst helps you build models in a way that takes into account the uncertainty inherent in the events,
and applies the Monte Carlo technique to simulate the outcomes of the models.
Risk Analyst provides a multitude of functions that enable you to model in MS Excel virtually any scenario
you can think of. It is fast and accurate, displaying the results of the simulation in a preview window. A fitting
tool is available to help identify appropriate distribution functions for the user data, and Quick Help can be
called from the tool to find out when to use each of the many functions.
Building models is a multifaceted process, based on solid facts and data as well as the modeler’s prior
knowledge. It borrows concepts directly from statistics, which may imply some study, and it wraps everything
up in spreadsheets, which may require some work. Risk Analyst makes available in one compact and
comprehensive tool all the resources needed by managers and business analysts to build and analyze
models concerned with important issues involving uncertainty.
Together with another MM4XL software tool called Decision Tree, Risk Analyst provides you with all the
resources needed to analyze even very complex business decisions.
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Risk Analyst Expert in a Few Minutes
Risk Analyst is a compact but feature-rich tool for building and simulating Excel models with the Monte Carlo
technique. The following brief instructions will show you how to run Risk Analyst for the first time, either using
one of the example sheets that come with the tool, or building a model of your own.
Using an existing model
In the MM4XL floating toolbar, you can open Risk Analyst by clicking the button shown to the left.
On the form that appears, click the Options button. On the new form, select the file NPV.xls from
the Open an example sheet… listbox, then click Cancel twice to go to the new sheet.
If you need help, click the button on the Options form to access Help with Distributions. This provides
quick online help, showing the syntax of each mmFUNCTION and offering suggestions on when to use them.
Step 1
If you are opening the file for the first time, you may see #NAME? displayed in all cells that contain a formula.
(If this is not the case, go to Step 2 below.
To get the formulas to work, select each cell that displays #NAME?, press F2, and then press Enter.
When all the formulas work, press F9. You will see the figures displayed in green change their values. These
figures are defined in the form of, say, a range of values rather than a single figure, and each time you press
F9 a new value in the range is chosen. For instance, in D17, mmTRI(5.8, 6, 6.5) is producing figures in
the range 5.8 – 6.5, with 6 being the most likely value. Every time F9 is pressed, a new value is displayed in
the cell. These are called Random Numbers, and they are the building blocks of simulation.
Step 2
Open Risk Analyst to simulate your first model. On the main form, click the Simulation… button. On the form
that appears, click Run Simulation. In the lower left corner of the window you will see a message
concerning the simulation trials. When the simulation runs are complete, the Preview form shows the results
of the simulation in four pages.
On the Preview form, click the Export button to paste a copy of the chart to the sheet.
Click the Print… button to access the form where you will define the simulation report. For this first exercise,
select the Complete report option. Click the Report… button to print the report either to the active worksheet
or to a new one, depending on your preference.
Step 3
Interpret the results of the analysis. For information on interpreting the results, refer to the appropriate
sections of this chapter. A background in Decision Analysis would significantly speed up the learning
process.
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Building your own model
Note:
Before proceeding, you should read the previous section Using an existing model.
To build a simulation model from scratch, you must identify and model the sources of uncertainty.
Step 1: Identifying the uncertainty
Say that we are modeling the Net Profit of a project, which is obtained by subtracting Cost from Revenue. If
Cost is equal to 30% of Revenue, then Revenue is the main source of uncertainty in this project, and we can
model it with an assumption (either based on solid facts and data or simply by using educated guesswork).
Step 2: Modeling the uncertainty
We can make a very basic assumption about future revenue for the project, such as that it will range
between $18 and $23 millions, with the most likely value placed around $20 millions. This assumption can be
modeled with the Risk Analyst formula:
mmTRI(18, 20, 23)
Step 3: Build the model
Open a new sheet. In cell A1 type the label Net Profit, in A2 type Cost, and in A3 type Revenue. In cell B1
type the formula +B3-B2, in cell B2 type +B3*70%, and in B3 type the following formula (Note: You may
need to replace the commas with the separator character used by your Excel release. Also, the formula
works after Risk Analyst has been launched at least once during an Excel session.):
=mmTRI(18, 20, 23)+mmOUTPUT()
Risk Analyst provides 27 different Probability Distribution functions (pdfs), three Property functions, and three
Utility functions. The online help that opens from the Help with Distributions button on the Options form
shows the syntax for each mmFUNCTION and offers suggestions on when to use them. mmFORMULAS can
also be entered from the Risk Analyst main form using the Paste to Sheet button, which copies to the active
sheet the contents of the Formula Bar to the right of the button.
Fitting data
When you are not sure which is the proper function to use, and you have data relating to the process you are
modeling, you can use the Fitting Data option to help you select the function that best fits the data. Say, for
example, that in the range B2:B6 we have sales values for five years: 20.2, 20.8, 21.5, 21.7, and 22.8, and
we want to find a fit for the data. Open Risk Analyst and click the Fit Data button. Select range B2:B6, and
click the Fit Data button. The Fitted Distributions field of the main form will display a list of fitted functions
sorted in descending order of fit accuracy. From the list, select the function you want to use in order to show
the chart, and click the Paste to Sheet button to paste its formula to the active sheet.
Step 4: Roll the model
In the MM4XL floating toolbar, open Risk Analyst by clicking the button shown to the left. On the
form that appears, click the Simulation… button and on the form that appears, click Run
Simulation to start simulating your first model with the Risk Analyst tool of MM4XL software.
There is much more to the Risk Analyst tool of MM4XL software than what has been described in this short
introduction. Read this entire chapter in order to uncover all the features and details of Risk Analyst.
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Introduction to Decision Analysis: Risk and Scenario modeling
Risk scenarios are representations of real issues that take into account the uncertainty involved in the
events. Scenarios can be reused over time, and they can answer one or more questions.
An illuminating article concerning the promising future of simulation techniques written by Rob Norton for
Fortune magazine in 1994 reports the words of Judy Lewent, Chief Financial Officer of Merck
Pharmaceuticals, who commented on the utility of scenario building and simulation techniques at the time
Merck was deciding whether to acquire Medco for $6.6 billions. She said:
“Monte Carlo techniques are a very, very powerful tool to get a more intelligent look at a range of outcomes.
It is almost never useful in this kind of environment to build a single bullet forecast.”
A typical scenario many managers build one or more times a year is a profitability statement. Such a model
is often built to estimate a Net Present Value (NPV), and it uses information that is not always obvious or
univocal. For instance, how many new competitors will enter the market in the next 24 months? How will the
market size change? What will our market share be? And so on. These are questions every manager could
give a rough answer to, but in general they are difficult questions to answer with absolute certainty.
Therefore, why should decision-makers rely on a ‘single-bullet model’ that cannot account for uncertainty?
During the past two decades this question has been approached by a number of economists, and the result
is the growing application of modeling techniques able to account for the uncertainty governing most
scenarios, including those relating to business activities. Launching new products, optimizing processes,
estimating future outcomes, finding optimal solutions, evaluating costs, scheduling operations, and more can
be approached from a completely new perspective that puts the whole decisional team and its individual
members in the position of thoroughly understanding the nature of managerial problems, explaining why one
solution may be better than another, and showing how an action today can affect results tomorrow.
Building successful models is not an easy task, but with practice you will find that modeling will become a
very rewarding activity, both in terms of your professional growth as a manager and of the wealth of the
business you work in.
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Introducing Risk Analyst with an Example
The workbook (Excel file) with the model described in this example is called Pkt-Entry.xls and can be found
in the directory Examples at the location where MM4XL software was installed.
This company will consider marketing a new product if in area tests at least 20% of potential buyers will
prefer it against the direct competitor brand A. So far, the investment has been relevant, and more is needed
if the product will be marketed. With the help of a simple model the marketing manager is trying to decide
whether to pursue the project further or cancel it. The measure of success is Net Profit.
The model
The first step to build a decisional model is to make it clear where its sources of uncertainty are, and a
Contributing Factor Diagram (CFD) can be of help.
We are modeling the entry of a product into portfolio (rectangle on the left in the following picture), with the
goal being to market it successfully. The success of the product is measured with its Net Profit (hexagon on
the right). The Net Profit is derived by subtracting costs from revenue. In our example, the overall Costs are
calculated by adding together the cost of developing the new product, the cost of testing the new technology,
and the cost required to market the product. On the other hand, the Revenue of the venture is derived by
multiplying the product market share times the size of the (growing) market. However, in order to gain market
share the product has to pass the user acceptance test, which is a decisional hurdle imposed by
management in order to consider a new project.
M arket
gro wth
M ngt
thresho ld
User
acceptan
P kt entry
M arket
share
Revenue
Net
P ro fit
M ktg co sts
Test co sts
Co sts
Dev't co sts
Modeling assumptions
In the CFD we recognize two major sources of uncertainty, User acceptance and Market share, and three
educated guesses, Marketing costs, Test costs, and Market growth. Each of the five assumptions has been
modeled with a Risk Analyst function.
Before modeling assumptions, we suggest building the model in Excel entering fixed values in the cells
hosting uncertain items. The following picture shows the Excel model used for this example. Cells D10, D11,
D16, D22, D24 and D26 contain Risk Analyst formulae that model our assumptions. For the sake of
explanation, in column B there is a shortened version of the formula used to model the assumption in the
corresponding row.
We arbitrarily split the model into four areas: Costs, Threshold, Market, and Profit.
Costs, the upper area, results in the addition into Total costs (D12) of three variables. Development cost (D9)
is a value we know for sure because $2.7 millions has already been spent, so it does not need to be
modeled. Test costs (D10) is what we call an educated guess, a value for which there is no certainty, yet its
real value lies in a range we can assume with confidence. In this case the cost of testing will be roughly $1
million (as shown in the model set to Show mode), and to model it we used a Uniform distribution ranging
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between 0.9 and 1.1, where every value in the range has the same probability of appearing. The third
variable, Marketing costs, will have a final value of around $3 millions, although it depends a lot on the kind
of pressure that will be put in place, which in turn depends on the kind of acceptance the product will have.
The selection of a Triangular distribution ranging 2.8-3.5 with modal value at 3 is compatible because it
assigns decreasing probability of occurrence to more extreme investments and because there is no
statistical evidence to apply a more rigorous probability distribution function.
The Threshold section contains two variables concerning the limit imposed by the management for the
inclusion of the product into portfolio: Required user acceptance (D15) and Product acceptance (D16). This
latter variable is important in the model because it filters, so to speak, the allowance to market the product,
and therefore to pick up revenues that will cover costs. D16 was modeled with a Binomial variate, which is
discrete and returns integer numbers. It takes two arguments: Trials and Successes. We assumed the
trials to be 100 potential buyers and the successes to be the proportion of potential buyers purchasing during
the area test, that is between 15% and 40% with average 26% (this may come from an ad hoc survey, for
instance, or it may be a guess). The Binomial function (100, 25%) returns values in the range 12-39, has
mode equal to 29, and about 10% of the values lie below the crucial number of 20 purchases out of 100 (you
can find this information using the chart in the Wizard window).
The Market area of the model holds one single, fixed number concerning the potential buyers in the market
(D19).
Finally, in the Profit area there are three items. The marketing manager of this project assumes that, if
launched, the market share of this new product could be roughly in the range 9%-15% with a most likely
value around 12%. In this case a Normal variate is used to model the assumption, rather than Triangular as
done above, because the manager assumes a lower chance of getting extreme values for the market share,
so there is no need to spread risk on the tails of the distribution and a Normal variate fits well. In D23 the
Profit per customer is a fixed financial value. In D24 Gross Profit is obtained with D19*D22*D23, and has
been modeled as an Output cell in order to evaluate its result against the other variables of the model. The
last variable in D26 is the main output variable of the model. It is obtained with an IF formula: if D16 is larger
than or equal to D15, then in D26 show Gross Profit minus Total costs, otherwise show only the costs
incurred so far, which is D9 plus D10.
Building the model
The model building phase may require several changes before reaching a final version. Typically, you build
the model by first typing formulae, values and labels directly in the cells of an Excel file. All assumptions are
typed as fixed values, or text labels suggesting the assumption (for instance, N12-1 for the normal function
used in cell D23). When the skeleton of the model is built you then access Risk Analyst using the formula bar
in the Wizard window. This way, selecting distributions and adding property functions becomes a smooth and
easy process. Working from the Wizard window is really helpful for experienced as well as inexperienced
users when defining assumptions, because the chart in the form helps you understand the shape of a
distribution and the range of values it covers.
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Simulation
The final report of this model was made by simulating 1000 runs, although during the fine-tuning phase it is
common practice to simulate only 100 runs in order to save time. Operational time, however, is a minor issue
with this model, because it runs very quickly and even 1000 runs may take just a few seconds.
The mmOPTNUM function run with the 1000 values simulated for the output variable Gross Profit (D22)
returned 662 as the number of runs needed to stabilize the mean value of the series with an interval of 20
values. It seems there is no real need to simulate more than 1000 trials with this model, although the old rule
holds: the more, the better.
Interpretation
This project is measured in terms of the Net Profit (NP) it can generate, so the output variable of interest is in
cell D26.
The following chart corresponds to the distribution on 1000 NP values gathered during the simulation. It
looks like the combination of two different Probability Distribution Functions (Pdf’s). On the right is a normal
distribution and on the left side is a spike made of one single bar. The bar on the left is generated by the NP
values simulated when the estimated product acceptance lies below 20%.
Output Chart: Net Profit - $D$26
140
47%
100%
100%
1100%
00%
97%98%99% 100%
93%
88%
80%
120
37%
100 9%
22%
80
60
59%
70%
30%
17%
40
11%
20
14%
10% 11%
9% 9% 9% 9% 9% 9% 9% 9% 9% 9% 9% 9% 9% 9%
Class 37; 4.292
Class 35; 3.855
Class 33; 3.418
Class 31; 2.981
Class 29; 2.544
Class 27; 2.106
Class 25; 1.669
Class 23; 1.232
Class 21; 0.795
Class 19; 0.357
Class 17; -0.080
Class 15; -0.517
Class 13; -0.954
Class 11; -1.392
Class 9; -1.829
Class 7; -2.266
Class 5; -2.703
Class 3; -3.141
Class 1; -3.578
0
This chart suggests that there is a 9% probability that the product acceptance will be less than 20%, and this
would return a net loss of some $3.6 millions. Moreover, there is a 1% probability that the NP will return a
negative value even if the acceptance boundary is 20% and more (class -0.517 and -0.080). Therefore, the
chance of failure for the project is 10%.
The most likely NP value will be around $1.67 millions, although the chance is high (43%) that the NP will be
between $1.450 and $2.325 millions.
There is 75% probability that the final NP will be in
the range $1.013 million and $2.981 millions, say
$1-3 millions.
Sensitivity Diagram
Output variable: Net profit - $D$26
$ D$ 16; 0.497
From the Sensitivity report we took the following
chart that shows the correlation of the output
variable NP with the Input variables in the model.
There is no surprise in seeing that the NP exhibits
$ D$ 10; -0.005
a strong, positive correlation with the variable in cell
D16, Estimated product acceptance, and with the
$ D$ 11; -0.098
variable Market share in D22. These are both
variables impacting heavily on NP in a positive
-100%
-50%
0%
manner, that is, the higher the product acceptance,
for instance, the higher the probability to sell and therefore to make profit.
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$ D$ 22; 0.410
50%
100%
165
When working with complex models made of many variables, the information coming from the correlations in
the Sensitivity report of Risk Analyst may offer very useful support to the analyst seeking to identify the items
with an impact on the overall outcome of the model or only on parts of it.
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How to run Risk Analyst
In the MM4XL floating toolbar, click on the button shown to the left here and Risk Analyst opens.
The risk analysis process is made up of three major operations: modeling, simulating and
interpreting.
Model building
Scenario models are built in order to evaluate and communicate. To prove effective, they need to be well
framed, that is, the problem must be clearly identified and its relevance must be understood within the
decisional team. For example, if we are facing a sharp loss in sales, it does not necessarily have to be a
matter of price, it could be an issue of product performance. A clear understanding of the business
environment is a fundamental requisite to identifying problems and framing models.
When the issue is clear, the analyst, alone or together with the decisional team, builds a model in MS Excel.
This is a common activity among business analysts and marketers. When working with Risk Analyst the
model is made of one or more input variables that, nested together according to the logic of the analyst,
produce an output result. The output result is the information that the decision-maker will use to make his or
her decision.
Assessing variable cells
We call variable cell assessment the definition of inputs and outputs in a model, and Risk Analyst allows you
to do this either manually, typing formulae directly in the spreadsheet cells, or using the Risk Analyst Wizard
shown in the picture below.
Risk Analyst makes available three new kinds of functions called distribution, property, and utility functions.
There are 27 Distribution Functions (DF’s or Pdf’s): 20 continuous and seven discrete. You can see the
complete list of Pdf’s by clicking the Distribution drop-down list shown in the picture above (in this list the
functions mmRANDBETWEEN and mmDISCRETE are missing). The reader is referred to the corresponding page
of this chapter for each DF.
There are three Property Functions (PF’s). The three PF’s mmOUTPUT, mmNAME, mmLOCK are key to building
scenario models.
The remaining three Utility Functions (UF’s) mmHISTO, mmOPTNUM, and mmCORREL are used for
computational purposes, and will be discussed later in this chapter.
In order to get a complete introduction to PF’s as well as to all other functions available in Risk Analyst, we
recommend reading the corresponding pages of this document.
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Output cells
When a model is run, Risk Analyst automatically identifies output variables and stores their value each time a
new trial is simulated. Output cells are the core element of a project. They are the variables for which the
model tries to provide more explanation.
An output cell is modeled simply by adding the function mmOUTPUT to the formula in that cell. When working
in Excel, we could type the function directly in the cell, which would then look like this:
=SUM(A5:A35)+mmOUTPUT()
The output function does not take any argument, it must be followed by brackets, and it can be used in any
position within the formula.
Locked cells
When there are many variable cells in a model, either outputs or another kind, we can use the property
function mmLOCK to avoid collecting the simulation results for one variable. This way, the simulation runs
faster, the results can be printed more quickly, the report looks less crowded, and it is easier to understand.
Adding the Lock property to a cell would result, for example, in the following formula:
=mmNORMAL(50, 5)+mmLOCK()
The formula above will still work in Excel, but it will not be accounted for by the simulation runs and it will not
be shown in the final report.
Naming variables
In order to make models neat and clear, the property function mmNAME can be used to assign a name to
variable cells and to assign a position to one cell within a series of cells using the same mmNAME formula. For
instance, in cell D12 we could have:
=SUM(A5:A35)+mmNAME(“Market size”)
When the simulation is run and the report is printed the results of the formula above are reported using the
label name defined between quotes. When no Name function is used, Risk Analyst assigns automatically a
more generic Item name followed by a progressive integer, such as Item 1, Item 2, and so on.
The property mmNAME can also be used to analyze the simulation of time series data. Say that we have three
items of the same series in the range D12:D14. The following formulae identify the name of the series and
the position of each element within that series:
=SUM(A5:A35)+mmNAME(“Market size”, 1)
=SUM(C5:C35)+mmNAME(“Market size”, 3)
=SUM(B5:B35)+mmNAME(“Market size”, 2)
When printed, the report attaches a label name to the cell and, for time series, it is possible to print a
separate report that sheds light on the time series as a whole rather than on the individual variable cells only.
This functionality is very useful, for instance, when analyzing market shares over time, when projecting sales,
when looking at profit over time, and more.
Formula bar
To add a function from the Formula Bar to a cell, in the Output cell field of the main window select on
sheet, using the mouse, the cell or cells where you want to add or modify a formula. Then either select one
function from the Distribution list or type it in the Formula Bar. Finally, press the button Paste to sheet or
click twice in the field of the formula bar and the formula is added to the selected cell.
The picture above shows an example. Note that the first part of the formula, the mmNORMAL function, is
defined by Risk Analyst when the selected distribution is a Normal one. The formula changes when a
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different distribution is chosen. The Output part of the formula can be either typed or added by clicking once
on the label Output above the formula bar. Clicking twice on the label Output removes the statement from
the formula bar. The same concept applies to the Lock and Name labels above the formula bar. One click
on the label adds the statement to the formula bar, two clicks on it removes the statement, two clicks in the
formula bar adds the formula to the selected cell.
The label Read sheet is used to show the contents of a cell in the formula bar, which is a useful feature to
make small changes to the model without needing to close the Risk Analyst tool. In the field Output cell
select a cell on the sheet using the mouse and click once on Read sheet to show the formula in the
selected cell. Click twice on Read sheet to read the result shown in the cell. For instance, in cell A1 type 2,
in cell A2 type +A1, in the field Output cell select A2, click once on Read sheet and the formula bar shows
the cell address, +A1, click twice on it and the bar shows 2, the value in the cell.
Defining distributions
In order to simulate a model there must be one or more formulae in it that change every time the model is
recalculated. This can also be accomplished using one single output formula, for instance like the one below,
where the mmRANDBETWEEN function makes the NPV function, an Excel own function, returning every time a
new value based on a different interest rate taken randomly from the range 3%-5%.
=NPV(mmRANDBETWEEN(3%, 5%), B12:E12)+mmOUTPUT()
Models built with one single variable cell, however, may satisfy very basic needs only. More complex issues
may well require larger models.
The 25 Probability Distribution Functions (Pdf’s) that Risk Analyst provides can model the vast majority of
common instances that can be handled by means of simulation. The formula below provides an example of a
variable that Risk Analyst treats as an input one:
=mmBINOMIAL(5, 0.5)
Defining a distribution function with Risk Analyst is this simple!
We do want to remind you to be very careful to write the functions correctly. From our experience working
with managers, we have found that many modeling problems arise from badly written or from poorly
understood formulae. The following pages of this chapter provide a detailed profile for each function
available in Risk Analyst. These pages are an important reference for newcomers to the art of decision
analysis, as well as for more expert modelers. We strongly recommend that you print them out and read
them carefully.
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Data fitting
There are many distribution functions in Risk Analyst. How do we know which is the best function to use in
each situation? If we do not have any previous knowledge of the process we are modeling, we can use the
fitting tool that opens by pressing the button Fit data in the main window of Risk Analyst.
For example, say we have a series of 100 monthly sales data and we want to find a function that fits them.
The function is to be used in a model that simulates cash flows. For explanatory purposes we have first
generated in A1:A1000 a series of 100 observations using the formula =mmNORMAL(2500, 50), to produce
normally distributed sales values with mean value of $2500 and standard deviation of $50 (that is, in the
range $2300-2700). We did so directly from the main window. We selected in the Output cell field the range
A1:A100, selected the Normal distribution and defined the parameters (2500, 50), the Formula bar
automatically updated to =mmNORMAL(2500, 50), and finally we pressed the button Paste to sheet.
With the data on the sheet, click the button Fit data in the window above and the form will show the fitting
options as in the form below. On the left side of the lower shaded region of the form, select in the first field
the range with the data to be fitted (A1:A100), by clicking in the field with the mouse and selecting the whole
range.
When fitting a series that you don’t know well, the option of the list box Fit all Pdf’s can be left as it is, and all
probability distribution functions will be fitted. Otherwise, one single distribution can be fitted. We have
unchecked the option Discrete while Continuous was left checked because the data we are working with
are of a continuous nature (see also the section Distribution types for more information concerning discrete
and continuous distributions). Finally, clicking on the button Fit data in the lower left corner of the window
performs the fit.
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The results of the fit are shown in the Fitted Distributions list in a sorted order from the best to worst, as in
the picture below.
In this example the tool suggests that the distribution closest to the fitted data is a Normal distribution with
Coefficient 1, the mean, equal to 2501.9 and Coefficient 2, the standard deviation, equal to 51.9. The
comparison of the Fit Index allows you to select the curve with the lowest index, which is the best fitted
curve. The fitting tool did a good job: for our original data with mean 2500 and standard deviation 50 it found
a curve that fits them quite well, and this Normal curve shows the best fit among all 19 fitted distributions.
Goodness of fit
The column Fit Index in the picture above shows a value that is used to rank the so-called goodness of fit.
This important index tells us how well a fitted curve adapts to the original data. Risk Analyst uses the
Kolmogorov-Smirnov (K-S) statistic to prove the goodness of fit, which can score from zero to one. The
picture below shows an example of comparison between original and fitted data.
100%
Distribution Fit
Original
Triangular
0.15
75%
Rayleigh0.43
50%
Poisson 0.41
25%
Uniform 0.39
0%
1
3
5
7
9
11
13
15
17
19
21
23
In the chart above, the Triangular distribution (0.15) fits the Original data better than the other three
distributions, and its K-S index is indeed the lowest.
To print all results of a fit analysis, in the Output cell field select the cell to start printing from and click the
Print fit button. You are warned if the output will overwrite existing data. The picture below shows the
printout of a fit analysis.
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Pdf’s are ranked from the best fitted down to worst fit. The Fit Index refers to the K-S index mentioned
above: the lower the index the better the fit. When N/A appears it means the tool could not fit the distribution.
The four Coef columns show the parameters of the fitted function. If we want, for instance, to use the Normal
function from the picture above, we would write in an Excel cell mmNORMAL(2500.232, 50.086) and the
function would return values that fit the original data rather well (0.0551).
Should we always use the best fitted curve? Well, common sense plays an important role in the selection of
the function to use in a model. The first thing to consider is the kind of process we are modeling: is it
continuous or discrete? Can the minimum value be less than 0? Is it a symmetrical or skewed process that
we are modeling? Answering common sense questions can help you select an appropriate distribution
function. To learn more, read the entire section What are probability distribution functions in this chapter.
Elapsed time
In the lower left area of the Wizard window there is a checkbox called Show elapsed time that, when
checked, shows the time taken to fit each of the distribution functions. When dealing with projects rich in
formulas it may prove useful to review the time elapsed to fit distributions, because it may prompt the analyst
to replace a slow function with a faster one.
The following picture shows the time elapsed to fit 100 values to the 25 distributions available in Risk
Analyst: 8.7 seconds in total (11.7 milliseconds to fit 100 values to the Normal distribution. It is fast!). Use the
Print button to print the results beginning from the sheet address selected in the field Output cell in the main
form of Risk Analyst. Continuous distributions are shown first followed by the discrete ones.
Show model
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Just above the Paste to sheet button beside the formula bar there is a label called Show model that, when
clicked, opens a useful form showing information concerning all Risk Analyst functions present in the model.
Here is an example.
Fit statistics
Summary statistics can be printed for the data to fit. To do so, click on the Fit Data button, select a data
range in the input field of the fit analysis, click the Show statistics button to unhide this portion of the
window, and finally select the Statistics fit data page, as shown in the picture below.
In the Output cell field select a cell on the sheet and click the Print statistics button on the left side of the
form above, and the statistic data shown below will be printed. The software warns the user when trying to
overwrite existing data.
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In general, the figures above give a description of the data to fit in terms of central tendency (Mean and
Median), spread (Standard Deviation, Range, Quartiles and Percentiles) and shape (Skewness and
Kurtosis), which are basic values to understand a distribution of values. A detailed explanation of the
meaning of the descriptive statistics in the table above can be found in Forecast Manager and in Descriptive
Analyst, both tools of MM4XL software. You can also read more in the section concerning the Report in this
chapter.
When clicked, the Print Chart button exports to sheet, in the form of a picture object, the image of the chart
shown in the window. Here is an example of a chart image.
Model simulation
When the model is ready, with all input and output functions in place, it is time to let it roll!
In the main window of Scenario Manager click the Simulation… button and the form below appears. There
are three pages in this form: Iterations, Report and Sampling.
Iterations Page
In this page we define how many simulations to collect in a trial. The Number of simulations option is set by
default to 100 and the maximum number is 60000, which is well beyond the needs of most business models.
1000 simulations means that the model is updated 1000 times, each with a different set of input values. To
change the number of simulations, simply type a number in the field or click on the small arrow on the right
and select a different value from the list. Click the Run simulation button to start collecting data for the 1000
trials.
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What is the right number of trials? This is an interesting question, especially when dealing with large models.
In general, the answer is “many”. However, models with many variables may require considerable time to
iterate very many times. In such cases, it helps to know how many trials are needed to collect enough data to
obtain a solid report. An answer to this question can be found with the help of the function mmOPTNUM, which
is explained in the Property Functions section of this chapter.
When the checkbox Show preview is selected, after the recording of data for the last simulation trial a
window appears where you can preview (before printing to sheet) the results of the simulation. Refer to the
Report preview section for more details concerning the preview option.
Sheet mode
The frame Sheet mode contains two important check buttons: Modal value and Random number.
Random numbers are the building blocks of simulation models. Nevertheless, they can be confusing when
working with a sheet that keeps changing every time a little change is made. In order to not keep numbers
rolling, the Show modal value option in the window above is set to active by default. This means that the
functions show on sheet a value corresponding to the modal value of the distribution they refer to, and this
value does not change when the sheet is recalculated. The mode of a Pdf changes only when the
parameters of the distribution change.
When the Sheet mode option is set to Show random numbers and the sheet is recalculated (with F9 for
instance), the Pdf’s change their value because random numbers take a different value every time that F9
rules.
When running a simulation, the option selected in the Sheet mode frame does not affect the functioning of
the simulation routine. Risk Analyst is able to work in both cases without requiring the intervention of the
simulationist. Although rare, it can happen that after a simulation session with Risk Analyst, Excel ends in a
different status than the original recalculation mode set by the user. Changing calculation mode manually
can be done in Excel by selecting the menu item Extra>Option…>Recalculation and ticking selecting either
the Manual or Automatic checkbox.
There are distribution functions that can return an undefined mode. For instance, the Beta distribution can be
bi-modal, the Integer Uniform can result in undefined, etc. In such cases Risk Analyst uses an approximation
for the mode in order to show a number in the cell rather than text, which would compromise the result of all
formulae in the model. For more information concerning undefined modes refer to the material on single
Pdf’s in this chapter.
Sampling Page
Use this page when you want to print a defined quantity of random numbers according to a given distribution
function. For instance, in the main tool window, in the Output cell field select an address on the sheet to
start printing from. From the Distribution list box select the option you want and set the distribution
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parameters. Then click on the Simulation… button and go to the Sampling page, shown in the picture
below. Type the quantity of random numbers you wish to print, or accept the default quantity, and click on the
Run simulation button to finish the operation.
During the simulation runs look in the lower left corner of the screen. Short messages are displayed that
indicate the operation being executed by Risk Analyst. There are cases when Risk Analyst becomes very
busy, and these messages may help you understand what is happening.
Random numbers can also be printed to sheet from the main window, with the difference that from the main
window you cannot select in advance how many numbers to print but you can select a range of cells that will
all be filled with random numbers. Moreover, random numbers printed from the main window are written in
the form of mmFUNCTION while random numbers from the Sampling page are in the form of values.
Note that if you select more columns in an output range, the second and following columns will be filled with
the same numbers printed in the first column.
Report Page
The default option for a Risk Analyst Report is set to Compact, as shown in the following form.
When selected, the Custom report option opens the window below (the selections refer to a Compact
report). Simply check or uncheck the desired options. Click on the label Back.. to return to the previous
page.
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You may wish to have the report printed to a new file (workbook). In this case you only need to check the
option New workbook in the Report location frame. The default selection is in the active file. In both cases,
each report is printed to a separate sheet, so the simulationist is not even required to select an output cell.
When the selection is made, click on the Report… button to start printing the simulation results to sheet.
The details concerning the single report options can be found in the section Interpreting results of this
chapter.
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Model report
The Complete report of a simulation model analyzed with the Risk Analyst tool is made up of six sheets:
•
•
•
•
•
•
Simulation page
Statistics page
Sensitivity page
Input charts
Output charts
Time series charts
Two different activities are required when modeling scenarios: calibration and simulation. During the
calibration phase you should usually limit the number of trials, while trying to refine the variables in order to
produce believable scenarios. During this phase take advantage of the Preview utility available in Risk
Analyst. In Preview the results of a simulation can be seen for evaluation before printing them on sheet.
All report pages begin with a heading and general information, such as the date, file name, number of
simulations, print time, etc.
A print report does not allow you to print more than 256 columns of data. Therefore, models using more than
256 variables will automatically be cut when the results are printed to sheet. This limitation does not apply to
the Tables page of the Preview form.
Simulation report
When the checkboxes Simulations of outputs and Simulations of inputs are active in the Report page of
the Simulation Settings window, Risk Analyst prints all simulated values for all reported variables.
Rows 13 to 16 of the simulation report show identifiers for the variables included in the model (more
precisely, for all variables not locked with the mmLOCK function). Row 13 contains the Variable type. Models
in Risk Analyst use two kinds of variables: Output and Input. Formula and Cell address are displayed as
indicated, and the Name row shows the name, if any, that the modeler entered in the function mmNAME for
the variable.
Examples of simulation reports can be found in the example files accompanying the Risk Analyst tool of
MM4XL software.
From row 18 on the individual simulated values for all unlocked variables are shown. Column A contains
progressive numbers, and from column B on the simulated values are contained. These values may be
useful to inspect the shape of the distribution modeled by any one function. You won’t often need to go into
such analytical detail when inspecting a model, unless you have a good reason to do it. Other reports may
help you get a better understanding of the simulated values. If you really need to, consider using the function
mmHISTO to group simulated variables in intervals as shown in histogram charts.
Statistics
When the Detailed statistics checkbox is active in the Report page of the Simulation Settings window,
Risk Analyst prints, for all reported variables, a number of descriptive statistics and percentile values.
In rows 9-16 there are eight descriptive statistics for each variable. The same values can be produced with
Descriptive Analyst, one of the MM4XL software tools, which can also print a box plot that shows in a very
intuitive manner the characteristics of the shape of a variable.
In rows 18-36 there are percentile values that show limits at fixed intervals of 5%. For instance, a percentile
value equal to 0.125 for 10% means that all random values for the variable with a value of 0.125 or less are
10% of all sampled values. If there are 1000 trials, about 100 would be equal to or smaller than 0.125.
Percentiles are also used to draw the Time Series report. They can be computed with the Excel formula:
=PERCENTILE(InputRange, %-Level)
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Sensitivity
When the Sensitivities and Tornado charts checkboxes are active in the Report page of the Simulation
Settings window, Risk Analyst prints a table of values and a bar chart for each output variable. The analysis
shows the correlation values (range from -1 to 1) of one output variable with each input variable in the model.
The same result can be obtained with the CORREL function available in MS Excel.
Correlation values help to identify the impact of each input variable on the output variable(s). The following
chart shows the correlation values of four input variables (bars) and an output variable called Gross Profit. It
is clear that the variable in cell C19 is exerting a strong, positive influence in orientating the results of the
output variable, while all other inputs have only a marginal impact. If we need to change the model in order to
produce a different outcome, variable C19 is the best candidate to start with.
Sensitivity Diagram
Output variable: $C$21 - Nam e: Gross profit
$C$19; .78
$C$10; -0.005
$C$5; -0.013
$C$6; -0.068
-150%
-100%
-50%
0%
50%
100%
150%
Input charts
When the Input charts checkbox is active in the Report page of the Simulation Settings window, Risk
Analyst prints, for each input variable in the model, a table of values and a histogram chart. The chart below
is from an input variable that refers to 1000 runs drawn with mmBINOMIAL(100,0.25). The chart shows the
shape of the distribution, which should be coherent with the simulationist’s assumption, the frequency and
relative frequency for each class. The smallest bar on the left, for instance, refers to 8 simulated values with
the value 14.727 and lower; in class 2, 39 values reported a value above 14.727 but equal to (although
impossible with a discrete pdf, which can return only integer values) or smaller than 17.455, and so on.
Input Chart: $C$10
300
271
250
221
96%
99% 100% 100%
77%
200
55%
134
150
136
100
100
28%
39
50
8
0
91%
1%
46
15%
34
9
5%
2
Class Class Class Class Class Class Class Class Class Class Class
1;
2;
3;
4;
5;
6;
7;
8;
9;
10;
11;
14.727 17.455 20.182 22.909 25.636 28.364 31.091 33.818 36.545 39.273 42.000
The same chart can be produced using the simulated values of any variable either with the function
mmHISTO or using the MM4XL tool called Descriptive Analyst. The latter tool can also draw box plots, which
are very useful charts to describe the shape of a distribution.
Output charts
When the Output charts checkbox is active in the Report page of the Simulation Settings window, Risk
Analyst prints, for each output variable in the model, a table of values and a histogram chart, exactly as
described in the Input charts section of this chapter.
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Time Series charts
Time series are arrays of values that follow a same time pattern and refer to the same process, such as
monthly sales, yearly net profit, etc.
In Risk Analyst time series are modeled using the mmNAME function. If there is at least one time series in a
model, in the Report page of the Simulation Settings window the checkbox Time series charts and the
listbox on its right are both active. Select an option from the listbox and Risk Analyst prints a table of values
and a line chart, for all or only one time series in the model.
When modeling scenarios aimed at simulating economic processes, Time series analysis helps you see the
curve shape over time of the observed variable. In the following example the series named Loan was
modeled using 6 variables as in the following picture. In the picture below, the formula used to model cell
C48 is:
=mmOUTPUT()+mmNAME("Loan", 0)+MAX(C4-C21, 0).
The time series chart produced with Risk Analyst follows. The upper green line shows percentile values at
the 95% level for each variable in the time series, and the lower green line does the same for percentile
values at the 5% level. The upper purple line (middle) refers to values at the 1 standard deviation level
above the mean value of the variable. Intuitively, the lower purple line (middle) shows values 1 standard
deviation below the mean, which is the bold red line in the middle.
Series: Loan
1380
1180
980
780
580
380
180
-20
$E$48
$F$48
-5% P erc
$G$48
-1SD
$H$48
M ean
$I$48
+1SD
$J$48
+95% P erc
The chart shows the entire range of values within which the model took form. If we were modeling market
share, for instance, we would have seen the boundaries within which the various share levels had been
generated across time.
The table of the Time Series report shows duplicated values from the Statistics report page.
Short report
From the Report page there is an option called Short that prints a compact summary report like the one in
the following picture.
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A compact summary like this is useful in cases where the analyst is only interested in one or a few output
variables, such as a sales forecast, the value of a market share, the size of a market, etc.
In the Examples section of this chapter you will find more information about the Short report.
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Report Preview
After every simulation run, the Preview form can be accessed either by clicking the Preview button in the
Wizard form, or Risk Analyst can open it automatically if the checkbox Do not show preview after
simulation in page Iterations of the form Simulation Setting is not checked.
The Preview window is not shown when Risk Analyst detects more than 100 Risk Analyst variables in a
model, or when the user asks to run more than 20000 simulations at once, or when the checkbox Show
Preview in form Simulation Setting is set to unchecked. In the first two cases the reason to not show the
window automatically is the remarkable amount of time such models may require. The user can still access
the window by clicking on the Preview… button in the main form.
There are four pages in the Preview window that show most of the information available in a print report:
•
•
•
•
Charts
Sensitivity
Time Series
Tables
The Show model button opens the form explained in the corresponding section of this chapter. The Print
button accesses the form with print options. The Export button prints to sheet a picture of the chart as seen
in the form. The Cancel button closes the form. After closing, the form can be reopened, and the same data
will be available as long as the main window of Risk Analyst has not been closed.
The Learning Center listbox in the lower left corner of the form is where you open the MM4XL online
Reference Manual, the Example sheet with test data, and other helpful utilities you can use for learning the
Risk Analyst tool as well as the whole MM4XL software.
Charts Page
The following picture shows the Charts page after 1000 simulations of a model built to measure the output
variable NPV. The large listbox on top of this page shows a list of all Output variables in the model. On the
lower left side of the form we see that the scale of measurement for the bars of the chart is in thousands.
The simulation returned values for the variable NPV ranging from a Min of 4.44 thousand, say dollars, to a
Max of $38.78k and Mean value equal to $17.2k. Originally, the chart was produced with 11 bars only. We
changed it to 19 with the listbox Number of classes.
The chart shows two series: frequency distribution (bars) and cumulative distribution (line) relating to the
variable shown in the listbox in the upper left area of the page, NPV in this example.
An explanation of how to interpret the chart can be found in the Examples section of this chapter.
The vertical separator with a small blue triangle at the top can be dragged in order to split the chart into two
halves. The box below the horizontal axis labels shows the corresponding cumulative percentages in both
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halves. In this example 52% of the simulation runs are in the range interval 9.95k-18.93k. The value below
the two percentages shows the unformatted value of the bar crossed by the vertical line. To move the
separator to a different position either left-click with the mouse on the small triangle, drag it to a different
position and release the mouse button, or click the spin buttons on either side of the rectangle to move the
vertical separator back and forth. If you click once on the chart surface to engage one of the spin buttons,
you can then use the direction arrow keys from your keyboard to move the separator.
Sensitivity Page
The listbox in the upper left side of this page shows a list with all Output variables in the model. The textbox
below the listbox shows two columns of data: correlations on the left and variable descriptions on the right.
For each Output variable in the model, Risk Analyst computes the correlation coefficient (ranges from -1 to 1)
against each Input variable in the model.
An explanation of how to interpret the chart can be found in the Examples section of this chapter.
The bar chart shows graphically the same data shown in the textbox. When an Input variable is identified
with the mmNAME function the variable is named accordingly, otherwise a more generic item name is
assigned automatically.
Times Series Page
The mmNAME function available in Risk Analyst takes two arguments: Cell Name and ItemNum. The second
argument is optional and must be an integer number that identifies the position of the item in the time series.
In the following form, for instance, the time series called Market is made of four items, as listed in the textbox
on the left side, with the first item in cell D23 of the model, the second in cell E23, and so on.
Scrolling the textbox on the right shows the data used to draw the chart. Each item is on a row, and there
are five columns of data: the column ADDRESS shows the cell address where the item is located, the
second column shows the 5% percentile point, then comes the -1 Standard Deviation, the Mean, the +1
Standard Deviation, and finally the 95% percentile point. All measures refer, in this case, to the 1000
simulation trials collected for the variable Market.
The chart on the right shows graphically the information from the textbox. The red line in the middle is the
mean, and the two shaded regions refer to plus or minus 1 standard deviation and to the 5% and 95%
percentiles respectively. The label at the top of the chart refers to the scale of the vertical axis.
A detailed explanation of how to interpret the time series chart can be found in the Examples section of this
chapter.
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Tables Page
The last page of the Preview window contains two tables of data: Show simulated data and Statistics and
percentiles. An explanation of the content of each table can be found on the corresponding page relating to
the print report.
A detailed explanation of how to interpret the data in this page can be found in the Examples section of this
chapter.
A comment must be made on the time required to reload the data of models made of many variables. In such
cases the computation can slow down the process. The solution is to use the function mmLOCK to avoid
loading unnecessary information.
The print report does not allow printing more than 256 columns of data. The limitation is not present in this
Tables page, although, as mentioned above, loading so many variables may result in a lengthy wait.
Generally, you should consider whether you need such a long array of single variables.
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Getting help
Before diving into the details of Risk Analyst, let’s see where the user can get help while working with it.
There are three major repositories of reference material concerning the use of Risk Analyst:
•
•
•
The Learning Center
Online help window
The Function Wizard
Learning center
The Learning Center listbox in the lower left corner of the form is where you open the MM4XL online
Reference Manual, the Example sheet with test data, and other material useful for learning the Risk Analyst
tool.
Online help
Click on the button Options in the main form, and in the form that appears click on the button Help with
distributions and the following window appears. This is a Quick Help that you can call to access short
descriptions of probability distribution functions. Simply click on the image of the distribution function you are
interested in and the region on the right of the form will display brief information concerning how to use that
function.
In addition, the How to model… listbox provides help with a number of other functions available in Risk
Analyst. Select the option you are interested in and an explanation appears in the What field.
Click on the label Launch help topic… to start the main MM4XL help reference at the relevant page.
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The Function Wizard
This is an Excel tool that lists all functions available to the user, as well as MM4XL software functions, and it
helps you to enter them correctly as well as to access reference material for the single function.
To access the Function Wizard click with the mouse on a cell and then click the small Fx symbol placed on
the left of the formula bar, as shown in the picture below.
Clicking on the Fx symbol opens the Function Wizard form shown below. In the example we see a German
version; the English one does not differ much from the one below. Select a function category from the list
and click on the function you want in order to show a short description for the selected function. Click on the
blue label in the lower left area of the form Help for this function (Hilfe für diese Funktion, in the picture
below) and the MM4XL Help file will be opened to the page covering the selected function.
Select a function from the list and click on the OK button, and the following form appears. This is the Wizard
that helps users enter a function when they cannot recall the parameters of the function, for example.
Selecting a cell with an mmFORMULA inside and clicking the OK button opens the form below showing the
function parameters in the appropriate fields of the form.
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When you cannot remember what attributes characterize an mmFUNTION, type in a cell the function name
followed by brackets and click on the Fx symbol to open the above form.
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Simulation? Never heard of it.
Simulation is the process of creating a model that imitates some type of real-life, uncertain behavior.
Repeating the model a number of times, each time using different input parameters, and synthesizing
appropriately the results of the repetitions, produces useful information that enables you to answer important
questions that in turn will reduce the uncertainty or risk associated with the model.
Basically, in a simulation model we define the objective of the analysis, such as what our sales would be with
and without advertising investment, and then we create the model in MS Excel. Some variables in the model
are defined in a way that makes them vary randomly within some user-defined range of values every time
the model is refreshed. In our example we could have two output variables, the sales level with and without
advertising, which may be the result of the interaction of several input variables, such as investment by
media channel, shelf saturation level, competitor’s sales, and so on. The model is then repeated hundreds or
thousands of times, each time saving the results.
This simulation technique is known as the Monte Carlo technique, for it works like spinning roulette wheels at
a casino. It was used for the first time in the 1930s when the US government was developing the earliest
atomic bomb. In the field of social science it has long been employed to study behavioral processes. And in
the 80s it was discovered by business, first to study issues in operations management, such as plant
efficiency, production quality and physical distribution issues, and more recently also in strategic and
operational management. For years, companies like Procter & Gamble, Merck, Kodak, United Airlines,
Burger King, and AT&T have used simulation models when dealing with complex and risky projects.
A lot of mind-numbing statistics lie behind simulation, and a rigorous approach to the subject can turn it into a
dry, tiring, and frightening topic. From working with managers on simulation, however, we know that building
models, refining them and interpreting the results is a very dynamic and involving process that managers can
do well. This modeling activity often helps to reinforce team cohesion and team members’ awareness of risk
faced in today’s competitive environment. If a little study can help a company move forward, every manager
should consider the investment worth making.
Risk Analyst solves the computational problem. This chapter provides you with the information you need to
get up to speed with the tool quickly. Read this material and work with the example sheets. At the end of the
first reading of this chapter you will have already learned a lot. By the time you have read it a second time,
you might well have become your company’s ‘risk analysis guru’! It’s up to you.
It must be said, however, that a simulation is only an approximation of the reality. An analytic model is
always preferable, whenever possible. Unfortunately, it is often impossible to create an analytic model, or
even if it is possible, it may prove difficult to build it in mathematical notation. On the other hand, risk analysis
through simulation is a rather intuitive subject that managers can grasp very well. The hurdle may be
understanding the concept of probability distribution functions. Read through this chapter and you will have
gained that understanding as well.
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Contributing Factor Diagram
All variables that contribute to the solution of a model can be arranged in a so-called Contributing Factor
Diagram (CFD), with the aim of making clear the relevant elements of the model: idea, variables, and goal.
CFD’s start from an idea and are constructed backwards. In the example below, for instance, while planning
the launch of a new product (idea on the left) the management of a hypothetical company built a simulation
model, and to evaluate the success of the project, chose a variable called Net Profit (the variable on the
right, which Risk Analyst calls an Output variable).
M arket
gro wth
M ngt
thresho ld
User
acceptan
P kt entry
M arket
share
Revenue
Net
P ro fit
M ktg co sts
Test co sts
Co sts
Dev't co sts
The next step in the process is to move backwards, asking what is the measure of success? In this example,
Net Profit is found by subtracting Costs from Revenues, and we see two ovals labeled accordingly pointing
their arrows directly to the (output) variable NP. In turn, the variable Costs is the sum of three sources of
expense: Development, Testing, and Marketing costs. Four variables relate to Revenues, although one only
directly: Market share.
Graphical representations of simulation models in CFD form can be a powerful tool for introducing complex
and new models to an audience. CFD’s are a simplified version of the more rigorous influence diagrams, but
they are not flow diagrams. The latter follow a time pattern which is not shown in a CFD. Influence diagrams
use utility functions and conditional probability to return expected monetary values. The same results can be
obtained with Decision Tree, one of the tools of MM4XL software.
It is easy to detect poorly designed CFD’s, as they look like indecipherable subway maps with lines crossing
each other all over the plan. These are models built using many variables. Not all models, however, must be
overcrowded. Building models made only of pertinent variables is becoming an art.
Contributing Factor Diagrams can be easily built in MS Excel using the drawing tools, which can then be
grouped to a single picture that is easily transportable. When a project requires greater detail, we suggest
using the MM4XL software tool Project (Mind) Map to draw more effective CFD’s. The mind map tool
enables you to draw CFD’s with links to documents, voice messages, Internet addresses and much more.
This can turn a flat CFD into a real repository of information for the whole model.
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What are probability distribution functions?
Probability distribution functions (Pdf’s) are statistical devices that marketers can use to model business
assumptions. For instance, a common business assumption concerns market share; the statement “next
year our market share will be in the range 3.5%-4.5%, most likely 3.9%” is equal to saying “next year our
market share will be distributed triangularly within Min = 3.5%, Max = 4.5%, and ML = 3.9%”. Also, “next year
market size will be between 85 and 115 Mio.” is equivalent to saying “next year market size will be normally
shaped with mean 100 Mio. and standard deviation 5 Mio.”.
Scenario modelers have found that old-style models built using single-bullet variables too often do not
represent an acceptable model of real events. For this reason, the old static modeling fashion has lost
ground in favor of dynamic modeling. With dynamic modeling, instead of inputting a fixed value for an
uncertain variable, say 5% for our future market share, more sophisticated models are built using variables
defined within a range of values. When the dynamic model is repeated many times (for example, 1000
times), and each time a new value within the boundaries of the distribution is used for the uncertain variable,
we can collect 1000 different simulated observations of our market share. When modeled well, a distribution
has a higher probability of including the real value of the uncertain variable than a single-bullet figure has.
There can be as many different kinds of assumptions as there are Pdf’s, and this may cause some trouble
for new users. However, there are many advantages to building models on assumptions defined with Pdf’s,
and they may justify the moderate learning effort required for applying such devices. It must also be said you
do not always need to use spectacularly complex Pdf’s to model assumptions. Many useful models are
based on fairly simple assumptions.
When working with Risk Analyst, values within boundaries can be produced for many different distributions.
We will begin by using perhaps the simplest of these functions:
=mmRANDBETWEEN(4%, 6%)
Copying the formula above in 1000 cells and summarizing the results in, say, 15 classes, yields a chart like
the one below (we used the function mmHISTO to summarize the 1000 trials). In Class 1, 69 simulated values
between 4% and 4.14% have been aggregated; Class 2 contains 55 values going from above 4.14% to
4.27%, and so on.
80
69
65
70
55
60
75
68
75
74
67
68
59
76
65
72
58
54
50
40
30
20
10
5.99%
5.86%
5.73%
5.60%
5.46%
5.33%
5.20%
5.06%
4.93%
4.80%
4.67%
4.53%
4.40%
4.27%
4.14%
0
This chart tells us that the 1000 runs were distributed in more or less equal shares across the 15 classes
(more simulation trials would smooth out the differences). That is, each number in the range 4%-6% had
equal likelihood of being chosen. This assumption of equal probability, however, is not always a reasonable
one because it does not permit spreading the risk across the possible outcomes of a distribution.
An analyst knowledgeable of their market could assume that the most extreme values close to the tails of the
distribution above may have a lower likelihood of occurring. In this case, the 4%-6% range could still be used
but it should also be specified that a most likely value may occur, for instance, in the 5% range. Repeating
the 1000 runs with the formula below produces a new distribution of triangular values:
=mmTRI(4%, 5%, 6%)
The chart below summarizes the 1000 triangular trials in 10 classes, and was made with the mmHISTO
function.
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184
200
180
160
145
140
120
158
90
85
100
80
60
40
162
58
57
40
21
20
0
0.04 0.042 0.044 0.046 0.048 0.05 0.052 0.054 0.056 0.058
There is a difference between the two pictures above. In managerial issues this difference is relevant
because it allows you to model the amount of risk linked to an event, and there is a lot of risk in
management. For this reason too, there are many distributions available, each used for modeling one or
more instances.
Random numbers
Random numbers are the building blocks of scenario modeling. They are numbers extracted randomly from
a given range of values in order to generate custom variables used in scenario models.
Excel generates random numbers between 0 and 1 with the function =Rand(). Readers interested in the
subject of random number generation with Excel may refer to the MS Excel User Manual. Also, the paper
from Keeling and Pavur Numerical accuracy issues in using Excel for simulation studies is an interesting one
that compares the accuracy of random numbers generated with different software packages, including
various versions of MS Excel.
Really random numbers satisfy two important properties: they are independent from each other and they are
uniformly distributed.
Independent random numbers means that if a random number is generated in one Excel cell and then a
second random number is generated in a second cell, there is no relationship between the two. That is, the
second number tells us nothing about the first number.
How frequently a random number is extracted depends on the kind of distribution and on its parameters. For
instance, the function =RAND assigns the same probability of occurrence to all values in the range, as the
previously mentioned function mmRANDBETWEEN does. This is called a Uniform distribution and it is often
shown as U(0,1). Then, there are functions that return values with a certain shape. The mmTRI(0%, 5%,
10%) in the picture below returns values in the range 0%-10%, and 5% is the modal value. Running this
function many times would return some 50% of the random numbers in the range 0%-5% and 50% of the
values would lie between >5% and 10%.
Testing the property of independence of random numbers can be done using the MM4XL function mmHISTO
as shown with the first chart in the section What are Probability Distribution Functions. The second property
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of random numbers, uniformity, can be tested by checking that 50% of random numbers are equal or smaller
than 0.5 and the remaining 50% of the numbers are larger that 0.5. However, this is less simple to test
because there may be (or may not be) combinations of large and small numbers that violate the assumption
of independence.
The Risk Analyst tool provides many different sheet functions that can be used to simulate random numbers
from as many different probability distributions. With such equipment available, managers can model virtually
any process in order to support critical business decisions.
Monte Carlo method
The Monte Carlo technique is used to create artificial representations of real-life issues, such as a new
product launch, the time to failure of a machine, or the probability of drilling an oil deposit. Monte Carlo uses
samples of random numbers from known populations. The concept behind the technique is that by drawing
many samples we can assess the behavior of the variable we are interested in.
Monte Carlo analysis done with the Risk Analyst tool follows a 4-step procedure:
1.
2.
3.
4.
Modeling: Specification of the distribution to draw samples from.
Sampling: Definition of how many trials to sample.
Storing: Storage of samples of random numbers.
Summarizing: Construction of relative frequency histogram of the sample data.
The process is relatively easy. The tough part of the job is selecting appropriate distributions, setting
accurate parameters, and interpreting the results. This chapter is intended to help you quickly get up to
speed with risk modeling.
Distribution types
Probability distribution functions (Pdf’s) can be discrete or continuous.
Pdf’s of the first class can take only integer values, and are sometimes also called integer distributions.
These Pdf’s are used to estimate numbers relating to people, errors, conformity, and other variables that can
only take an integer value such as 1, 2, 3, 1878, and so on. Continuous variables, as suggested by the
name, can take any value within their range, including non-integers. Continuous Pdf’s are used for modeling
variables such as time, speed, sales, costs, profit, and so on.
Pdf’s can be symmetrical or asymmetrical.
The left and right sides (tails) of the symmetrical distribution below have the same area under the curve
(blue region). This means that there is an equal probability of obtaining values either below the mean value
of the distribution or above it. This is the typical case of events such as the gender of a new born or the size
of a new market. The asymmetrical distribution below, on the other hand, is telling us that the distribution
produces a lower portion of values below the mean and more values above the mean. This could be the
case of a growing market.
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Pdf’s can be mono-modal, bi-modal, or have an undefined mode.
The picture below on the left shows a mono-modal distribution. If, for example, it refers to the number of
client calls by day of the week, the pdf is telling us that the peak (modal value) occurs in the fourth class, on
Thursday. Some processes, mainly operational, may peak at two points as shown in the picture on the right,
and are said bi-modal. Finally, there are cases, mainly with continuous variables, when the distribution does
not exhibit a mode (most frequent) value, and it is called a pdf with undefined mode.
Pdf’s can be infinite, or truncated at one or both ends.
The picture below on the left shows an infinite distribution, such as a Normal one, where there is an
infinitesimal probability of getting a very large value (infinite indeed) either above or below the mean. The
other two charts refer to a truncated distribution. The one in the middle, for instance an Exponential pdf, is
truncated at one side: it cannot take values below zero but it can expand to infinity on the positive side. The
Triangular pdf on the right is truncated at both ends and allows only values ranging within the minimum and
maximum value on the horizontal axis.
Interpreting distributions
There are two major elements playing a role in the shape of a distribution and, therefore, in its meaning: the
range (x- or horizontal axis) and the probability of occurrence (y- or vertical axis). Range and probability of
occurrence allow you to set some general rules for interpreting distributions that apply to both risk-adverse
and to risk-taker decision-makers.
Rule 1:
When dealing with distributions characterizing variables for which more is better, such as profit or sales, the
distribution with the higher values is the most appealing. The example below shows two equally shaped
distributions. The one on the right, however, is more appealing because it represents less risk having more
positive values. When modeling variables where less is better, such as costs, the distribution on the left
would become more appealing.
Rule 2:
Between two distributions with the same range, the distribution with a triangular shape is more appealing
than a uniform distribution. The picture below on the right shows a less risky distribution, whilst the uniform
likelihood of occurrence of the one on the left makes it less appealing.
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Rule 3:
Between two distributions, the one with the greatest range spread is less appealing. The picture below on
the right shows a less risky distribution, whilst the larger range of the distribution on the left makes it less
appealing.
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Chance of failure
The chance of failure (CoF) is the probabilty that the object of the risk assessment will fail, which is a similar
concept to that of Break Even Point (BEP). The BEP is that point where all costs of a venture are covered by
the revenues and no profit has yet been made. The CoF is that value in the distribution before which there
are unsustainable values for the venture and above it there are acceptable values. For example, a new
product launch is acceptable to top management only if it generates over 6 millions in sales. The chart below
shows a 9% CoF as the result of a simulation session for the variable Sales.
CoF refers only to the probability that the whole project (the object of the risk assessment) fails. If any
variable without the power of causing the whole system to fail shows values in the unfavourable region of
that distribution this is not CoF. A car provides a good example: virtually any part of a car can fail, however
only some parts have the power to stop the car from running. Opposed to the CoF there is the Total Cost of
Success (TCoS), calculated with ∏ (1 − CoFx ) .
i
A typical pitfall is that of replacing undesired simulation values with zeros, to avoid falling in the failure region
of the distribution. This is not a good idea for a number of reasons, one of which is that the system may
generate incomparable arrays of simulated values due to their varying length. Refer to Koller (1999) for more
detail.
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Why the mode?
Simulation deals with distributions, which are long arrays of values that may take various shapes. In the
Quick Help window you can see pictures of all distribution functions supported by Risk Analyst. To get the
most from this variety of distributions, it is important to have a good understanding of the common measures
that describe distributions: central tendency and dispersion, or, more simply, mean, mode and standard
deviation.
The following picture shows the result for several measures computed on the same variable. The user is
referred to any book of basic statistics for a technical explanation. Readers can also find information in the
chapters Quality Analyst and Descriptive Analyst in this manual.
Frequency
Count Exp.
16.0
14.0
12.0
10.0
8.0
6.0
4.0
2.0
0.0
Min 303
384 Max
18.6
1 Standard
deviation
Mode 366
Median 364
Average 360
Range 81
We would like to just briefly discuss the measure of central tendency known as mode. The modal value, or
mode, is the figure repeated most often during the simulation trials of one individual variable. In the picture
above we see that out of 100 trials, the figure 367 was returned 14 times, and has the highest frequency
among all bars. 367 is the modal value of the distribution shown in the picture. In other words, it is the value
with highest probability of being sampled.
The mode is an important measure in simulation because it is often used to replace random numbers on the
computer screen. Risk Analyst, as well as other popular software for risk analysis, can show the result of its
functions either as random number or as mode.
For instance, the function mmBINOMIAL(5, 0.5) returns a random value ranging from zero to 5 and its
modal value is 2. Every time the sheet is recalculated a new random value between 0 and 5 is shown in the
cell. When Risk Analyst is set to show modal values, however, the function returns always the modal value 2,
even when the sheet is recalculated, because the mode of the Binomial distribution identified with the
arguments Trials equal to 5 and Successes equal to 50% is always equal to 2. You can verify this
statement using the Risk Analyst Wizard.
On one hand, it can be an advantage to deal with a model that does not change its figures every time a
change is made in a cell. On the other hand, modellers are required to develop a certain level of sensitivity
on the subject of distribution functions and their shape in order to have tight control on their work.
Understanding how the mode works is a good first step.
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Why correlated variables?
In statistics, the correlation coefficient is a measure of the strength of the relationship between two variables,
and it varies between -1 and 1. In business, for instance, there is typically a negative correlation between
price and demand: when the price goes up the likelihood is high that the demand goes down. On the other
hand, there may be a positive correlation between the number of phone calls made by sales representatives
and the number of appointments set. No correlation is found in most events, such as between the
temperature of the cup of coffee on my desk and the colour of the next car driving past my office building.
In modelling scenarios, there are cases when it is important to take correlation into account, for instance,
when estimating market share as shown in example 3 of this chapter. Products where the purchase is driven
by strictly utilitarian principles, such as pharmaceuticals and industrial products, supply perhaps the best
examples of market share being influenced by technical attributes of the product. When one process has an
impact on another we can reasonably believe they are correlated. If the relationship is relevant it should be
measured and included in the simulation model.
Risk Analyst uses the function mmCORREL to generate correlated variables according to the Scheuer-Stoller
method (read also the material concerning the function mmCORREL in this chapter). The following tables have
been made from the file example mmCORREL.xls accompanying Risk Analyst. In the first table we have
target values. These are values entered by the user and they specify the desired level of correlation between
variables.
In the range C16:E16 of the following table we entered the array formula:
=mmCORREL(C10:E12)
While in row 17 we entered the formulae:
=mmNORMAL(10, 1, C16)
=mmNORMAL(10, 1, D16)
=mmNORMAL(10, 1, E16)
Finally, in row 18 of the table above we entered the formulae below and we ran 1000 simulations:
=+C17+mmOUTPUT()+mmNAME("Color")
=+D17+mmOUTPUT()+mmNAME("Appeal")
=+E17+mmOUTPUT()+mmNAME("Time")
From the Sensitivity page of the Preview window we exported the charts below, which show the level of
correlation between the three variables object of the simulation.
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The returned values are remarkably close to the target values. This means that the variables generated in
B23:D1022 follow a correlation pattern very close to the desired one. When modelling processes where
accuracy plays an important role, the mmCORREL function can be a great help.
The correlation coefficient is reliable only where there are linear relationships. If the relationship between two
variables follows a non-linear pattern, then the correlation coefficient becomes a weak estimator and may
lead to wrong conclusions.
MM4XL software offers two tools called Smart Mapping and Benchmark Map to draw bubble maps, which
are very effective charts for detecting correlation. Read more about these tools in the corresponding
chapters.
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Summary of functions available in Risk Analyst
Property functions
N.
1
Name
mmOUTPUT()
What it does
Used to identify output cells in a model. The results of the simulation of output
variables are reported in a separate sheet together with the respective
histogram charts showing the distribution of each variable. At least one output
variable is needed to run the Sensitivity Analysis in the final report. Models
without output cells do not tell the analyst very much.
The function does not take any arguments, its only job is to identify output
variables and make them available as such to the simulation engine.
2
mmNAME(“Cell Name”,
[Optional: ItemNum])
This function assigns a name to the cell where it is entered. The name is used
in the reports.
The function takes two arguments: cellName and ItemNum. The second
argument is necessary for the analysis of time series data.
This function prevents a formula from being sampled in a simulation model. It
does not take any argument.
3
mmLOCK()
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When this function is entered in a cell hosting a Risk Analyst function, the
results of the cell are not sampled in the simulation and, therefore, the report
will not account for the cell holding such function and the simulation will run
faster.
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Utility functions
N.
Name
What it does
1
mmHISTO(InputRng, [Optional:
Classes])
This is an array function that returns the number of elements by class of a
column of data. It can be used to produce the data needed to draw a histogram
chart like that drawn for output variables with Risk Analyst.
2
mmOPTNUM(InputRng, [Optional:
StablePeriods], [Optional:
SelectionLimit])
3
mmCORREL(CorrMtx)
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This function finds the number of simulations for an Output variable where the
standard deviation (sd) of the mean of the simulation trials tends to stabilize.
This is useful information to reduce the number of trials and save time during
the simulation or, alternately, to increase the number of trials if the analysis is
not stable enough.
This array function returns values useful to create correlated random variables,
and is mainly used jointly with distribution functions available in Risk Analyst.
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Distribution functions
N.
Name
Chart
What it does
1
mmBETA(Scale, Shape)
Probability of an event occurring. For instance, the probability that
the next client will buy.
2
mmBETAGEN (Scale, Shape, )Optional:
lower], [Optional: upper])
Like Beta with lower and upper bounds.
3
mmBINOMIAL(Trials, Successes)
The number of events that occur. For instance, the entrance of a
new competitor in the market.
4
mmCHI2(Degrees)
The amount of mutually exclusive events. For instance, years of
experience in using a PC.
5
mmDISCRETE(InputRange, Probabilities)
Occurrence of a given number of events only. For instance, the
lights of a semaphore.
6
mmERF(Mean)
Returns extreme values. For instance, forecast errors as computed
with Forecast Manager tool of MM4XL software.
7
mmERLANG(Mean, Phases)
Amount of time between events. For instance, the client flow in a
fast-food restaurant.
8
mmEXPON(Mean)
Amount of time between events. For instance, how long it takes
between client arrival and departure.
9
mmEXTVALUE(ModalValue, StDeviation)
Simulates extreme values. For instance, the maximum time taken
to serve a client.
10
mmGAMMA(Mean, StDeviation)
Amount of time between events. For instance, the time to issue an
order for sodas at a retail store.
11
mmGAUSSINV(Mean, Lambda)
Response time in sequential patterns. For instance, web surfing
behavior of car buyers searching for information.
12
mmGEO(Trials)
The number of trials before a positive event. For instance, number
of cold calls before we reach a potential buyer.
13
mmHYPERGEO(Sample, Defects, BatchSize)
The number of expected defects in a sample of a given size
according to the number of defects expected in the whole batch.
14
mmINTUNI(Min, Max)
Numbers with equal probability within a Lower and a Upper bound.
For instance, the preference of clients ordering one of three kinds
of pizza.
15
mmLOGISTIC(Mean, StDeviation)
Returns values more spread in the tails of the distribution. For
instance, the response of demand to advertising investments.
16
mmLOGNORMAL(Mean, StDeviation)
The product of several independent events. For instance, the
monthly value of a market.
17
mmNEGBIN(Failures, Successes)
Number of trials before reaching a certain number of successes.
For instance, the number of pedestrians exposed to a billboard to
obtain 10 visits.
18
mmNORMAL(Mean, StDeviation)
A normally distributed value around the mean. For instance, the
growth of a given market for successive years.
19
mmPARETO(Location, ModalValue)
Can return extreme values. For instance, the spread of income
among social classes.
20
mmPARETO2(Location, ModalValue)
Can return extreme values starting from zero. For instance, the
mean number of active sessions at a website.
21
mmPOISSON(Rate)
Number of events occurring given a mean occurrence value. For
instance, the population size at different points in time.
22
mmRANDBETWEEN(Min, Max)
Values in a given interval range. For instance, the pedestrian flow
on a sidewalk.
23
mmRAYLEIGH(ModalValue)
Simulates time to perform. For instance, wind speed over a year to
estimate the energy recovery from a wind turbine.
24
mmSTUDENT(Degrees)
Events for which we have a mean but not a standard deviation. For
instance, the weight of biscuit boxes.
25
mmTRI(Min, ModalValue, Max)
Events for which the distribution is unknown and thought to be
asymmetric. For instance, the long-term sales of a new product.
26
mmUNIFORM(Low, High)
Bounded by a min and max value, and all values in between have
equal likelihood. For instance, the price of a series of products.
mmWEIBULL(Shape, Spread)
Models failure time. For instance, the time when a machine enters
the critical time for maintenance.
27
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Examples
Example 1: Media Choice
A hypothetical product manager is planning next year’s budget for coupons to redeem product samples
placed in two magazines. The question is whether to purchase only medium A, only medium B, or both
media. If any medium is purchased, the next question is whether to purchase only for half a year or for the
whole year.
For this example see file Advertising.xls.
The model
The following Contributing Factor Diagram (CFD) shows the model in a pictorial manner. The Media plan of
choice will be the one with the lowest index, which measures the average cost per redeemed coupon and it
is found using the size of the Redemption and the Cost of the medium.
Index A
Redemption
Index B
Media Plan
Best
Plan
Cost
Index C
This table shows the fixed parameters of the model for each media.
A coupon is redeemed when a customer returns it through an authorized store. From past experience the
product manager could make estimates of the probability of redeeming given levels of redemption ranging
from 1% to 6% (column B of the following picture). Media A, for instance, was assigned a probability of 5% to
the possibility that only 1% of the Net Audience will redeem the coupon, 30% probability that 2% of the
audience will redeem, and so on.
The data in the table above was used to build the formula that returns the Index that measures the
‘goodness’ of each of the three plan options, as shown in the table that follows. The formula in cell C28, for
instance, is as follows and it is copied across the whole range C28:H81:
=$B28*C$12*(1-F28) / ($B28*mmDISCRETE($B$19:$B$24,C$19:C$24)*C$10) +mmLOCK()
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The first part of the formula finds the cost of placing the coupon in one issue of medium A and the second
part, after the sign divided, estimates the number of readers that will redeem their coupon. The formula uses
mmLOCK to make the simulation engine run fast.
The Discrete distribution is explained later in this chapter file. For now it is only necessary to know that it is
designed to extract each of the values in the range B19:B24 according to the probabilities of occurrence in
the range C19:C24, for instance, or in the range D19:D24, or in another range. Multiplying the returned value
times the value in C10, we obtain an estimate of people redeeming from each issue. The formula in column I
returns the column number of the best plan as from columns C:D. The best plan is the one with the lowest
cost by redeemed coupon.
Finally, the last three rows of the following table host the Output variables of this model. That is, those values
that we want to monitor in order to judge the outcome of the model. Row 13 says that 44% of the time Media
B was the best option of the three in terms of Cost/Redemption. If the product manager was to buy a space
in 54 issues, the media of choice should have been the media with the largest percentage in row 13.
Whether to buy for the whole year or for half the year can be determined from the data in row 14 and 15. In
order to answer, the model must be run to produce the simulated values.
Simulation
The model was run 1000 times, and then the Short Report was printed, as shown in the following picture.
Interpretation
From rows 10:12 of the table above we see that the best plan among the three is the one with Media B only,
called Best 2, where ‘best’ is the plan with the highest Mean value, that is the plan that during the 1000
simulations happened to return most often the lowest cost per redeemed contact. In 475, or 47.5%, of the
simulated trials Media B had the lowest cost. Although, it must be said, a certain level of uncertainty is
associated with the outcome, which can be seen in the broad range of values the variable can take, from
25.9% to 74.1%.
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Concerning whether to buy for one semester or two, rows 13:15 of the table above refer to the Mean cost of
each media over the first 27 weeks while rows 16:18 refer to the Mean of weeks 28 through 54. In this case
the lowest value is better because we are referring to cost by redeemed coupon. Cell E15 suggests that for
the short run, one semester only, the best option is to use both media A and B because together they return
the lowest cost per redeemed coupon. On the other hand, going for the whole year it would be best,
according to these results, to employ Media B only.
Although it is the preferable plan, Plan C shows a larger standard deviation than Plan B, which means that its
simulations were more spread in value than those for Plan B. Therefore, in order to validate the results of this
simulation, we computed confidence intervals as shown in range C21:F34 of sheet Short Report1 of the
Excel file relating to this example. The figures in D31:F31 do not overlap with values in D33:F33, so we can
conclude it could be really better to buy only Media B for the whole year.
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Example 2: Net Present Value
The Excel workbook with the model described in this example is called NPV.xls and can be found in the
directory Examples at the location where MM4XL software was installed.
This company is launching an innovative product. They know the competition will launch a competing
product 6-12 months later, and have modeled a simple scenario to get an idea of the profitability of the
product five years after launch. The measure of success is Net Present Value (NPV).
The model
The following Contributing Factor Diagram (CFD) shows a model concerning the 5-year Profitability of a new
product (rectangle on the left in the picture) measured through the Net Present Value (hexagon on the right).
M arket
size
M arket
share
Revenue
New
co mpetito r
P ro fitability
NP V
M ktg co st
Co sts
Lo gistic co st
Dev't co st
The Net Present Value is found with an Excel built-in function that uses a yearly discount factor of 6%
applied to the 5 years of a variable called Net Profit. In this example, the overall Cost is made up of the cost
of development, the cost of logistics activities, and the cost of marketing. On the other hand, the Revenue of
the venture is derived by multiplying the market share times the size of the market. From year 1 on, the
market share is impacted negatively by the entry in the marketplace of new competitors.
In the CFD we recognize two major sources of uncertainty, Market share and New competitor, and three
educated guesses, Marketing costs, Logistic costs, and Development costs. Each of the five assumptions
has been modeled with a Risk Analyst function.
Before modeling assumptions, we entered fixed values in the cells hosting uncertain items. The following
picture shows the Excel model used for this example. For the sake of explanation, in column B there is a
shortened version of the formula used to model the assumption in the corresponding row.
We arbitrarily split the model into three areas: Costs, Market, and Profit. In Costs, the upper area, three
variables are added into Total costs (D12). Development cost in D9, and Logistic costs in D10 are what we
call educated guesses, values for which there is no certainty but whose real value lies in a range we can
assume with a good level of confidence. In this case the cost of Development will be roughly $1 million in
Year Going (as shown with the model set to Show mode) down to $0.2 millions in year 4. A Uniform
distribution ranging at different values over the years was used to model it. The cost of Logistics was
modeled with a Uniform variate, but at a constant rate over time.
The third variable, Marketing costs, has been modeled with a Triangular distribution that takes a declining
shape over time. It starts at $6 millions in Year Going and lowers to $1.5 millions in the last year, due to the
entrance of new competitors in the market.
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In the Market area of the model both the number of potential buyers (row 15) and the Growth rate (row 16)
are fixed values entered by the analyst. In row 17, the number of new competitors is modeled with a Binomial
distribution (discrete), built on the assumption that there may be a maximum of 3 competitors in the market
with 40% as a constant probability for a new entry. The Binomial function 3, 40% returns values in the range
0-3 and has mode equal to 1 (you can find this information using the chart in the Wizard window).
In the Profit area there are three items. The marketing manager of this project assumes that, if launched, this
innovative product could immediately capture some 25% market share, which will start declining as soon as
the competition enters the arena. We used a Normal variate to model the assumption because the manager
assumes a lower chance of getting extreme values for the market share, so there is no need to spread risk
on the tails of the distribution and a Normal variate fits well. In D 21 the Profit per customer is a fixed financial
value. In row 22 Gross Profit is obtained with D15*D20*D21, and it has been modeled as an Output cell in
order to evaluate its result against the other variables of the model. In row 24 the output variable Net Profit is
obtained with D22 minus D12. In D26, Net Present Value is the decisional variable of this model and is found
using the Excel built-in formula NPV with 6% interest rate and the Net Profit values in row 24 as the input
range.
As may already be understood, time series play an important role in this model. Risk Analyst offers the
necessary tools to make an accurate and synthetic analysis of simulation data from distribution functions
used in the form of time series (for instance, like the values in the range D24:H24).
Simulation
The final report of this model was made by simulating 1000 runs, although during the fine-tuning phase it is
common practice to simulate only 100 runs in order to save time.
The mmOPTNUM function run with the 1000 values simulated for the output variable Gross Profit (D22)
returned 592 as the number of runs needed to stabilize the mean value of the series with an interval of 20
values. We kept using it with 1000 trials.
Interpretation
According to this model, this project could return an NPV at 5 years ranging from 7 to 38 million dollars, with
modal value at $15.3 millions. The following chart suggests that there is a probability of 33% that the most
likely range within which the real value of the project could fall is $13.6-$18.5 millions, although a remarkable
27% probability extends the most-likely upper boundary to $25.1 millions.
Management has made it known that they have no interest in projects contributing below $10 millions. In this
project there is a probability of about 11% to return an NPV below this limit. To find the exact probability of
return below a certain level we made an ascendant sort of the simulations produced for the variable NPV,
and counted how many values lay below the chosen boundary. It is now a matter of risk attitude whether to
accept the venture.
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Not surprisingly, we found from the Sensitivity report that NPV has a strong negative correlation with the
values produced for the year 1 and 2 of the variable New competitor entry.
The several time series we built using the function mmNAME help to show the tendency of the various
variables across time.
The following picture shows how the variable Net profit develops over time. The values used for tracing the
colored regions correspond to the values in both reports Time series and Statistics. The chart is telling us
that NP tends to stabilize after year 2 due to the entry of new competition in the market. Therefore, from a
managerial perspective, action should be taken to prevent or at least delay the competitor entry. The longer
our product stays free of competition the larger market share we can gain.
The width of the interval between boundaries of the periods in this series points out the high uncertainty
involved with the project (Y-axis going from $0 to $10 millions).
The next picture is for the variable Gross Profit. It shows a slope with a marked declining tendency after year
1, again due to the effect of competition. It seems clear that management should focus on maximizing sales
in the first 2 years.
Developing share, however, might require more marketing investment, which might require modeling new
scenarios with different levels of investment in order to evaluate the impact on the profitability of the whole
project.
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Finally, a note on the shape of histograms. The three pictures below show, from left to right, the frequency
distribution of the simulations for the variable Market share without competition (year 0), with and without
competition (year 1), and with competition (year 3).
It is interesting to notice how the shape of the distribution varies from a normally distributed one, to a
combination of two normal distributions, to a scattered distribution. In year 1, the image in the middle, you
can see that between the distribution on the left and the one on the right there is a gap of some 6 percentage
points, which is the cost of competition being introduced to the market. It would be perfectly acceptable to
raise legal hurdles to the entry of competition.
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Example 3: Correlated variables
The Excel workbook with the model described in this example is called Correlated-Variables.xls and can be
found in the directory Examples at the location where MM4XL software was installed.
This example demonstrates how to use the mmCORREL function to estimate product acceptance of
pharmaceutical drugs. The model can be enlarged and applied to other product categories too.
The model
A survey study run with 1000 physicians found that safety, efficacy and price of the drug have a strong
impact on the prescribing behavior of the sample. Our marketing manager is now wondering whether these
variables could help to build a model to find out whether to market one of two new products in development.
The following Contributing Factor Diagram (CFD) shows the model for the selection of the New Product that
should be launched (rectangle on the left in the picture), if any. The Best Product (hexagon on the right) is
found by selecting the highest Score as provided by the model.
B rand A
Safety
New P ro duct
Efficacy
B rand B
Sco re
B est
P ro duct
P rice
Each run of the model simulates the prescribing behavior of one doctor, and the brand each doctor prefers is
chosen according to the assumption that the best brand is the one producing the highest score. The score is
obtained as the sum of weighted attribute values, that is:
∑ (Attribute i ⋅ Score j )
Or, for instance, the score of the Existing Brand is:
(70 ⋅ WeightSafety ) + (75 ⋅ Weight Efficacy ) + (78.25 ⋅ WeightPrice )
The modeler assigned objective values to efficacy and safety of the existing brand and to the new products
in development, called New Brand A and New Brand B. In other industries less well regulated than the
pharmaceutical one the modeler can still use survey data to evaluate attributes.
The 1000 doctors also assigned a score ranging 0-100 to the importance they attributed to safety, efficacy,
and price of the existing brands. From the answers, the mean and standard deviation for each variable were
found and the correlation coefficient was computed, as shown in the following tables.
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Cells displaying in green host two kinds of Risk Analyst formulae. In row 21 there is the array function
mmCORREL, which produces values used in row 28 by three mmNORMAL functions to estimate attribute
weights correlated according to the correlation coefficients in the range C18:E20. Our sample said that safety
and efficacy are both strongly correlated to the price of the drug. This fact may be interpreted as if the
sample doctors believe that safe and effective drugs cost more, perhaps due to the cost of the primary
research.
In G11:G13 of the table below there are SUMPRODUCT formulae that find scores by multiplying the values in
row 21 with the attribute values in each of the rows 11:13. This means that the higher the score, the higher
the value a doctor from the sample attributes to the brand.
Finally, in I12:I13 we use the following formula to identify the Best Product:
=mmOUTPUT()+IF(G12>G11,1,0)+mmNAME("New Brand A")
In row 29 the Dummy Weights are required only to show in the Sensitivity page of the Preview form the
correlation between attributes. Indeed, they get very close to the desired level of correlation demanded by
the modeler.
Simulation
This model was simulated 1000 times, although during the fine-tuning phase it was common practice to
simulate only 100 runs in order to save time. The operational time, however, was a minor issue with this
model, because it runs fast and even 1000 simulations take just seconds to be produced.
The Short Report was used to evaluate the model. Basically, the core information we looked for was the
number of times each New Brand produced better results (score) than the existing brand.
For the sake of accuracy, from the Sensitivity page of the Preview window one can see that the model
produced correlation levels for the three attributes in accordance with the values of the table Correlations.
Interpretation
From range E10:E11 of sheet Short Report1 of file Correlated-Shares.xls we can see that in 71% of the
cases the model found New Brand B to have a higher score than the Existing Brand, as opposed to only
44% of cases when New Brand A performed better than the existing one. According to these results, the
modeler can assume that New Brand B could be preferred over the Existing Brand, and the project should be
pursued further.
This model is rather simplistic but nevertheless it shows effectively how to use correlated variables in
simulation models.
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Technicalities
Issue
Maximum number of simulation runs
Maximum number of fitted values
Maximum number of input variables
The system plays a BEEP
Limit
60000.
Limited by the number of rows in MS Excel 2003.
Limited by the number of cells in a worksheet.
Reports limited by the number of columns available, 256 in MS Excel.
At the end of the simulation runs.
When a pdf cannot be fitted.
When there is a problem with the pdf coefficients.
Known issues
When opened for the first time the example files made with Risk Analyst may require you to remove the path
address in front of formulae. To remove the path, select a cell with a Risk Analyst formula inside, select the
path address with the mouse, and press Ctrl+C to copy it to the clipboard. Exit the cell and open the Find tool
by pressing Ctrl+F, paste the path address with Ctrl+V, click on the Replace button and leave the text field
blank. Click the Replace All button to replace all path addresses in the sheet.
While working in the Preview window the chart of the main (Wizard) window disappears. To reset the chart
simply select a new item from the Distribution listbox and the chart will reappear.
The vertical arrow of the Pdf chart does not reach the minimum and/or maximum value of the chart, for
instance, Exponential, Gamma, Uniform.
There may be a delay before the Preview form appears. This is due to the number of simulations and the
number of variables in a model.
Some distribution functions take longer than others to return a value. This is due to the complexity of the
algorithm. Use the Time Elapsed tool to find out which Pdf’s are faster and which are slower.
In certain cases the function mmHYPERGEO can get trapped in a long-running loop that may keep the system
busy for a long time. This is due to the fact that the function finds a random variable with the desired shape
using a random number seed. The random seed ranges in the interval zero to one, when it takes unusually
high or low values this may result in the mmHYPERGEO function getting stuck. In this case simply press the
ESC key or the Break key, and click on Stop in the window that appears. Then it may be worth reviewing the
arguments of the mmHYPERGEO function that caused Risk Analyst to get stuck.
The chart of the Triangular distribution is drawn with a slightly cut peak, especially when working with figures
smaller than 1. To correct this annoyance you can remove the decimal separator. For instance, mmTRI(0.1599, 0.0347, 0.0977) returns a cut peak while mmTRI(-1599, 347, 977) does not.
A Pdf chart in the main window (Wizard) splits in two halves, disappears, or gets completely filled in blue
when Excel fails to solve the probability function of a value.
On chart in the main (Wizard) window:
•
•
•
Binomial can take a maximum number of Trials equal to 1000.
Inverse Gauss gets stuck with very large values due to an endless loop. Press the Ctrl+Break key to
exit the loop and click on the Stop button in the window that appears.
LogNormal may lose its traditional shape with large values, but only on the chart.
Slight computational differences can be due to MS Excel rounding activity and to approximations.
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Histograms with many classes may overlap in the reports. To reduce the size, select a chart (or many charts
at once by pressing the CTRL key and selecting the charts). Then drag the lower marker of one horizontal
side of one of the charts and release it to the desired height. All charts will be resized.
Time series are not taken into account if there is no Risk Analyst function in the model. In this case you can
use a fictitious function, for instance multiplying the product of one cell times a function like mmUNIFORM(1,
1), which always returns a 1 and therefore does not affect the result in the cell.
The Function Wizard built in Excel 97, 2000, and 2002 (version 8, 9 and 10 respectively) may fail to create
user defined categories for the three kinds of Risk Analyst functions. Excel XP, or version 11 also called
2003, on the other hand does not suffer from this problem.
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Property Functions
Function mmOUTPUT()
This is perhaps the most important function of Risk Analyst. It is used to identify output cells in a model. The
results of the simulation of output variables are reported in a separate sheet together with the respective
histogram charts showing the distribution of each variable. Moreover, at least one output variable is needed
to run the Sensitivity Analysis in the final report. Models without output cells do not tell the analyst very much.
The function does not take any arguments, its only job is to identify output variables and make them
available as such to the simulation engine.
Like any other MM4XL function, mmOUTPUT may be typed directly in the cell. It is entered by adding it to a
formula already present in the cell, which this way becomes an output variable.
Example
When entered as an output, this formula:
=MAX(G1:G10)
becomes:
=mmOUTPUT()+MAX(G1:G10)
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Function mmNAME(“CellName”, [Optional: ItemNum])
This function assigns a name to the cell where it is entered. The name is used in the reports.
The function takes two arguments.
CellName is the name that you wish to assign to the cell, and it must be entered between quotes.
ItemNum is an optional argument that identifies the position the item takes in the series it belongs to. When
the ItemNum is missing the name argument will be used to identify the formula in the cell.
The ItemNum argument is necessary for the analysis of time series data, such as the net present value
(NPV) of a project over a certain number of time periods.
Remarks
The CellName must be entered in quotes.
Valid cell references can be used to define names.
Example
The formula below assigns the name Market Size to the formula in the cell and makes it the third element of
the time series:
mmNORMAL(100, 5)+mmNAME("Market Size", 3)
When the report Time Series is printed, the elements of the series Market Growth can be analyzed further by
means of a time series chart. For more information concerning Time Series reports of simulation models,
refer to the corresponding section in this chapter.
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Function mmLOCK()
This function prevents a formula from being sampled in a simulation model. It does not take any argument.
When this function is entered in a cell containing a Risk Analyst function, the results of the cell are not
sampled in the simulation and, therefore, the report will not take into account the cell holding such function.
All other formulae in the model using an mmFUNCTION are automatically taken into account and are shown in
the report.
The usefulness of this function is to be found in models crowded with variables and in models accounting for
long series of mmFUNCTIONS. Locking one or more variables enables you to print synthetic reports that run
faster, take less time to be produced and that help you focus on the relevant elements in the model.
Example
When a simulation is run, the formula below produces values from the Triangular distribution and its results
may be printed in a report:
mmTRI(100, 160, 300)
When the formula above is changed to the formula shown below, the formula is still working in the model but
its results are no longer sampled and the report shows no information about it:
mmTRI(100, 160, 300) +mmLOCK()
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Utility Functions
Function mmHISTO(InputRng, [Optional: Classes])
This is an array function that returns the number of elements by class of a column of data. It can be used to
produce the data needed to draw a histogram chart like that drawn for output variables with Risk Analyst.
An array formula is entered with Ctrl+Shift+Enter, and it requires selecting a large enough range of
cells in order to print the whole results.
The function takes two arguments:
InputRng is the range on sheet containing the data to be classified. In the picture below this would be
B20:B5018.
Classes is an optional argument that tells the function the number of classes that the input data has to be
grouped into. When omitted, the argument is set by default to a number of bins according to the solution
described in the ASTM manual:
Round (1 + 3.3 ⋅ Log (NumItems ))
Example
We have 5000 simulations and would like to draw a histogram with a different number of classes than that
produced by Risk Analyst. For example, we would like to have the chart split into 15 classes rather than the
11 produced automatically.
Referring to the data in the picture above (mind the hidden rows), we select with the mouse the whole range
D1:G15 and enter the following formula in one of the cells, we did so in cell D1:
=mmHISTO(B20:B5018, 15)
Then, rather than pressing Enter as usual, we press simultaneously Ctrl+Shift+Enter. The picture
below shows the result of the function in 15 classes.
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Column C contains class labels, in column D we see the upper class boundary, column E displays the
number of items by class, and column F shows the cumulative percent values after each class. In the picture
above, in row 1, class 1 accounts for 191 items with a value of 12.8 or less, which account for 4% of the
5000 trials. Class 5 has 533 items with a value less than or equal to 23.2 and larger than 20.6, and so on.
The data in column E and F can be used to draw a new histogram as in the picture below:
100%
600
90%
500
80%
70%
400
60%
50%
300
40%
200
30%
20%
100
10%
0%
0
Class
1
Class
3
Class
5
Class
7
Class
9
Class
11
Class
13
Class
15
A question that often comes up when dealing with histogram charts is “How many classes should be used?”
mmHISTO by default defines the number of bins according to the solution described in the ASTM manual.
However, there is no fixed rule, and the user is free to choose the solution they feel is appropriate.
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Function mmOPTNUM(InputRng, [Optional: StablePeriods], [Optional: SelectionLimit])
This function finds the number of simulations for an Output variable where the standard deviation (sd) of the
mean of the simulation trials tends to stabilize. This is useful information to reduce the number of trials and
save time during the simulation or, alternately, to increase the number of trials if the analysis is not stable
enough.
There is no real statistical backup to the assumption that the sd of the mean is an estimator of the time to
stop producing simulation values because the next value will not contribute to the analysis with ‘enough’
incremental information. However, Koller suggests that: “A simple method for determining whether a
sufficient number of comparisons have been made is to inspect the mean of the “answer variable”
distribution…”. An answer variable in Risk Analyst software is clearly an Output variable.
This function takes three arguments:
InputRng is the range with the simulation values for the variable under inspection.
StablePeriods is an optional argument that sets the number of periods that the sd of the mean has to be
equal to or smaller than the SelectionLimit. When missing, the default number of stable periods is set to
20.
SelectionLimit is an optional argument that sets the level at which the absolute difference between the
sd at time t+1 has to be equal to or smaller than the same limit for the sd at time t. When missing, the default
level is 0.0005.
⎛ ⎛σ
ABS ⎜1 − ⎜⎜ 2
⎜
⎝ ⎝ σ1
⎞⎞
⎟⎟ ⎟
⎟
⎠⎠
The function returns zero if it cannot find an optimal number of simulations. This suggests that more
simulation trials have to be produced.
The following two functions produce the same result:
=mmOPTNUM(B14:B5013, 20, 0.0005)
=mmOPTNUM(B14:B5013)
The following chart refers to the sd of the mean of 5000 trials. The function mmOPTNUM suggests that 976
trials are required to achieve stability at the 0.0005 level. Note that the maximum value of the vertical axis
was rescaled to allow the curve to be seen, which otherwise was pushed down to the zero level by extreme
values occurring in the initialization phase of the algorithm.
Std Dev of the Mean of 5000 Simulation trials
0.40%
Standard Deviation
0.35%
0.30%
0.25%
0.20%
0.15%
0.10%
976
0.05%
0.00%
1
501
1001
1501
2001
2501
3001
3501
4001
4501
Simulations
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Function mmCORREL(CorrMtx)
This array function applies the Scheuer-Stoller method, and returns values useful to create correlated
random variables according to a specified correlation matrix. It is mainly used jointly with the distribution
functions available in Risk Analyst.
An array formula is entered with Ctrl+Shift+Enter, and in this case it requires you to select as many cells as
columns in the input range. The function takes one argument.
CorrMtx is the matrix of correlation coefficients. It must be a square table (the same number of rows and
columns), at least 2x2, with the values on the diagonal being all ones and the values in the lower half being
equal to the values in the upper half of the matrix (symmetric matrix). Correlation coefficients can vary
between -1 and 1.
Example
The following formula creates a Normal variable correlated according to the coefficients in the second
column of the input matrix in the range C9:E12 of the file mmCORREL.xls. Range C16:E16 hosts the values
returned by the mmCORREL function:
mmNORMAL(10, 1, D16)
More information concerning the application of the mmCORREL function can be found in the section Example
3: Correlated-Shares of this chapter. Read also the section Why correlated variables? in this chapter and
study the example file mmCORREL.xls.
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Distribution Functions
mmBETA(Scale, Shape)
Example
=mmBETA(2, 4) can equal 0.304847002
Application
This function is used to determine the probability of an event, given a number of trials and successful events.
This distribution is mainly used for inference purposes, that is, when the data from a sample is used to
project the data for the whole population. It is often used in the absence of data. See also mmBETAGEN.
How to use
It returns the probability of an event occurring. This helps, for instance, when we need to estimate the
probability that the next client will buy. For instance, if for every 100 calls 15 would buy, we could use the
formula below to estimate the probability of the next purchase occurring:
=mmBETA(15, 86)
The formula accounts also for the rare event of zero purchases out of 100 calls. Copy the formula above in
100 cells. You will find that the minimum and maximum value will score around 10%-30%. If we were
modeling the outcome of a direct marketing campaign, we could use the mmBETA function times the number
of calls to determine the number of incoming clients by time unit, for instance one day.
Technical profile
Type
Continuous distribution.
Syntax
=mmBETA(Scale, Shape)
Domain
0 ≤ RndNum ≤ 1
If Scale > 1 ; Shape > 1 then =
Mode
Scale − 1
Scale + Shape − 2
If Scale = 1 and Shape = 1 then the mode is Not defined.
Parameters
Scale = v > 0
Shape = w > 0
Remarks
If any argument is nonnumeric, mmBETA returns the #VALUE! error value.
If Scale ≤ 0 or Shape ≤ 0 mmBETA returns the #NUM! error value.
Relationships
It is related to the Binomial, Gamma and to the Normal variates.
mmBETA(2, 4)
mmBETA(4, 2)
Graphs
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mmBETAGEN(Scale, Shape, [Optional: Lower], [Optional: Upper])
Example
=mmBETAGEN(2, 2, -2, 2) can equal 0.765094757
Application
This function is used to determine the probability of an event given a number of trials and successful events.
This distribution works like mmBETA with the difference that it allows you to define a Lower and Upper
boundary. It is often used in the absence of data.
How to use
It returns the probability of an event occurring. It helps when we need an estimate of the probability that, for
instance, the next client will buy. Replacing the mmBETA shown previously with the formula below we can
estimate the probability of the next purchase occurring, exactly as we would do with mmBETA(16, 85):
=mmBETAGEN(16, 85, 0, 1)
Changing the Lower and Upper bound to a larger and smaller value respectively, would shrink the range of
values the function would draw from. For instance, the formula below draws random numbers from the 50%
and 90% percentile interval of the mmBETA(16,85) distribution:
=mmBETAGEN(16, 85, 0.5, 0.9)
The formula accounts also for the rare event of zero purchases out of 100 calls. Copy the formula above in
100 cells. You will find that the minimum and maximum values will score in a range >50% and <90%. If we
were modeling the outcome of a direct marketing campaign, we could use the mmBETAGEN function to
determine the number of incoming clients by time unit, for instance one day, according to the incoming calls.
Again, this function is often used in the absence of data.
Technical profile
Type
Syntax
=mmBETAGEN(Scale, Shape, [Optional: Lower], [Optional: Upper])
Domain
0 ≤ RndNum ≤ 1
min+ (max − min) ⋅
Mode
Parameters
Scale − 1
Scale + Shape − 2
If Scale = 1 and Shape = 1 then the mode is Not defined
If NOT (Scale >= 1 And Shape >= 1) or
NOT (Scale < 1 And Shape >= 1) or
NOT (Scale >= 1 And Shape < 1)
then the mode is Bimodal at Lower and Upper
scale= v > 0
shape= w > 0
Lower, optional = lower bound
Upper, optional = upper bound
Remarks
If any argument is nonnumeric mmBETAGEN returns the #VALUE! error value.
If Scale ≤ 0 or Shape≤ 0 mmBETAGEN returns the #NUM! error value.
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Relationships
It is related to the Binomial, Gamma and to the Normal variates.
mmBETAGEN(2, 2, -2, 2)
mmBETAGEN(4, 4, -4, 4)
Graphs
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mmBINOMIAL(Trials, Successes)
Example
=mmBINOMIAL(5, 0.5) can equal 3
Application
This function is used to determine the number of events that occur given a certain probability of occurrence.
There are only two possible outcomes for each trial, true/false, pass/fail, etc. The trials are independent,
which means previous trials have no effect on successive trials. The probability of occurrence does not
change between trials.
How to use
This function returns the number of events that occur. This helps, for instance, when we need to estimate the
entrance of a new competitor in the market.
Say that we are launching a new product in a new market category and we need a model to estimate the
profitability over the next 5 years. We expect competition to enter the category, and based on previous
knowledge we estimate a maximum number of 5 competitors to enter the category in 5 years with a
probability of 40% for these events to occur. The formula below estimates the number of competitors
entering the market in one year:
=mmBINOMIAL(5, 0.4)
Copy the formula above in 100 cells. You will find that the maximum value will be 5, as the number of
competitors that we expect, and most estimates (about two thirds) suggest the entry of one to two new
competitors. If we were modeling the outcome of a new product launch, we should use a limiting factor
across the years in order to avoid the entrance of more than 5 players in the given period of time.
Technical profile
Type
Discrete distribution.
Syntax
=mmBINOMIAL(Trials, Successes)
Domain
RndNum = integer
0 ≤ RndNum ≤ Trials
Mode
Integer = Successes ⋅ (Trials + 1) − 1 ≤ x ≤ Succeses ⋅ (Trials + 1)
Otherwise = Succeses ⋅ (Trials + 1)
Parameters
Trials is the number of independent trials.
Successes is the number of successes in trials.
Remarks
If any argument is nonnumeric mmBINOMIAL returns the #VALUE! error value.
Relationships
It is related to the Beta, Hypergeometric, Negative Binomial, Normal, Poisson
and to the Student’s t variates.
mmBINOMIAL(5, 0.5)
mmBINOMIAL(20, 0.5)
Graphs
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mmCHI2(Degrees)
Example
=mmCHI2(5) can equal 1.313942432
Applications
This distribution is used to calculate the probability that one of two mutually exclusive outcomes will occur. It
may help, for instance, to calculate the number of smokers versus non smokers. It is modeled using one
parameter only, the degrees of freedom. The larger the number of degrees, the more the Chi2 distribution
resembles the Normal one.
How to use
This function returns the amount of mutually exclusive events. Say that we are modeling the employment of
a new professor for an MBA course and we need an estimate of the experience, in years, of use of the PC.
We expect it to range between zero and 15 years. The formula below may be used to estimate the years of
experience for each candidate:
=mmCHI(2)
Copy the formula above in 100 cells. You will find that most simulated values will range between 0 and 15,
with 50% of the values being less than 1.4 years. Not really an unmatchable expectation.
Technical profile
Type
Syntax
=mmCHI2(Degrees)
Domain
0 ≤ RndNum < ∞
Mode
If Degrees < 2 then = 0
Otherwise = Degrees - 2
Parameters
Degrees is the number of degrees of freedom.
Remarks
If Degrees is nonnumeric mmCHI2 returns the #VALUE! error value.
If Degrees is not an integer it is truncated.
If Degrees < 1 returns the #NUM! error value.
If Degrees > 680 then mmCHI2 approximates the value.
Relationships
It is related to the Gamma, Normal, Poisson and to the Student’s t variates.
mmCHI2(5)
mmCHI2(100)
Graphs
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mmDISCRETE(InputRange, Probabilities)
Example
=mmDISCRETE({5\10\20},{30%\20%\50%}) is equal to 5 in roughly 30% of the cases, to 10 in roughly
20% of the cases, and to 20 in roughly 50% of the cases.
This is an array function that is entered with Ctrl+Shift+Enter. It can also be entered by selecting a range on
sheet as in the following formula.
Applications
This function is used to simulate the occurrence of the given number of events only. For instance, it could be
the lights of a semaphore, the winners of a horse race, which counter will host the next client, or any other
process that returns a limited number of events only.
How to use
Say we are modeling the sales of a product line made up of three items: reference A, B, and C. Last month
sales in volume were 28% for product A, 42%, for product B, and 30% for product C. The price of the items is
108.50, 66.30, and 29.80 respectively, as shown in the following picture.
The formula below may be used to simulate the next sales value among the three options in the picture
above according to their probability of occurrence:
=mmDISCRETE(B2:B4, C2:C4)
Copy the formula above in 200 cells. You will find that the values returned correspond to one of the three
prices in the table above. About 30% of the values relate to product A (price 108.50), about 40% to product
B, and the remainder to product C.
Technical profile
Type
Discrete, custom distribution.
Syntax
=mmDISCRETE(InputRange, Probabilities)
Domain
−∞ < RndNum < ∞
Mode
InputRange item for which the Probability is the greatest.
Parameters
Arrays entered as range on sheet or as values directly in the formula.
Remarks
If any argument is nonnumeric mmDISCRETE returns the #VALUE! error value.
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mmERF(Mean)
Example
=mmERF(1) can equal -1.231669545
Applications
The Error Function, also called Erf, is used to calculate failure times in engineering, mortality in population
biology, event histories in sociology, and more. It looks like the Normal distribution, but it assigns more
importance to extreme values than the Normal one does.
How to use
This formula returns extreme values. Say we are working on short-term sales levels and we are modeling
forecast errors as computed with the Forecast Manager tool (refer to the example file Forecast Manager.xls,
sheet MM4XL – Forecast, range L33:L90). The formula below may be used to simulate the errors produced
with the times series of the forecast example:
=mmERF(0.1276)
The Mean level for the formula above has been found using the Fitting tool with the data in range L33:L90,
yet this is the same mean value that one can find in cell H17.
Copy the formula above in 100 cells. You will find that most simulated values will range, roughly speaking,
within plus or minus 15%, whilst the actual error terms produced with Forecast Manager range from -9.5% to
10.6% (in the example file mentioned above see cells H16 and H20, respectively).
Technical profile
Type
Syntax
=mmERF(Mean)
Domain
Mode
0
Parameters
Mean is the location parameter.
Remarks
If the Mean is nonnumeric mmERF returns the #VALUE! error value.
Relationships
It is related to the Normal and to the Uniform variates.
mmERF(1)
mmERF(10)
Graphs
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mmERLANG(Scale, Shape)
Example
=mmERLANG(2, 1) can equal 0.520087719
Applications
This distribution is most used in relation to waiting-line theory, and it is used to calculate the time elapsing
between events. It may help, for instance, to calculate how long it takes until the next client enters the shop,
how long it takes to produce a handmade decoration, and so on.
How to use
This formula returns the amount of time between events. Say we are modeling the client flow to our fast-food
restaurant. As a result of regular observation, we know that it takes 3 minutes for an employee to serve a
client. The formula below may be used to simulate the amount of time between 0 and 5 minutes needed to
serve a client:
=mmERLANG(3, 0.373)
Copy the formula above in 100 cells. You will find that most simulated values will range between 0 and 5,
with over 98% of the values being less than 3 minutes.
Technical profile
Type
Syntax
=mmERLANG(Scale, Shape)
Domain
0 ≤ RndNum < ∞
Mode
if Scale ≥ 1 then = Shape ⋅ (Scale − 1)
Parameters
Scale = b > 0; b = integer
Shape = c > 0
Remarks
If any argument is nonnumeric mmERLANG returns the #VALUE! error value.
Relationships
It is related to the Exponential and to the Gamma variates.
mmERLANG(2, 1)
mmERLANG(20, 5)
Graphs
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mmEXPON(Mean)
Example
=mmEXPON(1) can equal 1.660898089
Applications
This function can model the amount of time between (or until) events, where the rate of occurrence is
independent from previous events.
How to use
This function returns the amount of time between events. This helps, for instance, when we need to estimate
how long it takes between client arrival and departure.
Say that we are modeling the client flow at a fast food restaurant and we need an estimate of the time
between arrivals, which is useful information to determine how much production capacity is available at any
time. Our records show that on average in a given day, we serve one client every 12 minutes. The formula
below estimates the time in minutes between client arrivals:
=mmEXPON(12)
Copy the formula above in 100 cells. You will find that most simulated values will spread around the 12
minutes and only a small portion of the 100 runs will show very large values, meaning that a long amount of
time elapses till the next client comes in.
Technical profile
Type
Syntax
=mmEXPON(Mean)
Domain
0 ≤ RndNum < ∞
Mode
0
Parameters
Mean = b > 0
Remarks
It is characterized by a ‘lack of memory’, like mmGEO.
If Mean is nonnumeric mmEXPON returns the #VALUE! error value.
If Mean < 0 mmEXPON returns the #NUM! error value.
Relationships
It is a special case of Gamma and Weibull variates.
It is related to the Rectangular, Erlang, Pareto and Extreme Value variates.
mmEXPON(1)
mmEXPON(100)
Graphs
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mmEXTVAL(ModalValue, StDeviation)
Example
=mmEXTVAL(1, 1) can equal -0.134865515
Applications
Also called Gumbel distribution, this function is used to simulate the occurrence of extreme values, either
maximum or minimum. For instance, it could be the maximum time to failure of a component of a parallel
circuit, the maximum water flow for a dam, or the minimum time to failure for a dispenser machine.
How to use
This function simulates extreme values. Say we are modeling the production capacity of a fast food
restaurant. During the weekend, when the employee at the window requires more than 4 minutes to serve a
client, the risk of losing a client in line is high. The formula below may be used to simulate the maximum time
taken to serve a client:
=mmEXTVAL(4, 0.525)
Copy the formula above in 100 cells. You will find that the returned values vary between 3 and 7 minutes,
which is the range of the extreme time to serve to a client (we might have found it out by collecting samples
of serving times at different hours). About 37% of the serving times lie below 4 minutes and about 14%
exceed 5 minutes.
Technical profile
Type
Syntax
=mmEXTVAL(ModalValue, StDeviation)
Domain
Mode
ModalValue
Parameters
ModalValue = a = the mode
StDeviation = b > 0
Remarks
If any argument is nonnumeric mmEXTVAL returns the #VALUE! error value.
Relationships
It is related to the Exponential, Weibull and to the Pareto variates.
mmEXTVAL(1, 1)
mmEXTVAL(100, 100)
Graphs
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mmGAMMA(Scale, Shape)
Example
=mmGAMMA(2, 1) can equal 2.073131782
Applications
This function is typically used to study variables that may have a skewed distribution and whose outcome is
not completely random. It can model the time elapsing between events, and it is commonly used in inventory
control and queuing analysis.
In many cases, this kind of event can also be modeled with mmNORMAL. The drawback is that mmNORMAL
accounts for negative numbers too and it is symmetrical. When it is desirable to work with a positive, right
skewed distribution the mmGAMMA or the mmLOGNORMAL can help. The Gamma function is less skewed than
the Lognormal, so it assigns lower probability to extreme values.
How to use
This function returns the amount of time between events. Say, we are modeling the time to issue an order to
restock the inventory of sodas at a retail store. The order can be issued only when all 3 brands of soda that
the store carries have one or zero units in stock. From historical data we know this happens every 28 days
plus or minus 7 days. The formula below may be used to simulate the time in days to reorder sodas:
=mmGAMMA(7, 4)
Copy the formula above in 100 cells. You will find the simulated values ranging from 0 to 70 days, and the
mean is centered around 28 days (the mean of the mmGAMMA is found by multiplying the Scale times Shape
parameters – 7 times 4 in our example equals 28 days to reorder sodas).
Technical profile
Type
Syntax
=mmGAMMA(Scale, Shape)
Domain
0 ≤ RndNum < ∞ ; generates positive numbers only
Mode
If Scale ≥ 1 then = Shape ⋅ (Scale − 1)
If Scale < 1 then = 0
Parameters
Scale = b > 0
Shape = c > 0
Remarks
If any argument is nonnumeric mmGAMMA returns the #VALUE! error value.
Relationships
When Shape is an integer the distribution function is the same as that of the
Erlang distribution.
It is related to the Chi2 distribution.
mmGAMMA(2, 1)
mmGAMMA(20, 10)
Graphs
www.mm4xl.com
230
mmGAUSSINV (Mean, Scale)
Example
=mmGAUSSINV(1, 1) can equal 0.444967568.
Applications
Also called the Wald’s distribution, this distribution is mainly used in sequential analysis. It is often employed
to test scientific models of unknown nature, to evaluate risk in the stock market, the price of a financial
derivative, or, more generally, response time such as the lifetime of a component. The failure rate of this
function increases until maximum is reached and then decreases towards the zero value as the lifetime
approaches infinity.
How to use
This function models response time in sequential patterns. Say we are modeling the web surfing behavior of
car buyers searching for information. From past experience we know that the number of links (pages) a
visitor follows in a website before jumping to the next website is about 3 (although 1 page is the modal value)
while the maximum number of pages visited is about 100. This surfing behavior can be modeled with:
=mmGAUSSINV(3, 6)
Copy the formula above in 100 cells. You will find that most simulated values will score around 1.5 rather
than 3, as stated with the Mean parameter, and this is compatible with web surfing behavior. Our personal
experience suggests that the Scale parameter can occasionally be found with the square root of the term
(MaxValue / 3), where MaxValue stands for the largest number of, in this case, visits to pages of one
individual website.
Technical profile
Type
Syntax
=mmGAUSSINV(Mean, Scale)
Domain
RndNum > 0
Mode
⎛
9 ⋅ Mean 2 3 ⋅ Mean ⎞⎟
Mean ⎜ 1 +
−
⎜
4 ⋅ Scale 2 2 ⋅ Scale ⎟⎠
⎝
Parameters
Mean = mu > 0
Scale = b > 0
Remarks
If any argument is nonnumeric mmGAUSSINV returns the #VALUE! error value.
Relationships
It is related to the Chi2 variate with 1 degree of freedom.
mmGAUSSINV(1, 1)
mmGAUSSINV(1, 10)
Graphs
www.mm4xl.com
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231
mmGEO(Trials)
Example
=mmGEO(0.5) can equal 2.
Applications
This function describes the number of trials until the first successful occurrence. The probability of success is
the same across runs. It can model many instances, the typical example is how many bets we need until we
win at roulette (2.63% probability that a given number is chosen). But it works also in quality analysis to
estimate sampling plans when seeking defects and in other situations when the outcome is of two kinds only.
How to use
This function returns the number of trials before a positive event. This helps, for instance, to estimate the
number of cold calls before we reach a potential buyer.
Say we run a telemarketing call center, and we need to estimate the number of telephone lines needed to
complete the action within a given timeframe. From past experience we know the conversion rate from call to
purchase is 0.65%. The formula below could help to estimate how many calls before we have a successful
one, which is a good hint to estimate the overall result of the action:
=mmGEO(0.0065)
Copy the formula above in 100 cells. You will find that most simulated values will be in the range 1 to just
below 1000. For example, if we get 233, it means a client is acquired after 233 calls.
Technical profile
Type
Syntax
=mmGEO(Trials)
Domain
RndNum ≥ 0 , an integer
Mode
0
Parameters
Trials = 0 < p < 1
Trials is the number of trials or failures before the first success.
Remarks
If Trials is nonnumeric mmGEO returns the #VALUE! error value.
Relationships
The Geometric variate is a special case of the Negative Binomial variate.
mmGEO(0.5)
mmGEO(0.25)
Graphs
www.mm4xl.com
232
mmHYPERGEO(Sample, Defects, BatchSize)
Example
=mmHYPERGEO(3, 3, 6) can equal 2.
Applications
This function describes the number of defects in a sample, which is a concept applied mainly to quality
analysis. When the BatchSize, or population, is 10 times or less the size of the Sample the number of
Defects in a lot can be estimated with mmHYPERGEO.
How to use
This function returns the number of expected defects in a sample of a given size according to the number of
defects expected in the whole batch. This helps, for instance, to estimate the number of defective computers
in lot of 5000 units. Say that 1% defects in a batch is the limit within we accept incoming goods. The formula
below estimates the number of expected defectives in a batch of 5000 using an inspection sample of 100
units:
=mmHYPERGEO(100, 50, 5000)
Copy the formula above in 100 cells. You will find that about 35% of the simulated values will be zeros and
45% of the values will exhibit 1 defect in a sample of 100 units. In about 25% of the simulations we will find a
sample with 2 or more defects.
Technical profile
Type
Syntax
=mmHYPERGEO(Sample, Defects, BatchSize)
Domain
RndNum ≥ 0 , an integer
Mode
Undefined
Parameters
Sample > 1
Defects > 1
BatchSize > Sample
Remarks
It is characterized by a ‘lack of memory’ like mmEXPON.
If Trials is nonnumeric mmHYPERGEO returns the #VALUE! error value.
Relationships
It approximates the Poisson variate as the parameters tend to infinity.
It can be approximated by the Binomial variate.
mmHYPERGEO(3, 3, 6)
mmHYPERGEO(30, 30, 60)
Graphs
www.mm4xl.com
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233
mmINTUNI(Lower, Upper)
Example
=mmINTUNI(1, 8) can equal 4.
Applications
Also called Rectangular Discrete distribution, this function assigns equal probability to the items between a
Lower and an Upper bound. It can be used to model a wide variety of instances when there is equal chance
that one outcome or another occurs, for instance, whether the next incoming client is male or female.
How to use
It returns numbers with equal probability within a Lower and an Upper bound. Say that we sell three
different kinds of pizza, and every week we sell roughly an equal quantity of each, 300 for instance. The
formula below could help to estimate the preference of clients ordering one of three kinds of pizza:
=mmINTUNI(1, 3)
Copy the formula above in 100 cells. You will find that about one third of values is a one, a two or a three,
according to the three pizzas.
Technical profile
Type
Syntax
=mmINTUNI(Lower, Upper)
Domain
Lower ≤ RndNum ≤ Upper , an integer
Mode
Not uniquely defined
Parameters
Lower = lower limit of the range
Upper = upper limit of the range
Remarks
If any parameter is nonnumeric mmINTUNI returns the #VALUE! error value.
Relationships
None.
mmINTUNI(1, 8)
mmINTUNI(1, 80)
Graphs
www.mm4xl.com
234
mmLOGISTIC(Mean, StDeviation)
Example
=mmLOGISTIC(0, 1) can equal 1.72044909.
Applications
This function describes many biological phenomena well, and it is often used to simulate population growth
over time (with constantly decreasing growth values). It resembles very much the Normal distribution with the
difference that mmLOGISTIC assigns higher probability to values in the tails of the distribution.
How to use
This function returns values more spread in the tails of the distribution. Say that we are modeling the
response of demand to advertising investments. We estimate that next year sales could be in the range
$1750 plus or minus $250, given that we invest the planned advertising budget. The formula below could
help to estimate the expected demand levels:
=mmLOGISTIC(1750, 45)
Copy the formula above in 100 cells. You will find that the simulated values will be produced in the range
1500-2000 in accordance with the next year sales estimate.
Technical profile
Type
Syntax
=mmLOGISTIC(Mean, StDeviation)
Domain
Mode
Mean
Parameters
Mean = a
StDeviation = b > 0
Remarks
If any argument is nonnumeric mmLOGISTIC returns the #VALUE! error value.
Relationships
It is related to the Exponential variate with mean = 1.
It is related to the Extreme Value variate with Mode = 0 and StDeviation = 1.
It is related to the Pareto variate.
mmLOGISTIC(0, 1)
mmLOGISTIC(2, 10)
Graphs
www.mm4xl.com
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235
mmLOGNORMAL(Mean, StDeviation)
Example
=mmLOGNORMAL(1, 1) can equal 0.370659727
Applications
This distribution is used to model the product of two or more independent variables. This situation is quite
frequent in nature, such as the volume of a natural gas reservoir or river flow rates. It also applies to things
like real estate values, income size, or bank deposits.
How to use
To model the product of several independent events, such as monthly sales: Assume that each customer’s
purchase is the product of many factors, such as salary times a weather factor times a mobility factor times
several other independent factors. If there are not too many customers with a lognormal sales shape, the
company sales will also tend to be lognormal. Otherwise, with many lognormal customers, company sales
will tend to be normally distributed due to the central limit theorem. The formula below can help to model the
sales of a not too large pool of customers with average sales of $50000 and standard deviation $10000:
=mmLOGNORMAL(50000, 10000)
Copy the formula above in 100 cells. You will find that the simulated values will be produced, roughly
speaking, in the range $30-$90 in accordance with the Mean sales and Standard deviation of the
sampled pool of clients. The formula above returns a value expressed on the metric unit, so there is not need
to use logarithmic values in the formula. For your information, the formula below transforms a logarithmic
value in metric unit:
=EXP(mmLOGNORMAL(100, 20))
Technical profile
Type
Syntax
=mmLOGNORMAL(Mean, StDeviation)
Domain
0 ≤ RndNum ≤ ∞ ; generates positive numbers only.
Mode
Exp Mean − StDeviation 2
Parameters
Mean = m > 0
StDeviation = s > 0
Remarks
If any argument is nonnumeric mmLOGNORMAL returns the #VALUE! error value.
Relationships
It is related to the Normal variate.
(
)
mmLOGNORMAL(1, 1)
mmLOGNORMAL(10, 1)
Graphs
www.mm4xl.com
236
mmNEGBIN(Failures, Successes)
Example
=mmNEGBIN(1, 0.5) can equal 1.
Applications
Also called the Pascal variate, this function returns the number of trials needed to reach a given number of
successes according to a given success rate. For example, you need to find 10 people with excellent
reflexes, and you know the probability that a candidate has these qualifications is 30%. mmNEGBIN(10,
0.3) calculates the probability that you will interview a certain number of unqualified candidates before
finding all 10 qualified candidates. It is also used to model the distribution of cavities in a group of dental
patients.
How to use
This function returns the number of trials before reaching a certain number of successes. Say that we are
planning to use outdoor advertising for our store and we are wondering about the visits to the store that
billboards can generate, which impacts on sales. From a survey study we know that 30% of the 25,000
pedestrians exposed to the billboard each day notice it, and 6.5% of the 30% enter the store. The formula
below can help to model the required number of pedestrians exposed to the billboard in order to obtain 10
visits:
=mmNEGBIN(10, 0.0195)
Copy the formula above in 100 cells. You will find that the most likely value is around 450, which means that
of every 450 people who notice the billboard, 10 enter in the store.
Technical profile
Type
Syntax
=mmNEGBIN(Failures, Successes)
Domain
0 ≤ RndNum < ∞
Mode
If a = integer then = a ≤ x ≤ a + 1
Otherwise = a+1
a=
Failures (1 − Successes ) − 1
Successes
Parameters
Failures = 0 ≤ x < ∞ , x = an integer
Successes = 0 < p < 1
Remarks
If any argument is nonnumeric mmNEGBIN returns the #VALUE! error value.
Relationships
It is related to the Geometric variate.
It is related to the Poisson variate as Failures tends to infinity and
Successes tends to 1.
mmNEGBIN(1, 0.5)
mmNEGBIN(10, 0.5)
Graphs
www.mm4xl.com
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237
mmNORMAL(Mean, StDeviation)
Example
=mmNORMAL(0, 1) can equal -1.277808189.
Applications
Sometimes called the Gaussian distribution, this function is used to draw normally distributed values around
the mean according to the standard deviation. It has a very wide range of applications, because there are
many variables that fall into a Normal distribution. These include such things as human height, the weight of
a pack of biscuits, intelligence scores, or the world temperature.
It is also frequently used to represent phenomena whose distribution is not known, but is thought to be
symmetrical to a given mean value.
How to use
This function returns a normally distributed value around the mean. This helps, for instance, to model the
growth of a given market for successive years. Say that we are looking into the profitability of a new product
launch and we need to estimate the market size for 5 consecutive years. The value of the market at year
zero is estimated in 1 million and will grow at a rate of around 5% a year. The formula below helps to model
this case:
=mmNORMAL(1.05, 0.01) * 1000000
Copy the mmNORMAL formula above in 100 cells. You will find that it produces values in the range 1.01-1.08,
which roughly correspond to 1.05 plus or minus 3 standard deviations. The mean of a Normal distribution
plus or minus 3 standard deviations is the range supposed to host 99.7% of the values. The value obtained
with mmNORMAL times the market value results in an estimate of next year’s market value.
Technical profile
Type
Syntax
=mmNORMAL(Mean, StDeviation)
Domain
Mode
Mean.
Parameters
Mean = mu
StDeviation > 0
Remarks
If any argument is nonnumeric mmNORMAL returns the #VALUE! error value.
If StDeviation < 0 mmNORMAL returns the #NUM! error value.
Relationships
It is related to the Beta, Binomial, Chi2, Gamma, Inverse Gauss, LogNormal,
Poisson and Student’s t variate.
mmNORMAL(0, 1)
mmNORMAL(10, 5)
Graphs
www.mm4xl.com
238
mmPARETO(Location, ModalValue)
Example
=mmPARETO(2, 1) can equal 6.156197548.
Applications
This distribution was developed to describe the spread of income, with a high proportion of a population
having low income and only a few people with very high income. mmPARETO can be used to model insurance
claims, the occurrence of extreme weather, and more.
How to use
This function can return extreme values. Say we are modeling the time duration of sessions at our web site.
From internal data we know that the minimum session is 1 second, while the maximum time spent at the site
depends on the interest generated in the visitor. The formula below models the time in seconds spent at our
site:
=mmPARETO(0.2, 1)
Copy the formula above in 100 cells. You will find that it produces values with the Mode, or most frequent
value, equal to 1 as required in our formula, and 50% of the simulated values are smaller than 32 seconds
spent with us. The extreme value we obtained with the formula above was 631.7 seconds.
Technical profile
Type
Syntax
=mmPARETO(Location, ModalValue)
Domain
Location < RndNum < ∞
Mode
ModalValue.
Parameters
Location = a > 0
ModalValue = c > 0
Remarks
If any argument is nonnumeric mmPARETO returns the #VALUE! error value.
Relationships
It is related to the Exponential variate with parameter b = 1/c.
It is related to the Gamma and Chi2 variate.
mmPARETO(2, 1)
mmPARETO(20, 1)
Graphs
www.mm4xl.com
8. Risk Analyst
239
mmPARETO2(Location, ModalValue)
Example
=mmPARETO2(3, 3) can equal 1.298089623.
Applications
Also called Lomax or the Johnson Type VI, the class 2 Pareto distribution is often used in queue analysis,
service-time distribution, network modeling, and discrete-event simulation. It behaves quite like the Pareto
distribution, but has a larger domain.
How to use
This function can return extreme values starting from zero. Say we are modeling the mean number of active
sessions at our website. From internal data we know that the average number of open sessions is 14. The
formula below simulates the number of open sessions at a given time:
=mmPARETO2(2, 14)
Copy the formula above in 100 cells. You will find that it produces values with a mean equal to 14 as
required in our formula and 75% of the simulated values lying below the 14 sessions. The extreme value we
obtained with the formula above was 1260.3 sessions open at one time.
Technical profile
Type
Syntax
=mmPARETO2(Location, ModalValue)
Domain
0 < RndNum < ∞
Mode
0.
Parameters
Location = a > 0
ModalValue = c > 0
Remarks
If any argument is nonnumeric mmPARETO2 returns the #VALUE! Error value.
Relationships
It is related to the Exponential variate with parameter b = 1/c.
It is related to the Gamma and Chi2 variate.
mmPARETO2(3, 3)
mmPARETO2(30, 3)
Graphs
www.mm4xl.com
240
mmPOISSON(Mean)
Example
=mmPOISSON(1) can equal 0.
Applications
This is a very popular distribution used to model the number of events that will occur given a known mean
occurrence value. It is useful to estimate the number of defects in a unit, incoming calls, insurance claims,
customer arrivals, and much more.
How to use
Say we are modeling the purchase cycle of a washing powder market of 20 million potential buyers. The
mmPOISSON distribution can be used to estimate the population at different points in time. When the
parameter of the mmPOISSON is very large, however, the result is approximated and the difference between
runs may become negligible.
=mmPOISSON(20000000)
An example where the parameter of the mmPOISSON distribution is not too large could be the number of
appointments made every day by a sales representative. If the average number of daily visits for a rep is 6,
the formula below helps to model this instance:
=mmPOISSON(6)
Technical profile
Type
Syntax
=mmPOISSON(Mean)
Domain
0 ≤ RndNum < ∞ , an integer
Mode
If Mean = integer then = Mean ≤ x ≤ Mean − 1
Otherwise = Mean
Parameters
Mean = a > 0
Remarks
If Mean is nonnumeric mmPOISSON returns the #VALUE! error value.
Relationships
It is related to the Binomial variate with parameter b = 1/c.
For large values it may be approximated by the Normal variate.
With parameters tending to infinity the Hypergeometric variate tends to a
Poisson variate.
mmPOISSON(1)
mmPOISSON(10)
Graphs
www.mm4xl.com
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241
mmRANDBETWEEN(Lower, Upper)
Example
=mmRANDBETWEEN(5%, 20%) can equal 6.05341792%.
Applications
This function is used to simulate values within a given interval range when we have only a vague
understanding of the event. For instance, it could be the probability that the next client orders a soda, the
cost of a clinical trial, the time taken to repair a machine. Each value in the range has an equal probability of
being extracted (Uniform pdf).
How to use
Say we are modeling the pedestrian flow of a sidewalk that our business display window faces onto.
According to internal data we know that every hour between 700 and 1000 people walk past our window.
The formula below may be used to simulate the next hour pedestrian flow:
=mmRANDBETWEEN(700, 1000)
Copy the formula above in 100 cells. You will find that it produces values in the range 700-1000.
Technical profile
Type
Syntax
=mmRANDBETWEEN(Lower, Upper)
Domain
Parameters
Lower = lower limit
Upper = upper limit
Remarks
If any argument is nonnumeric mmRANDBETWEEN returns the #VALUE! error value.
www.mm4xl.com
242
mmRAYLEIGH(ModalValue)
Example
=mmRAYLEIGH(1) can equal 0.391181737.
Applications
This is a distribution used to model the time to perform some work, the time to fail of a component of a
machine; it is used in the study of sound, light and signal processing, wind speed and other situations where
the time variable is crucial.
How to use
The Rayleigh distribution is used to simulate time to perform. Say we are modeling wind speed over a year in
order to estimate the energy recovery from a wind turbine. The formula below simulates wind speed in miles
with a modal value equal to 8.5 miles per hour:
=mmRAYLEIGH(8.5)
Copy the formula above in 100 cells. You will find that it produces values of wind speed with mode equal to
8.5 miles per hour. Roughly 40% of the simulated values lie below the 8.5 miles and 60% lie above.
Technical profile
Type
Syntax
=mmRAYLEIGH(ModalValue)
Domain
0 ≤ RndNum < ∞
Mode
ModalValue
Parameters
ModalValue = b > 0
Remarks
If any argument is nonnumeric mmRAYLEIGH returns the #VALUE! error value.
Relationships
It is a special case of the Weibull distribution.
It is related to the Chi2, to the Exponential, and to the Normal variate.
mmRAYLEIGH(1)
mmRAYLEIGH(10)
Graphs
www.mm4xl.com
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243
mmSTUDENT(Degrees)
Example
=mmSTUDENT(6) can equal 0.750778794.
Applications
Also called the Student’s t, this is a distribution used to model events for which we have a mean but not a
standard deviation (as in most cases). It could be blood pressure, amplitude of noise, financial returns during
normal times, small samples arising in statistical quality control, and more.
It is bell-shaped with peak at zero like the Normal distribution. However, the spread of values around the
mean is heavier than that of the Normal distribution, which means the Student distribution attributes more
probability to extreme values than the Normal distribution does. As the degrees of freedom get large, the t
distribution gets closer to the standard normal distribution. When the degrees of freedom are more than 30
the Normal approximates the Student distribution. In a way, we can think of the Normal distribution as a
special case of the t-distribution appropriate when sample sizes are large.
How to use
Say we are modeling the weight of biscuit boxes. In order to measure the accuracy of production, we select
15 boxes from each production lot and measure an average weight of 720 grams with standard deviation
equal to 25 grams. The formula below produces t values that can be used to simulate box weights. It is a
two-step process. Step 1: the formula below produces a t value:
=mmSTUDENT(14)
Step 2: the obtained t value is used within the TDIST function, built in to MS Excel, in order to simulate the
average box weight. If this falls outside certain limits it could require the production supervision to reject the
box, and rejections produce costs that management dislikes. The following formula returns weight in the
range 720 plus or minus 25, according to the t distribution:
=720-((25*mmSTUDENT(14))/Sqrt(15))
Technical profile
Type
Syntax
=mmSTUDENT(Degrees)
Domain
Mode
0.
Parameters
Degrees = v > 0, an integer = Sample size – 1
Remarks
If Degrees is nonnumeric mmSTUDENT returns the #VALUE! error value.
Relationships
It is related to the Chi2 and to the Normal variate.
mmSTUDENT(6)
mmSTUDENT(60)
Graphs
www.mm4xl.com
244
mmTRI(Lower, ModalValue, Upper)
Example
=mmTRI(-2, 0, 3) can equal 1.538490851.
Applications
This is one of the most commonly used distributions. It models events for which the distribution is unknown
and thought to be asymmetric; for example, it could be the cost of a project, the time to complete a task, or
the price of a good.
mmTRI is a very simple and self-explanatory distribution without theoretical justification. It is useful in many
situations where a simple and intuitive understanding, as well as flexibility, is of great importance.
How to use
Say we are modeling the long-term profitability of a new product and we need an estimate of our market
share. We assume that future market share will be in the range 20%-70% with the most likely value being
40%. The formula below helps to model this instance:
=mmTRI(0.2, 0.4, 0.7)
Copy the formula above in 100 cells. You will find that it produces values in the range 20%-70% and the
most likely value (or the average, if the mode cannot be computed) will be around the desired 40%.
Technical profile
Type
Syntax
=mmTRI(Lower, ModalValue, Upper)
Domain
Lower ≤ RndNum ≤ Upper
Mode
ModalValue.
Parameters
ModalValue = the mode
Lower = lower limit
Upper = upper limit
Remarks
If any argument is nonnumeric mmTRI returns the #VALUE! error value.
If Lower >= Upper OR Lower > ModalValue returns the #VALUE! error value.
Relationships
None.
mmTRI(-2, 0, 3)
mmTRI(10, 30, 100)
Graphs
www.mm4xl.com
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245
mmUNIFORM(Lower, Upper)
Example
=mmUNIFORM(-1, 1) can equal -0.073249459.
Applications
Also called Rectangular Continuous distribution, this is the distribution of choice when dealing with a variable
bounded by a known minimum and maximum value, and all values in between have equal likelihood. It is
used to model events such as the defective items in a lot, the generation of random numbers, the estimation
of a competitor’s bid, and more. It becomes very useful when we have an idea of the range of the variable
and no clue about its most likely value.
How to use
Say we are modeling the financial sheet of a new store, and we are wondering about the price of a series of
products. In the area surrounding the new store one of the items in our list is sold for a minimum price of
$4.80 and a maximum of $9.50. We know our price will be in this range too, but we are unsure about the
actual final price. The formula below can help to model this instance:
=mmUNIFORM(5.80, 9.50)
Technical profile
Type
Syntax
=mmUNIFORM(Lower, Upper)
Domain
Lower ≤ RndNum ≤ Upper
Mode
Undefined.
Parameters
Lower = lower limit of the range
Upper = upper limit of the range
Remarks
If any argument is nonnumeric mmUNIFORM returns the #VALUE! error value.
Relationships
None.
mmUNIFORM(-1, 1)
mmUNIFORM(10, 100)
Graphs
www.mm4xl.com
246
mmWEIBULL(Life, Shape)
Example
=mmWEIBULL(1, 5) can equal 0.661022544.
Applications
This is a distribution often used to model failure time (lifetime expectancy), fatigue and fracture, as well as
distributions of physical quantities, such as wind speed. Some authors mention the employment of the
Weibull distribution to model the “years to failure for a business”.
How to use
Say our company distributes sodas through dispensers placed in crowded areas. On average, after 90 hours
a machine needs maintenance. Without maintenance the machine stops working and must be reset before
being put back in service, which carries higher costs. We are modeling a project to decide whether to
increase the number of machines or not. The formula below can help to model the time when a machine
enters the critical time for maintenance:
=mmWEIBULL(1.3, 93)
The chart below shows that 61.7% of the machines of our example will require maintenance within 90 hours.
Attributing the correct values for Life and Shape, the parameters of the Weibull distribution, is not always
easy. We suggest you use the Fit data option available in Risk Analyst in order to estimate reasonable
parameters from existing data.
Technical profile
Type
Syntax
=mmWEIBULL(Life, Shape)
Domain
0 ≤ RndNum ≤ ∞ ; generates positive numbers only
Mode
If Shape ≥ 1 then = Life ⋅ ⎛⎜⎜1 − 1 ⎞⎟⎟
Shape
⎝
1
Shape
⎠
If Shape ≤ 1 then = 0
Parameters
www.mm4xl.com
Life = b > 0
Shape = c > 0
8. Risk Analyst
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Remarks
If any argument is nonnumeric mmWEIBULL returns the #VALUE! error value.
Relationships
It is related to the Exponential, Rayleigh and Extreme Value variate.
mmWEIBULL(1, 5)
mmWEIBULL(10, 5)
Graphs
www.mm4xl.com
248
Probability Functions
These are the probability functions built into Risk Analyst. They can be used from the sheet like any other
function. They return the probability of occurrence of an event, according to the arguments specified in the
function.
When the argument CumulProb is set to TRUE they return the cumulative probability of occurrence.
When the argument CumulProb is set to FALSE they return the probability of occurrence.
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mmBETAc(Probability, Mean, StDeviation, [Optional: CumulProb])
mmBETAGENc(Probability, Mean, StDeviation, [Optional: Lower], [Optional:
Upper], [Optional: CumulProb])
mmBINOMIALc (Probability, Ntrials, PSucc, [Optional: CumulProb])
mmCHI2c(Probability, Degrees, [Optional: CumulProb])
mmERFc(Probability, Mean, [Optional: CumulProb])
mmERLANGc(Probability, Mean, Phases, [Optional: CumulProb])
mmEXPONc(Probability, Mean, [Optional: CumulProb])
mmEXTVALc(Probability, ModalValue, StDeviation, [Optional: CumulProb])
mmGAMMAc(Probability, Scale, Shape, [Optional: CumulProb])
mmGEOc(Probability, Trials, [Optional: CumulProb])
mmHYPERGEOc(Probability, Defects, Sample, Universe, [Optional: CumulProb])
mmINTUNIc(Probability, Lower, Upper, [Optional: CumulProb])
mmINVGAUSSc(Probability, Mean, Scale, [Optional: CumulProb])
mmLOGISTICc(Probability, Mean, StDeviation, [Optional: CumulProb])
mmNEGBINc(Probability, Failures, Successes, [Optional: CumulProb])
mmNORMALc(Probability, Mean, StDeviation, [Optional: CumulProb])
mmPARETOc(Probability, Location, ModalValue, [Optional: CumulProb])
mmPARETO2c(Probability, Location, ModalValue, [Optional: CumulProb])
mmPOISSONc(Probability, Mean, [Optional: CumulProb])
mmRAYLEIGHc(Probability, ModalValue, [Optional: CumulProb])
mmSTUDENTc(Probability, Degrees, [Optional: CumulProb])
mmTRIc(Probability, Lower, ModalValue, Upper, [Optional: CumulProb])
mmUNIFORMc(Probability, Lower, Upper, [Optional: CumulProb])
mmWEIBULLc(Probability, Life, Shape, [Optional: CumulProb])
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8. Risk Analyst
249
Sources
S. Christian Albright, et al
Data Analysis and Decision Making with Microsoft Excel
Duxbury Press; 2 edition, 2002
N. Balakrishnan and V. B. Nevzorov
A Primer on Statistical Distributions
John Wiley & Sons, Inc., 2003
Karl V. Burg
Statistical Distributions in Engineering
Robert T. Clemen
Making Hard Decisions: An Introduction to Decision Analysis
Duxbury Press; 2 edition, 1997
Committee E-11 on Quality and Statistics
Manual on Presentation of Data and Control Chart Analysis
ASTM International, 2002
Merran Evans, Nicholas Hastings and Brian Peacock
Statistical Distributions, Second Edition
John Wiley and Sons, Inc., 1993
M. Granger Morgan and Max Henrion
Uncertainty
Ronald A. Howard and James Matheson
The Principles and Applications of Decision Analysis (2 volumes)
Palo Alto, CA. Strategic Decion Group, 1983
Kellie B. Keeling and Robert J. Pavur
“Numerical accuracy issues in using Excel for simulation studies “
Proceedings of the 2004 Winter Simulation Conference
Koller, Glenn R.
Risk Assessment and Decision Making in Business and Industry: A Practical Guide
CRC Press Llc., 1999
Philip Kotler
Marketing Decision Making: A Model-Building Approach
Holt, Rinehart and Winston, Inc., 1971
Dennis V. Lindley
Making Decisions
Wiley, NY, 1985
George E. Monahan
Management Decision Making: Spreadsheet Modeling, Analysis, and Applications
Christopher Z. Mooney
Monte Carlo Simulation
Sage Publications, Inc., 1997
Howard Raiffa
Decision Analysis
Addison-Wesley, 1968
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250
David C. Skinner
Introduction to Decision Analysis
Probabilistic Publishing, 2001
E.M. Scheuer and D.S. Stoller.
“On the generation of normal random vectors.”
Technometrics 4:278-281, 1962.
Harrison M. Wadsworth, Jr., Editor
Handbook of Statistical Methods for Engineers and Scientists
The Mcgraw-Hill Companies, 1990
Nancy Weida and Ronny Richardson
Operations Analysis Using Microsoft Excel
Brooks/Cole, 2001
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8. Risk Analyst
251
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252
9. Decision Tree
Decision Tree in a Nutshell
Decision trees provide a framework for analyzing decision problems that involve uncertainty. They present all
important aspects of the problem in a concise and structured pictorial representation, showing decision
alternatives, expected outcomes, probabilities of occurrence, and chronological order of events.
Common problems in marketing management approached with decision trees include new product launch,
marketing research go/no go, investment planning and allocation, pricing issues, strategy selection, and any
other important decision taken frequently that may put the business at risk, though not in a life or death
situation.
Trees are made of nodes, decisions or chances, and nodes are made of branches. Filling out the tree
structure with values returns an analytical view of the decision problem. This view can help fact-and-data
driven managers to make better informed decisions because problems are framed in a well-organized
manner, they are evaluated objectively, and they can be easily modified.
Decision-makers can be risk adverse, neutral, or risk takers. Thanks to utility functions, MM4XL’s Decision
Tree, DTree, enables you to incorporate risk attitude into the model, so that the end result reflects the
propensity toward risk of the decision-maker.
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9. Decision Tree
253
An example as appetizer
There are many decisional situations when marketing managers can apply decision trees. The example we
introduce here is only one of the many possibilities, and it was drawn to help a company deciding which of
the identified alternative strategies to follow.
Note:
Background
While researching for fighting rheumatoid arthritis, scientists at VitroLab, a biotech company in Palo Alto,
California, discovered a molecule with a broad spectrum of applications. The case was investigated by the
New Business Development department and the assessment produced the alternative strategies
summarized in the table below (figures in millions of dollars).
VitroLab cannot afford to enter more than one business, so the question the board is called to answer is
which sector to enter, if any.
Surgery
IT partner
Coating
Sell out
IT alone
•
•
•
•
Investment
18
12
11
0.25
21
Expected sales
0 – 145
65 – 180
60 – 100
25 – 31
35 - 45
EMV
89.8
84.9
79.8
27.6
21.5
The new molecule is attractive to the surgical industry because it increases the performance of other
materials used in human implantations. To approach this segment would require new production
facilities and an expansion of the sales organization. The investment is estimated at $18 million.
Expected sales range between 0, should they fail to get FDA approval, and $145 million.
The molecule is appealing to the IT industry for replacing more expensive and less performing
components in storage media such as CDs and DVDs. VitroLab has solid relationships with several
medium and large IT companies, and the alternative routes they considered are two: either (i) to find
a partner, which would lower their financial exposure, or (ii) to enter the business alone. Having a
partner would require an investment of $12 million and could bring sales between $65-180 million.
Going alone raises the investment to $21 million but is expected to produce sales for $35-45 million
only.
The military industry found the molecule useful as coating material for preventing damage and
increasing performance of parts exposed to such things as flying, boating, and drilling objects. To
enter the business VitroLab need production and logistic facilities for an investment of $11 million
and could expect sales in the range $60-100 million.
Finally, VitroLab considered out-licensing the molecule for a value estimated between $25-31 million.
What would you do?
Discussion
We have distinguished three investor profiles: risk averse, neutral, and risk taker. VitroLab’s board is
discussing a challenge the company can basically afford, and they are also taking into account selling the
molecule. This lets us speculate that they are at the low end of the risk scale, although they are ready to take
some risk. We developed the tree below to identify the most appealing investment for this moderately risk
averse company, which is the investment with the largest Expected Monetary Value (EMV).
EMV can be interpreted as a weighted average of the outcomes of an event. For example, the branch
Coating paint was assessed as to return with 60% probability of Great sales results, estimated at $100
million; Good sales results ($80 million) with 30% probability, or Poor sales ($60 million) in 10% of cases.
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254
The sum of probabilities is 1 and the EMV of the branch, $79.0 million, is obtained with the sum of the
weighted monetary values times their probability of occurrence minus the initial investment required for the
venture.
In other words, EMV is assuming that if we, for instance, pay a ticket of $11 to spin a wheel and in 60% of
cases we win $100, and so on according to the values we used before, in the long-run we win $79. DTree
applies consistently the concept above and its output result consists of a structured and utilitarian
comparison of all available possibilities.
Recommended strategy
Following the path of the branch recognized as TRUE we find that our example suggests entering the
Surgery business, although it is supposed to produce lower revenue and to run a higher margin of risk (due
to the possibility of making zero sales if FDA does not approve the molecule use). Indeed, this is the strategy
that is supposed to return the largest payoff among the alternative options. This is, however, a challenging
venture associated with a considerable level of uncertainty. What if we were not really ready to take on all of
this risk? In other words, if we were to act more conservatively, which would be the most appealing strategy
to follow?
Great
Coating paint FALSE
-11
Tip:
To copy a tree in Word, Power
Point or in any other Windows
applications, select the tree with
the mouse and press Ctrl+C, to
store the tree in the clipboard.
Go to Word, for instance, select
the place where you want to
insert the tree, select menu item
Edit>Paste Special, and select
Graphic in the form that
appears.
89.0
0.0%
30.0%
80
10.0%
60
69.0
0.0%
49.0
0.0%
Coat
79.0
Good
Poor
65.0%
130
Approved
86.7
25.0%
Good
65
10.0%
Poor
40
Great
70.0%
0
Yes
Surgery
TRUE
-18
111.9
45.5%
46.9
17.5%
21.9
7.0%
FDA Approval
81.6
70.0%
125
Approved
85.3
20.0%
Good
60
10.0%
Poor
40
Great
85.0%
0
Yes
30.0%
0
No
Take less risk
We can tell DTree to take into
account the investor’s attitude
toward risk. To take less risk, we
imposed on the example above
a Risk attitude index that makes
the selection criteria more
cautious. The lower the index
the more risk averse the model,
and vice versa. In the following
sections of this chapter there is
more to read about how to take
into account the investor’s
attitude toward risk.
60.0%
100
41.8
5.1%
21.8
2.6%
Rejected
69.8
15.0%
0
No
New Molecule EMV
106.8
17.9%
-18.2
4.5%
Best Deal
81.6
10.0%
150
138.0
0.0%
Int'l
115.0
65.0%
Good
130
25.0%
Poor
110
118.0
0.0%
98.0
0.0%
Great
International
Find partner TRUE
-12
30.0%
0
Partner
79.3
40.0%
85
National
64.0
30.0%
Good
75
30.0%
Poor
65
Great
National
IT fiber
FALSE
0
70.0%
0
73.0
0.0%
63.0
0.0%
53.0
0.0%
IT Fiber
79.3
Great
60.0%
45
24.0
0.0%
We used R equal to 84 to draw
FALSE
Alone
Go alone
-21
21.5
the tree below and the best
30.0%
19.0
Good
40
0.0%
decision shifted from the risky
10.0%
14.0
Poor
Surgery venture to the less
35
0.0%
30.0%
30.8
Great
remunerative and yet still
31
0.0%
FALSE
Sold
rewarding
Coat
business.
Sell out
-0.25
27.6
According to the common sense
50.0%
26.8
Good
27
0.0%
of a risk averse decision-maker
20.0%
24.8
Poor
this can be seen as a
25
0.0%
reasonable alternative decision. Indeed, it requires the lowest investment among the three most
remunerative strategies, it is estimated to provide a reasonable sales level, and it does not incur the risk of
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9. Decision Tree
255
loss. The IT strategy was less appealing to the model because it implies a higher degree of uncertainty due
to the fact that this branch requires 2 decisions to be made: (1) whether to enter the market, and (2) whether
to enter it with a partner or not. The higher uncertainty coupled with a rather low expected value for the IT
alone strategy made this option less appealing then the Coat one.
Great
Coating paint TRUE
-11
60.0%
100
89.0
60.0%
30.0%
80
10.0%
60
69.0
30.0%
49.0
10.0%
Coat
77.9
Good
Poor
65.0%
130
Approved
78.7
25.0%
Good
65
10.0%
Poor
40
Great
70.0%
0
Yes
Surgery
FALSE
-18
111.9
0.0%
46.9
0.0%
21.9
0.0%
FDA Approval
70.7
70.0%
125
Approved
78.0
20.0%
Good
60
10.0%
Poor
40
Great
85.0%
0
Yes
30.0%
0
No
New Molecule EMV
106.8
0.0%
41.8
0.0%
21.8
0.0%
Rejected
54.6
No
15.0%
0
International
30.0%
0
-18.2
0.0%
Best Deal
77.9
10.0%
150
Int'l
114.2
65.0%
Good
130
25.0%
Poor
110
Great
Find partner TRUE
-12
National
FALSE
0
40.0%
85
National
63.6
30.0%
Good
75
30.0%
Poor
65
70.0%
0
73.0
0.0%
63.0
0.0%
53.0
0.0%
IT Fiber
75.8
Great
Go alone
FALSE
-21
Poor
Great
FALSE
-0.25
60.0%
45
24.0
0.0%
30.0%
40
10.0%
35
19.0
0.0%
14.0
0.0%
Alone
21.4
Good
Sell out
118.0
0.0%
98.0
0.0%
Partner
75.8
Great
IT fiber
138.0
0.0%
30.0%
31
30.8
0.0%
50.0%
27
20.0%
25
26.8
0.0%
24.8
0.0%
Sold
27.5
Good
Poor
Good modeling is a matter of exercising logical reasoning. The great advantage of having such models
available is that managers can easily and quickly change scenarios to look at the same issue from different
perspectives.
The more accurate the information used for building the tree, the more the result of the analysis will be
shared and supported by the decision makers, often a team of people with different backgrounds.
At first, the whole topic of decision analysis may seem hard to master. However, believe us, it is worth the
effort!
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256
How To Run DTree
Building decision trees is a loop activity made up of four phases:
1.
2.
3.
4.
Plan the model
Gather the data
Create the tree
Interpret results
Phase 1 is a matter of objectives and of creative thinking. Decision trees can handle both simple and
complex problems. The more complex the issue the more planning is required.
Phase 2 often involves gathering survey data, educated guessing, and creating simulation models.
This section deals with phase 3. We must say that making decision trees with DTree is really very easy. We
suggest that you spend time learning the different options the tool offers and how to build meaningful
models.
Finally, in phase 4, interpreting the tree output provides managers with feedback information, which may be
used for adapting and improving the model, and the loop for building a solid tree starts again.
Create a new tree
To start DTree, on the floating toolbar, click the button shown here and a new tree is added to the
selected cell as shown in the picture below.
A tree is made of graphic objects, formulae, and user inputs. Clicking on
any of the graphic elements opens a form. In the picture to the right we
see three items: the label and the line open the form Tree Settings while
the triangle (end node) opens the Decision Tree form.
To assign a meaningful name to the tree, click on the label, type the text you wish in the Tree name field of
the window that pops up, and click OK.
Add and modify a tree node
Click on the end node and the Node Settings window pops up.
Select one of two node types (also called arches), and click OK.
In our example, we accept the default option and click on OK to
add a Chance node with two branches to our tree above, which
will then look like the one below. Type some text in the box Node
label if you want to assign a custom name to the node. Otherwise,
the default label Chance is shown.
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9. Decision Tree
257
Each branch can be modified. Click on either the label or the line of My 1st Branch (we changed the label
text) and the form below pops up. Beside changing label text, there are three options available in this form:
the branch can be moved upward or downward, or it can be deleted.
To change the type of an existing node, click on the shape and
select the appropriate type in the window shown below. When a
colored shape is clicked the buttons on the upper side of the
form are activated. These four basic options are very useful
particularly when working with large trees.
To copy one or more branches select the first shape of the area
you are interested in and click the Copy button (see the form
above). The selection is now saved in Excel’s clipboard. Select
the shape where you want to attach the copied selection and click Paste. If you want to remove one or more
branches select the first shape and click Delete in the form above. The Collapse button is particularly useful
when printing large trees and we are only
interested in a small part of it. Selecting one
shape and clicking Collapse hides the unneeded
tree section behind the shape we selected. An
example of collapsed tree is shown to the right.
Click the + sign to enlarge the tree to its original
size.
The Add branch button in the Node Settings form is used to add new branches to an existing arch. This is a
straightforward operation done simply by entering an integer number in the form that appears and clicking
OK. The number of branches that can be added to the same node is limited to 30, which is well beyond the
maximum number of branches required in most real-life trees.
That’s it! These are the basic operations for shaping decision trees with the help of DTree.
Decision path
Technical details regarding tree settings can be found in the Technicalities section of this chapter. In this
section we focus on the tool functionality.
After the graphic appearance of the tree is shaped, click on the tree label (column A in the picture above) to
display the Tree Settings form. This is where you select the kind of analysis to perform. Enter the tree label in
the Tree name field.
DTree maximizes Expected Monetary Value (EMV) by default, as shown in the Optimum path list box.
Alternatively you can choose to Minimize EMV or to apply naïve multiplicative formulae.
Select the checkbox Only tree, no math to
remove all formulae from the tree and only
leave the graphical shapes on sheet.
Click on the Delete tree button to remove a
tree from sheet. Be careful, because once
removed a tree cannot be retrieved from the
basket.
More details about DTree reports and utility
functions can be found in later sections of
this chapter.
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258
Anatomy of a Decision Tree
MM4XL’s DTree allows you to draw two main types of trees: naïve trees and decision trees. Both use the
same graphic structure, but the cell contents vary significantly. In all, there are ten different types of trees
available, which cover most of the decision problems managers may be challenged with. The tree below,
created with the no math option selected, synthesizes all the possible trees you can draw with DTree.
Naïve trees
No Math
There are 2 kinds of naïve trees:
multiplicative trees and blank trees.
These are trees are not commonly
cited in decision analysis books,
because they do not really apply any
appreciable model to the data. They
are included in the tool as a graphical
aid to MM4XL users, who can this way
draw effective trees in a quick and
easy manner.
Naïve
Multiplicative
DTrees
Blank tree (no math)
Expected value
Exponential
Utility
Expected utility
Certainty equivalent
Maximize
(profit)
Logarithmic
Utility
EMV
Expected value
Blank trees are the most naïve kind of
tree in DTree. They show only the
graphical structure without figures.
They can be used when describing
processes,
strategic
alternatives,
reasoning paths, and the like.
Exponential
Utility
Expected utility
Minimize
(cost)
Multiplicative tree
When using multiplicative trees the value in the cell under the tree root (cell A8 in the picture below) is
multiplied according to the percentage values in the upper cell of each branch. For instance, the value 21200
in cell B4 is obtained by multiplying 212000 times 10% (A8*B3). The value in C2 is found by multiplying
21200 in cell B4 times 23% in C1, and so on. The end values show the overall size of one branch in
percentage.
If we use the example of a population of 212,000
individuals, 10% of whom like the new product
concept and 23% of whom are ready to buy it.
The overall percentage of people who like it and
are ready to buy is equal to 2.3% of the original
212,000, as shown in cell D2.
Multiplicative trees can be useful for
summarizing target segmentations, geographic
splits, sources of sales, development paths,
alternative decisions, etc.
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9. Decision Tree
259
Decision trees
Decision or probabilistic trees are made up of a graphic structure and formulae. Details about the latter can
be found in the Technicalities section. There are three classes of graphic elements in a DTree:
1. The tree root
2. Tree nodes
3. Node branches
Let us use an example for purposes of explanation. The tree below analyzes the decision whether to bet $5
at the horse races. There is a 1% probability of winning $100 or losing all. When maximizing the expected
value criteria, one would expect the gambler to lose $4 in the long run (cell C4), so betting in this instance is
not a value maximizing decision.
The tree root is essentially a label that shows the main idea of the project. It can be modified, as with any
other label in the tree, by clicking on it and entering the desired text in the box that appears.
Chance node
Node branch
Tree root
End node
Decision node
Click the tree root, cell A7 in the picture above, to determine what kind of tree to draw. There are three
options: Maximize, Minimize, and Multiply. The example above is a case where the expected monetary value
(EMV) is maximized.
Decision node
Decision nodes (green squares) indicate a time when a decision has to be made. In our example the
decision is whether or not to bet. If we bet we incur a payment of $5 (cell B4) otherwise it costs us nothing
(cell B10). The Boolean value in cell B9 is set to TRUE meaning that the Don’t bet branch is the most
appealing one according to the EMV criteria, and the green value in cell B8 shows the payoff value, which
corresponds to the payoff of the branch with the highest expected value.
Indicates whether this
branch was chosen
Node name
Decision node
Branch name
Expected value
at this node
Branch value
The node above indicates we either bet $5 or do not bet at all. Given that this event implies a negative
return, DTree identifies the lower branch, Don’t bet, as the option that maximizes the payoff and the Boolean
value in cell B9 is set to TRUE. This is a very reasonable suggestion according to the very low probability of
success implied with the bet. On the other hand, if we were to choose among projects that had a cost for us,
we would have minimized the path and DTree would have identified the opposite branch as true.
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260
Chance node
Chance nodes (pink circles), sometimes also called event nodes, represent uncertain events and their
probability of occurrence. In our example there is a 1% probability (cell C1) of winning $100 (C2) and 99%
(C5) probability of losing all (C6). The sum of the probabilities of a chance node must add up to 1, otherwise
the formulae return an error.
Probability of this branch
Node name
Chance node
Expected value at this node
Payoff of this path
Branch name
Value of this branch
Path probability of
this specific path
End node
End nodes (blue triangles) indicate the end of a branch and show its payoff value (cell D5) and probability of
occurrence (cell D6). The probability is computed only when DTree recognizes the branch as the best
opportunity.
Optimum path
Click on the tree root and the Tree Settings window pops up. By changing the option set for the Optimum
path list box and clicking the OK button, you can define the kind of tree DTree draws. The default setting
maximizes the EMV of the decision. Alternatively you can minimize the path or simply chose a multiplicative
structure.
We maximize the path of the tree when we go for profit and we minimize it when we analyze costs. More
details about paths can be found in the Technicalities section. The multiplicative rule is explained in the
Naïve trees section.
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9. Decision Tree
261
Anatomy of a DTree Output Report
When your tree is complete, click on the Print report button in the
Tree Settings window and the form to the right appears. Select a
cell in the sheet where you want to start printing the report, check
one or more options in the Report frame, and click on OK.
When all options are selected, DTree returns the table and the
three charts shown below.
Risk profile
When the Risk Profile option in the form above is selected, DTree prints
the table to the right, which summarizes the payoffs and probabilities of
the selected profiles, and draws the Optimum path chart shown below. In
the table, one profile corresponds to one branch or to the joint display of
several branches that reached the same payoff and for this reason were
identified as optimal solutions. When several selected branches have the
same profile they are grouped together in the table and are shown as one
single profile.
In our example there are seven profiles. Profile 1 shows a 4.5%
probability the project will have a negative return of, say, $18 millions, and
there is a 2.55% probability it will return $21.8 millions. The sum of (value
* probability) for all profiles returns the Mean expected value of the
project, $20 millions in our example.
50%
MM4XL - Decision Tree Risk Profile Report
Tree: New Molecule EMV of VitroLab.xls
Created on 19.05.2003 at 00:42:12
Risk Profile
Profile #
1
2
3
4
5
6
7
Mean
Minimum
Maximim
Value
-18.2
21.8
21.9
41.8
46.9
106.8
111.9
81.6
-18.2
111.9
Probability
4.50%
2.55%
7.00%
5.10%
17.50%
17.85%
45.50%
45.50%
Optim um Path: New Molecule EMV
45%
The Optimum path chart shows graphically
the probability values associated with the
chosen profiles. When the Cumulative
profile and Scatter profile checkboxes are
selected in the form above, DTree draws
the two charts to the right, which are
intended as visual aids to interpreting the
probability associated with the projects.
Note that in order to draw the Cumulative
Probability chart the code writes 500 cells of
values in one column below the chart.
Therefore, be careful that you have not
stored data in the region of the sheet where
you have selected to print the chart
35%
30%
25%
20%
17.50%
17.85%
47
107
15%
10%
4.50%
5%
7.00%
2.55%
5.10%
0%
-18
22
22
42
112
Value
Optim um Path (scatter)New Molecule EMV
50%
45.50%
45%
40%
Probability
Charts
Probability
40%
35%
30%
17.85%
25%
20%
17.50%
15%
10%
5%
7.00%
2.55%
4.50%
0%
-40
-20
0
20
5.10%
40
60
80
100
120
Value
120%
Cum ulative Probability: New Molecule EMV
Cumulative
Probability
100%
80%
60%
40%
20%
0%
-25
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1
14
27
40
53
Value
66
79
92
105
118
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Technicalities
Decision trees provide a framework for analyzing decision problems that involve uncertainty. They present all
important aspect of the problem in a concise and structured pictorial representation that shows decision
alternatives, expected outcomes, probabilities of occurrence, and chronological order of events. The
chronology of events goes from left to right, while the tree is solved from right to left using a process known
as rolling back method. Solving a tree means finding the best alternative according to the rules of the
decision set by the decision-maker.
Let us use the example of a company
wondering which of three marketing activities
should
be
run
to
support
the
commercialization of product X. In real life
one might expect to have a composite
portfolio of activities. We have simplified the
case for the sake of explanation. The table to
the right summarizes the four alternatives we
are considering: direct to consumer
advertising, a direct marketing campaign, an
in-store promotional campaign, or doing
nothing.
Implementing a DTC campaign would cost 18
millions dollars (cell B4), direct marketing
action would require 7 millions, then 9
millions and zero for the store promotion and
doing nothing respectively. Each of the
activities was coded to report great, good, or
poor results. DTC advertising, for instance,
has a 10% probability (cell C1) of having a
great return equal to $215 millions (cell C2),
50% probability of returning $160 millions,
and 40% probability of returning $100
millions. Analogous reasoning was used to
input figures in the other three branches, and
the tree to the right is the result of the
exercise.
According to the rule of expected value maximization, DTree is suggesting to select branch number two (cell
B18), direct marketing action, as the most appealing alternative for the long-term, because this is the activity
that is supposed to produce the largest payoff, $150.3 millions. The second best alternative would be a
Promo action at $149 millions, and finally DTC advertising at $123.5 millions.
Expected monetary value can be interpreted as a long-term weighted average of branch values times the
corresponding probability. The interpretation of the above outcome should sound approximately like this “if
we run a large enough number of investments like the one depicted in branch DMarketing we can expect in
the long-run to have earned on average $150.3 million per project.” This kind of utilitarian reasoning applies
best to decisions that the company is frequently faced with, and it works best with important decisions that
require only a minor part of the company’s resources.
The same interpretation would be done when examining a decision concerned with a minimization problem,
such as selecting the less expensive project, but the terms of the evaluation would be, of course, reversed:
the lower the outcome value, the more appealing the alternative.
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9. Decision Tree
263
Assessing probabilities
One major issue newcomers to decision trees face is “how can I get the probability of an event?”. In other
words, how can I say that the DTC campaign will return $215 millions with a 10% probability, $160 millions
with a probability of 50%, and so on?
This is a legitimate question that cannot be answered by axiom. Ad hoc marketing research has traditionally
served managers when assessing potentials and probability of success, and it will keep doing so. Nowadays,
there are also other techniques gaining momentum among academics and practitioners interested in
assessing complex and multifaceted situations. One of these techniques is scenario simulation. We
recommend that the dedicated manager take a close look at how decision models can be set up and run with
the aid of simulation. By the time you have gotten interested in the technique, MarketingStat will be releasing
the tool you need for modeling absolutely first class decision models.
In general, a lot of previous knowledge on the part of the decision-maker goes into setting probabilities of
occurrence for future events, and this should be regarded as a positive aspect of decision trees. Allowing
managers to be involved in the decision is a good means for obtaining a complete buy-in to the project by
the decision-makers, often a team of individuals with different backgrounds. Another advantage of DTree is
that it brings people together and animates the discussion around a common issue. Massing forces may help
to assess probabilities and reach a solution more quickly.
Read Skinner (2001) for a very fluid introduction to decision analysis. It is a text written for practitioners.
Risk attitude
Decision-makers can behave in different ways when dealing with risk. In decision analysis we distinguish
three investor profiles: risk averse, risk neutral, and risk taker.
When the risk increases, people tend to avoid it in favor of the expected monetary value principle. For
instance, at the casino you are faced with the possibility of betting $1 on a number and eventually getting
$100 back. What do you do? Well, you could bet for fun. But what if you are told to bet $10,000 and win $10
million? Most probably the EMV principle will prevail and you will draw back. The venture is too risky and
does not make sense to you. For risk averse people, the curve of interest for ventures does not grow linearly,
but rather it grows on a declining level. On the other hand, the CEO of a bank may be attracted to increasing
returns and takes more risk, up to a certain point.
Utility
Risk Averse
Risk
Taker
Payoff
The picture above shows that the same monetary payoff has very different utility values for each of the three
investor profiles. Risk averse investors show a diminishing marginal utility for increasing payoffs, they are
ready to draw back from the venture, and sacrifice some EMV, in order to avoid a risky gamble. The marginal
utility for the risk taker increases with increasing payoffs. Finally, the risk neutral falls between the two and
shows a constant utility function.
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Utility functions
If you want to include your attitude toward risk in a decision analysis made with DTree, select the Use utility
function checkbox in the Tree Settings form that appears when you click on the tree root label. The utility
function along with the Risk attitude index (called R) describes the investor attitude toward risk, converting
EMV in expected utilities. DTree uses two utility functions: exponential and logarithmic.
Assessing one person’s or company’s utility function is done with a tedious loop of questions aimed at finding
tradeoffs that best reflect the investor’s attitude, to ultimately find the value that makes the decision-maker
indifferent between:
•
•
Obtaining no payoff, or
Having 50% probability of either winning R dollars or losing R/2 dollars.
For instance, we ask the marketing manager of company X to tell us the largest investment and loss she can
calculate for any of her projects’ portfolio? If she answers $-50,000 and $250,000, these are the boundaries
we use in the utility assessment. Then we ask the manager: would you prefer a certain payoff of $100,000
(we begin halfway between -50k and 250k) or would you rather go for the second option with 50% probability
of losing $50,000 and 50% probability of winning $250,000 on this project? If she says she will take the
certain $100,000, we now know that her indifference value is below $100,000. We now ask: what about a
certain payoff of $50,000 versus a gamble with 50% probability of losing $50,000 and 50% of winning
$250,000? This time the manager chooses to gamble. The loop continues, exploring values between
$50,000 and $100,000 till we find the value that makes the investor indifferent between gambling and
accepting the given payoff, which is called indifference value. At this point we have enough information to
depict on a chart the curve representing the utility function of the marketing manager. This curve can also be
used for future application as well.
It goes without saying that applying this process to estimate the utility function of a complex organization can
be extremely challenging. Moreover, the process is tedious and not easy to understand. For these reasons
classes of ready-made utility functions have been developed, which have the advantage of requiring only
one adjustable value, called the risk tolerance value or R.
Risk Tolerance
How much risk a decision-maker is ready to take before he or she gives up the venture is measured with the
Risk attitude value R. R is the only measure needed for assessing one person’s risk attitude, and it must be
larger than zero. The larger R is the less risk averse the decision-manager is.
There are several ways to determine the right R value for a decision-maker, a single person or a company,
ranging from educated guessing to linearly optimized models. In all cases we look for the value of R that
makes the decision-maker indifferent between the tradeoffs of:
•
•
Obtaining no payoff, or
Having 50% probability of either winning R dollars or losing R/2 dollars.
Fortunately, R can be defined in a straightforward way with the help of common sense. For example, if we
are indifferent between launching a direct marketing campaign where there is 50% probability of either
winning $100k or losing $10k, and not betting at all, our R value is approximately 100k. The practice
suggests that wealthier investors have larger values of R.
1.2
Exponential utility function
Exponential Utility Curves
1
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R=50
R=100
0.8
Utility
Perhaps the most common kind of utility function is the
exponential one, defined by U ( x ) = 1 − exp(− x / R ) ,
where R is the Risk attitude coefficient of the decisionmaker that can be set in the Tree Settings form (click on
the tree root label). Small values of R indicate risk
aversion. As R increases the risk tolerance of the
decision-maker increases as well. The picture to the right
shows four typical exponential utility curves.
9. Decision Tree
R=200
0.6
R=400
0.4
0.2
0
0
100
Value
200
300
400
265
Logarithmic utility function
Logarithm ic Utility Curves
Utility
Investors with large amounts of funds available may find risk
more attractive (decreasing risk aversion) than other less
wealthy individuals. Such situations are typically handled
with a logarithmic utility function of the form
U ( x ) = ln ( x + R ) .
R=50
R=20
R=10
When the EMV is maximized, DTree adds R to the
expression in order to not take the logarithm of a negative
R=0
number, which would return an error. Should you get a
0
100
Value
negative value, use a large enough R value so that x+R is
not less than zero. The picture above compares logarithmic
utility functions. Changing the value of R simply shifts the curve up the Utility axis.
200
300
400
Expected monetary value (EMV)
Expected monetary value is interpreted as a long-term weighted average of branch values times the
corresponding probability. This kind of utilitarian reasoning applies best to decisions that the company is
frequently faced with, and it works best with important decisions that require only a minor part of the
company’s resources.
When the investment is substantial, investors may become less inclined to take risk. In this case the EMV
can be computed in a way that takes the attitude of the investor into account. To do so, in the Tree Settings
form set a Risk attitude index (R) larger than zero and lower than the maximum value at risk in the model.
The final decision will be more conservative or more adventurous, depending on the level of R you set.
Expected utilities
Expected utilities are a transformation of monetary values into utility values, according to the decisionmaker or company risk tolerance. EU embodies the concept that the utility of money grows at a slower rate
than the value of money, for instance, the utility of $10 for a homeless person and for a millionaire.
There are situations when investors do not behave according the EMV maximization. This shift in behavior,
although not completely explored yet, has found the agreement of many researchers that in certain situations
investors are expected utility maximizers. For example, how many of us do not buy car collision insurance for
a new car? We know the premium is possibly much higher than the cost of damage, and nevertheless we
buy. This is not a behavior that maximizes EMV, yet it is fully reasonable. DTree allows you to take such
aspects into account.
The certainty equivalent (CE) is that amount of money one would accept to avoid the risk of the venture. If
we had to choose one of two options, say, entering the business or saving X dollars by not entering it, what
is the value of X, the CE of the risky venture, that would make us indifferent between the two options? In this
sense, CE’s help to determine the value of projects as risk increases. DTree takes care of all the tedious
aspects of the computation and switches easily between values.
Tip:
Subtracting CE from EMV returns the risk premium, which is the price one is willing to pay in order to avoid
risk. This could be useful to the marketing manager opting for running a marketing research study, as long as
the cost of the study does not exceed the risk premium.
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Known problems
There are a few things users of DTree should be aware of:
1. The maximum number of branches that can be attached to one arch is 30.
2. The sum of probability values entered in a chance node must add up to 1, or 100%, otherwise Excel
returns an error displayed as #NV.
3. Row 64000 and columns GR of the Excel sheet are the last row and last column where you can
place a tree. After that row and column a message warns the user that it is not possible to create a
new tree.
4. The security level of Excel must be set either to medium or low, otherwise MM4XL cannot work. If
you experience strange symptoms, such as you do not see the MM4XL menu in the Excel menu,
select Tools>Macros>Security and make your selection in the Security level page. Then enable
Trust Access To Visual Basic Project on the Trusted Sources tab.
References
Baird, Bruce F.
Managerial Decisions Under Uncertainty: An Introduction to the Analysis of Decision Making
John Wiley and Sons, 1989.
Clemen, R.T.
Making Hard Decisions: An Introduction to Decision Analysis
PWS-Kent Publishing Company, 1991.
Cockett, J. R. B., and J. A. Herrera.
Decision Tree Analysis
Journal of the Association for Computing Machinery. 37: 815-842, 1990.
Kneale T. Marshal, Robert M. Oliver
Decision Making and Forecasting
McGraw-Hill Inc., 1995
Lilien Gary L., & Rangaswamy, Arvind
Morgan M. Granger, Henrion Max
Uncertainty, A Guide to Dealing with Uncertainty in Quantitative Risk and Policy Analysis
Oliver, Robert M., and James Q. Smith
Influence Diagrams, Belief Nets and Decision Analysis
John Wiley and Sons, 1990.
Precision Tree User Manual
Palisade
Raiffa, Howard.
Decision Analysis: Introductory Lectures on Choices Under Uncertainty
Addison-Wesley, 1968.
Skinner David C.
Introduction to Decision Analysis
Probabilistic Publishing, 1995
Winston, Wayne, L., and Albright, S. Christian
Practical Management Science
Duxbury, 2001.
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Marketing Manager for Excel – MM4XL© Software, Reference Manual 7.0
MarketingStat.com
268
Section 2: Analytical Tools
Analyze data for describing, inferring and finding relationships.
CROSSTAB
SAMPLE MANAGER
PROPORTION ANALYST
VARIATION ANALYST
DESCRIPTIVE MANAGER
CLUSTER ANALYSIS
SEGMENTATION TREE
GRAVITY ANALYSIS
(8)
Analytical (8)
Analytical
Strategic(9)
(9)
Strategic
•CrossTab
•CrossTab
•
Sample
Manager
•Sample Manager
Manager
•Proportion
•
Descriptive
Manager
•Descriptive Manager
•ClusterAnalysis
Analysis
•Cluster
•SegmentationTree
Tree
•Segmentation
•GravityAnalyst
Analyst
•Gravity
•VariationAnalyst
Analyst
•Variation
•BCGPortfolio
PortfolioMatrix
Matrix
•BCG
PortfolioMtx
Mtx
•McKinsey
•
Brand
Switch
•Brand Switch
•BrandMapping
Mapping
•Brand
•
Forecast
Manager
•Forecast Manager
•ProfileManager
Manager
•Profile
•QualityAnalyst
Analyst
•Quality
•DecisionTree
Tree
•Decision
•RiskAnalyst
Analyst
•Risk
CHARTS
&
MAPS
ANALYTICAL
STRATEGIC
(6)
Charts&&Maps
Maps(6)
Charts
•SmartMapping
Mapping
•Smart
Semantic
•Differential
•
4D
Map
•4D Map
•StackedCharts
Charts
•Stacked
•
Benchmark
Map
•Benchmark Map
•Project(Mind)
(Mind)Mapping
Mapping
•Project
Survey tools: Sample Manager, Proportion Analyst, CrossTab, Descriptive Analyst, Group Variation Analyst
Analysis is the starting point of the typical marketing cycle. It aims at gathering and analyzing relevant data for the
purpose of planning. When the data is gathered with ad hoc surveys MM4XL can help with:
- Planning the survey, with the goal of gathering solid data while saving money
- Analyzing the data and getting more information out of studies
Segmentation tools: Cluster Analysis, Segmentation Tree, Gravitation Analysis
Markets are said to be made of homogeneous segments. There are two main frameworks for segmentation in marketing:
- Independence techniques (cluster, factor, correspondence, discriminant)
- Dependence techniques (AID, CHAID, THAID, etc.)
The tools in this suite cover both groups and are written to help managers, not statisticians, running the appropriate
segmentation technique to different data arrangements, in order to obtain information they can act on.
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10. Gravitation Analyst
Gravitation Analyst in a Nutshell
William J. Reilly published a classic work in market analysis entitled The Law of Retail Gravitation. Inspired
by the formula for gravity, Reilly proposed that a similar formula could be used to calculate the point at which
customers will be drawn to one or another of two competing centers. In other words, Reilly's formula allows
us to determine in Km, for instance, the area within which an outlet is most likely to draw its customers. On
the map below, the heavy blue line delimits this area.
The MM4XL software tool Gravitation Analyst applies the Law of Retail Gravitation as originally postulated by
William J. Reilly. This analysis can be a great help to marketing and sales managers when segmenting
territories for assigning budgets, planning surveys, measuring advertising, circumscribing area test markets,
assessing performance, etc.
Gravitation Analyst lets users customize labels and it recognizes automatically whether to run a single or a
multi-city analysis. The map you see to the right is created using Excel and can be edited just like any other
Excel chart.
Note:
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271
How to run the Gravity Model
On the MM4XL floating toolbar, click this button
to display the window shown to the right.
Basically, you can accept the default values and simply
hit the OK button. However, you may want to assign a
custom title to your analysis, which will be displayed at
the top of the numerical report as the map title. You can
also choose to format map labels according to one of the
four available label styles.
The Hide data sheet checkbox is used to show or hide
the sheet, which holds the data used for drawing the
map. The Print map(s) checkbox is useful when you want to analyze more than 56 items. In fact, beyond
this limit Excel cannot display all points correctly on the map. Therefore, if you have more than 56 items,
clear this checkbox. But don’t worry if you forget, becauseMM4XL will do it for you automatically.
When you click OK, the tool will prompt you to enter the data for the analysis.
Data Input
Gravitation Analyst requires you to input three main kinds of data, as shown in the picture below: one column
of labels and two columns of values, the population size and the distance from the central item. As an
example, we will use the case of a hypothetical department store called Jumbo that sells toys and whose
management wants to determine Jumbo's gravitational retail area compared to six of its competitors located
in the same area.
The Single-Map Case
The map we saw above helps to clarify the concept. There is one central
item and all around it are spread, according to the distance value, the
peripheral items. In the table to the right, the first row corresponds to the
central item (Jumbo) and its distance value (column D) must be zero. The
third value (column C) is the size in squared meters of each store.
Tip
You can use either the store size in square meters
or the number of residents (population) in the area.
Read more about population in the Technicalities
section.
In our example, the range D2:D8 goes in the input field above. Simply select the range with the mouse and
hit enter.
A second window, similar to the one
above, requires you to enter the Size or
Population range (C2:C8) while the labels
range (B2:B8) goes in the third and last
window. Finally, hit OK to start the
analysis.
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The Multi-Map Case
Gravity Analysis
Gravity Analysis
Gravity Analysis
City C
Size : 345
Dist : 57.8=45%
Place E
City I
Size : 654
Dist : 17.0=30%
Size : 673
Place D
Size : 1233
Dist : 14.2=24%
Tow n C
Size : 9856
Dist : 34.3=22%
Dist : 69.4=37%
Place F
Size : 795
City D
Place B
124
Dist : 34.8=28%
Size : 128
Dist : 8.2=37%
Dist : 69.6=92%
City
G
234
Size : 265
Dist : 17.4=48%
Tow n A
785
Tow n B
Size : 6253
Dist : 31.9=26%
City H
City A
Size : 2
Size : 54
Size : 357
Dist : 43.7=57%
City F
Place C
Dist : 20.5=60%
Place H
City B
Size : 65
Dist : 88.4=65%
Place G
Size : 34
Size : 76
Dist : 18.1=72%
Dist : 43.7=56%
Tow n D
Size : 5987
Dist : 26.1=27%
City E
Size : 98
Dist : 20.6=61%
The same input process is followed for mapping several areas at once. The picture to the right shows how to
group the data for a multi-item analysis. Make sure the input data ranges are all of the same length (that is,
the y contain the same number of cells). In the sample above, for instance, the distance data corresponds to
the range E3:G11 and the other two ranges, B3:D11 and H3:J11, have exactly the same shape.
The multi-case analysis may result in a particularly useful chart for comparing shape and characteristics of,
for instance, several regions served by different sales persons. The picture above shows an example of map
comparison.
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Tip:
You can use the labels to record additional information to be displayed on the map, such as sales data,
number of employees, etc.
Data Output
It takes a few seconds for Gravitation Analyst to print the output of
your analysis. The table below was returned for our example.
Columns B, C and D reflect the user input. Column E shows the
break point beyond which customers are less likely to go shopping
to the central item. In column F the same values as in column E are
shown in percentages
All data shown in the table can also be found in the map. The map
title is from cell B11, which corresponds to the job title you entered
in the first window. The length of the dotted whiskers is proportional
to the distance values in column C. The bubble size is proportional
to the values in column D. Finally, the gravitational vertexes correspond to the values in column E.
Connecting all break points (or vertexes) on the map gives us a rough idea of the areas that may be
expected to be dominated by the central outlet mall.
All the data described above could also be shown in the form of the item label. The data is ordered on the
map from the center to the right, or counter-clockwise.
Technicalities
The likelihood that a city (or shopping center) will attract shoppers from the hinterland increases with the size
of the city (or shopping center) and decreases with distance from the center. Reilly's formula, below, yields
the break point between customers who will go to one center and those who will go to the other one, located
on an ideal line connecting the two.
d xj =
d ij
1+
In the formula, dij is the distance
between the two centers, Pi is the size of
the peripheral center, and Pj is the size
of the central one. Sometimes, however,
the definition of population is not a
straightforward one, so you can add
several groups together. For instance, if
your target includes drug stores,
prescribing doctors, and hospitals, add
them together. Each population could be
weighted (multiplied) according to such
factors as square footage, local tax level,
or any other variables you may consider
relevant.
Pi
Pj
Gravity Analysis
PlayLand
Size : 480
Dist : 586.8=52%
Chicco
Size : 200
Dist : 406.9=63%
Pollicino
Size : 900
Dist : 286.6=44%
Jumbo
560
Jumbo attracts
clients mainly
within this area
Toys R' Us
Size : 710
Dist : 446.9
=47%
WonderToy
In other cases, the population may be
Disneyland
Size : 290
expressed as the size in square feet of
Size : 620
Dist : 482.7=58%
Dist
:
438.6=49%
several competing outlets, as in our
example. Larger places attract more
people, so finding more goods and services available at the same location is a strong attraction for
customers. This fact can be taken into account, and it may make sense to do so, for supermarkets for
instance. But also Hi-Tech stores, casinos, restaurants and bars, discos, cinemas, and more can find this
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274
measure useful.
The distance can also be adapted. Indeed, you may consider using a functional distance instead of the
actual one. Functional distance could be the walking time, driving time, or the flying time that it takes
customers to reach a given place.
Finally, some criticisms raised against this technique. William J. Reilly expanded the gravity model and found
the law of retail gravitation. The gravity model, or the modified law of gravitation, takes into account the
population size of two places and their distance apart. Since (1) larger places attract people, ideas, and
commodities more than smaller places, and (2) places closer together have a greater attraction, the gravity
model incorporates both these features. Opponents of the gravity model say that the whole rationale behind
the model has not yet been confirmed scientifically, and it is only based on observation.
Tip:
For accurate reproduction of any geographic locations, we suggest that you visit www.mapquest.com and
see if you can find the map of the region(s) you are working with.
References to the Gravitation Analyst
O'Kelly, M.E.
Trade-area models and choice-based samples: Methods.
Environment and Planning A. 1999; 31(4): 613-627
William J. Reilly
The Law of Retail Gravitation.
New York, Knickerbocker Press, 1931.
Sen, A. and T.E. Smith
Gravity Models of Spatial Interaction Behavior.
New York Springer, 1995.
Isard, Walter et al.
Methods of Interregional and Regional Analysis.
Ashgate 1998, ch.6 ("Gravity and Spatial Interaction Models"), pp. 243ff.
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11. Cluster Analysis
Cluster Analysis in a nutshell
Cluster analysis is used for segmenting items or people in homogeneous groups. Myers (1996) noticed that it
is generally agreed that the most appropriate interdependence statistical techniques for segmenting markets
are those known as clustering methods. Anderberg (1973) wrote:
The value of exploratory cluster analysis is primarily in
the tendency for new arrangements of data units or
variables to suggest relationships and principles
previously unnoticed. The substantive results are not
the output of the computer but the new ideas prompted
in the analyst’s mind.
Dendrogram
Novo Nordisk
Sanofi
Basf
Boehring I.
Bayer
Warner Lambert
AHP
Lilly
J&J
Abbott
Schering-P.
SKB
BMS
Pharmacia
Pfizer
Aventis
Roche
Novartis
Glaxo
AstraZeneca
Merck
0
200
400
600
Index
800
1000
In marketing, segmentation needs arise often
linked to differentiation matters, which relate
to positioning and require data on behavior
and attitude. But it is also often used when
analyzing performance, for instance of
affiliate
companies,
points
of
sale,
distributors, etc.; for clustering satisfaction of
internal and external customers; and also for
treating profiles of products, companies,
geographic regions, and so on.
The many available clustering methods are divided into two main groups:
•
•
Hierarchical methods, which group data row by row and do not require you to specify in advance the
desired number of clusters.
Partitioning methods, which assign items to a user-defined number of clusters.
MM4XL makes available the most popular methods from each of the above groups, Ward’s clustering
method and Centroid method (also known as K-means clustering method), respectively. The former is
typically run first, to get an understanding of the data structure, and the latter method is used for refining the
clusters.
Note:
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How to run Cluster Analysis
On the MM4XL floating toolbar, click this button to display the window below.
In the Input range field select the range where
the input data is stored, and select an Output
range where you want to print the resulting output, starting
at the upper left cell. If your data set does not have row
and/or column labels, clear the corresponding option in the
frame.
The Normalize input data (standardization) option is
selected by default. More information about standardizing
data is provided later in this chapter.
Clicking on the K-means or Ward’s tab selects the
respective clustering method. For the K-means method
the Number of clusters is needed as input from the user.
The frame Termination Condition hosts two options for
stopping the cluster algorithm from reiterating. Find exact
solution stops when the best partitioning is reached, and
the default option is stopping the algorithm at the Best of
n iterations. Each time the algorithm runs, items are
assigned to a certain group and a new ratio (Inertia
Between Group) / (Inertia Within Group) is computed. The
highest ratio of all iterations is then chosen as the best
partition.
Tip:
The order of data entry changes the partition. This is due to the random start seed the cluster analysis uses.
Therefore, when working with the option Best of n iterations you should repeat the K-means several times
and choose the partition with the highest Trace(B) / Trace(W) ratio.
The Dispersion chart is a quick visual aid that shows how items are clustered in groups. Print cluster
numbers prints, in the first available column beside the input data set, a new column of numbers
corresponding to the cluster group each item belongs to.
The Ward’s method is very easy to run. You can simply
accept the default setting and click the OK button. But
you can also determine when and how to terminate the
algorithm reiteration. The first option, Automatically,
stops when all items are grouped in one cluster only.
Alternatively, you can stop the tool when the desired
Number of groups is reached. The third option stops the
algorithm when the desired Inertia level is reached. For
either of the latter two options, simply check the corresponding option and type an integer value in the input
box. MM4XL warns you if you make an incorrect entry.
Note:
Although the Find exact solution option produces the most accurate partition, it may take a long time to test
all re-arrangements of the input data. 10 items measured on 4 variables may take up to 1 minute. The time
grows exponentially as new items are added.
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What is segmentation?
The concept of market segmentation was first treated formally by Wendel Smith (1956). According to Smith,
the basic proposition of segmentation is that markets are made of segments that are relatively homogeneous
in terms of needs, wants, and offer.
Segmentation approaches
Myers distinguishes between two basic conceptual frameworks for segmentation:
•
•
Customer-based versus Product/Service-based segmentation
A priori versus Post hoc (a posteriori) segmentation
The former group belongs to dependence techniques, which use one or more independent variables to
explain and predict a dependent variable. Among the most common dependence techniques are AID,
CHAID, regression, and discriminant analysis.
The latter group belongs to independence techniques, which are typically used for grouping people or items
that are found to be similar in terms of one or more describing variables. Among the most common
dependence techniques are hierarchical clustering, partition clustering, and other multivariate analysis
methods such as factor analysis, correspondence analysis (see also the chapter on Brand Mapping in this
manual), and principal components analysis.
Segmentation procedure
Most segmentation studies follow a general procedure consisting of at least the following steps:
•
•
•
Select the segmentation variables
Select and run the segmentation methodology
Identify and describe segments
1. Select the segmentation variables
The selection of the appropriate kind and number of variables to be clustered depends on the ultimate study
goal. In most cases, however, two important issues arise:
•
•
How to handle variables measured on different scales?
How many variables to include in the model?
The available literature suggests handling the first issue by means of standardization. Cluster Analysis
performs Complete standardization, as opposed to Centering standardization, and it can be done by
selecting the checkbox Standardization in the user dialog. See also the Technicalities section for more
details on standardizing variables.
The number of variables to include in
Sales
US
EU
J
Others
GPs
the model can only be determined by
US
36%
the analyst using a trial and error
-41%
-93%
approach. In general, we suggest Europe
Japan
-34%
-65%
48%
beginning by selecting a data set
Others
6%
38%
16%
-61%
considered relevant for the cluster
General Practitioners
-12%
20%
13%
-18%
-57%
analysis, and running a Correlation Hospitals
12%
-20%
-13%
18%
57%
-100%
analysis to highlight relationships
between variables. Excel computes correlations in two ways: either with built-in functions (such as
=CORREL() ) or using the add-in Data Analysis in the Tools menu. We used the latter option to make the
table above, and the raw data we used can be found in the section An example: clustering company profiles.
The relationship here is measured by means of the Pearson’s Correlation Coefficient (for more information
about correlation coefficients press F1 in Excel and then type Correlation). Variables that do not seem to be
correlated to other variables in the data set can be thought of as having less differentiating power between
clusters, so they might be removed from the analysis. Punj and Stewart (1983) warn: A variable that is not
related to the final clustering solution, i.e. does not differentiate among clusters in some manner, causes a
serious deterioration of the clustering method.
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To be certain that you have removed variables that do not make a relevant contribution to the analysis, we
suggest that you remove all the apparently irrelevant variables and then run the cluster analysis. Then run it
again, adding back the first of the removed variables. Run it a third time adding back the second removed
variable, and so on for all non-relevant variables. If all partitions look the same you can safely conclude that
the removed variables do not make a difference to any of the clusters. The matrix above suggests that Sales
levels are positively correlated to the US and negatively to Europe. This means large companies have a
larger share of revenue in the US than in Europe. The same relation is found with GP’s and Hospitals. Large
companies make larger sales to hospitals than small companies do. Finally, companies with strong
penetration in Europe tend to be strong in Japan and Other markets. On the other hand, companies with
solid sales in the US tend to do little business abroad. So all the variables we used appear to be relevant to
the analysis.
2. Select and run the segmentation methodology
There is a wide range of methodologies available, and it is not always true that the most sophisticated
methods yield better results than simpler ones. Sometimes applying more than one method together is
recommended, and this is one reason why MM4XL makes available one of each of the most appreciated
techniques, K-means and Ward’s method, respectively.
In addition, we recommend Brand Mapping as a tool for segmentation. Read the chapter on Brand Mapping
for more details.
3. Identify and describe segments
Identifying and describing segments from a segmentation study is more of an art than a scientific practice.
The experience, expertise, and intuition of the analyst plays a primary role in the selection phase. However,
tools can be a significant help, and this chapter will show you how to take full advantage of the visual
inspection tools provided in Cluster Analysis.
The description phase is usually done with the support of contingency tables that describe the cluster
configuration in terms of the variables used for the analysis. As a descriptive aid the K-means prints a
Dispersion chart and a Summary table. The table summarizes the minimum, average, median, and
maximum values of each variable for each cluster. It is very useful for grasping quickly the main profile of
each group. The chart shows which item merged with its cluster and when it happened. The Ward’s method,
on the other hand, prints a dendrogram as a descriptive, visual aid.
Note:
Excel can display only a limited number of points on a chart, so our Dispersion charts cannot display more
than 255 items on the same chart. Fortunately, the Dendrogram chart does not suffer from this limitation,
because when it has more than 255 points it becomes an image.
An example: clustering company profiles
This section presents an example of cluster analysis with MM4XL. This example is intended simply to
describe the technique, and is hypothetical although the data is adapted from reliable sources. The goal of
the study described is classification of pharmaceutical companies, to highlight any relationships between
company size, geographic area, and market segments where the companies do business.
The raw data below are 1999 estimates that describe 21 large pharmaceutical companies in terms of:
•
•
•
Sales volume (.000US$)
Percentage of sales by company in various geographic regions (US, Europe, Japan, and Other
countries)
Percentage of sales by company split into market segments (General Practitioners, and Hospitals)
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Merck
AstraZeneca
Glaxo
Aventis
Pfizer
BMS
J&J
Novartis
Roche
Lilly
Pharmacia
SKB
AHP
Schering-P.
Warner Lambert
Abbott
Bayer
Sanofi
Boehring I.
Basf
Novo Nordisk
SALES
US
EU
J
OTHERS
GPs
HOSPITAL
17500
14700
13700
13200
12200
11700
10700
10600
9400
9400
9100
8500
8100
7700
7600
5700
4600
4300
4000
2200
2200
60
48
42
29
60
64
60
34
38
61
56
53
59
63
71
63
42
12
38
41
15
22
23
34
46
23
25
30
38
36
25
27
34
24
21
21
22
33
65
35
38
50
7
5
7
8
8
8
3
10
6
4
8
4
4
3
2
4
13
7
13
6
21
11
24
17
17
9
3
7
18
20
10
9
9
13
13
6
11
12
16
14
15
14
30
60
60
85
80
75
90
70
70
90
75
50
85
75
95
70
75
80
90
85
90
70
40
40
15
20
25
10
30
30
10
25
50
15
25
5
30
25
20
10
15
10
For this example we follow the Punj and Stewart (1983) suggestion of a 2-step clustering approach. They
recommend first running a hierarchical methodology such as Ward’s method, to determine an initial number
of clusters, and then running a partitioning technique such as K-means, for refining the segmentation.
Step 1: Clustering with Ward’s method.
Levels histogram
The Levels histogram helps to identify the relevant number of
clusters. There is no formal rule to interpret this chart. Starting
from the bottom, it is typical to take the number of clusters that
have a sharper cut from the remainder. In our example the
lower three bars show this characteristic, which suggests
running a three-cluster partition.
Dendrograms are tree-like structures used to
graphically display when and how the various
mergers between pairs of items happened. We
found between three and six major partitions,
as shown in the dendrogram to the right.
Step 2: Clustering with K-Means method.
We can now run a K-means partition selecting
at least three clusters as target seed, but we
can even consider increasing the number of
clusters to six, according to the dendrogram.
Before doing so, however, we suggest using
Smart Mapping; another MM4XL tool, to look
at the partitions on a different picture.
1
4
7
Knot
The data above was used as input to the Ward’s algorithm set
at Automatically for the Termination condition. The software
produced the two charts and the table shown below. This
output offers enough detail for a first understanding of the data
and the way they cluster in groups.
10
13
16
19
0.0
200.0
400.0
600.0
800.0
1000.0
Index
Dendrogram
Novo Nordisk
Sanofi
Basf
Boehring I.
Bayer
Warner Lambert
AHP
Lilly
J&J
Abbott
Schering-P.
SKB
BMS
Pharmacia
Pfizer
Aventis
Roche
Novartis
Glaxo
AstraZeneca
Merck
0
200
400
600
800
1000
Index
The chart below was drawn using the column of data labeled Ordinates in the Ward’s output, together with a
second column of progressive values ranging from 1 to the number of clustered items, 21 in our case. Smart
Mapping allows you to place labels on scatter charts, which is a feature not supported in Excel. The bubble
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281
size is proportional to Sales in the picture below. Read
the chapter on Smart Mapping for more information
about how to draw Smart Maps.
Bubbles = SALES - M ax = 17'500
Pharm a Co's: Ordinates fm Ward's
Boehring I.
Abbott
17
We opted for a K-means clustering with 3 groups and
exact termination condition. The partition is
summarized below in table form:
Bayer
Schering-P.
Basf
Novo
Nordisk
Sanofi
Warner Lambert
AHP
Pharmacia
SKB
12
Lilly
Group 1
9
Pfizer
BMS
J&J
Lilly
Pharmacia
AHP
Schering-P.
Warner Lambert
Abbott
Group 2
4
Merck
AstraZeneca
Glaxo
SKB
Roche
Novartis
Group 3
8
Aventis
Novartis
Roche
Bayer
Sanofi
Boehring I.
Basf
Novo Nordisk
7
J&J
BM S
Astra
Zeneca
Pfizer
2
Glaxo
-1
M erck
Aventis
4
9
O ridna t e s
14
19
-3
The partition is shown again in the form of an item dispersion chart. The chart shows which items belongs to
which cluster. The length of the arm shows how soon or late each item joined its cluster. Finally, the bubble
size is proportional to the values in the first column of the input range.
Item Dispersion Around Group Center
AstraZeneca
Roche
J&J
Lilly
Pharmacia
AHP
Pfizer
Novartis
Bayer
BMS
Glaxo
Merck
Abbott
Sanofi
Aventis
Boehring I.
Schering-P.
Warner Lambert
SKB
Basf
The tool also prints the Between-, Within-, and Total inertia values (see the
table to the right). These values are used for comparing the accuracy between
partitions.
Novo Nordisk
Inertia
Between-group
Within-group
Total
Values
14.32
21.56
35.87
According to our segmentation procedure there is only one phase left: to identify
and describe the clusters. Indeed, although MM4XL has partitioned the input data, it is wise to take a look at
the quality of the partitions before interpreting the results. Two questions should be answered before
describing the partitions:
1. Is the number of clusters appropriate?
2. How homogeneous is each cluster?
The first question can be answered by a simple visual inspection of the dendrogram shown above. When
working with partitioning methods such as K-means, however, one can employ a more formal rule. Calinski
and Harabasz (1974) suggested a method that selects the maximum of C as the appropriate number of
clusters, where C is found as follows:
Trace( B )
g −1
C=
Trace(W )
n−g
Trace(B) is the Between-group inertia, trace(W) is the Within-group inertia, g is the number of clusters, and
n is the number of items. For our example we have C = 5,9, which suggests rerunning the analysis and
partitioning the data set in six clusters rather than three. It is a matter of choice, but not purely so: clusters
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282
too small in size may not be appealing to management, so a higher number of clusters might be less
accurate in formal terms, and yet be viable for business.
The second question about homogeneity of clusters can be answered by inspecting the Item Dispersion
chart. For each cluster found with the K-means method, this chart shows which items belong to it and when
they joined the cluster. The longer one whisker, the later the item joined the cluster, and therefore the less
similar that item profile is to other items in the same cluster. According to the chart in our example, cluster 1
seems to be the least homogeneous of the three.
Cluster description
The summary report generated by the K-means method helps to describe the clusters.
Average
Group 1
Group 2
Group 3
Total
Sales
9133.3
13600.0
6312.5
8909.5
US
61.9
50.8
31.1
48.0
EU
24.2
28.3
42.6
32.0
J
4.9
5.8
10.5
7.2
Others
9.0
15.3
15.8
12.8
GPs
81.7
50.0
80.6
75.2
Hospitals
18.3
50.0
19.4
24.8
The values above are all averages. The rows labeled Group 1 to Group 3 show the average value of each
variable in the input data set. The last row shows average values for each variable computed on the whole
data set.
For the sake of the exercise we assigned the following names to the clusters of our example:
Group 3: Pachyderms.
These are large companies, covering the whole world, selling through both channels.
Group 2: American practitioners.
These are mid-size companies, with business mainly in the US and low penetration in the hospital segment.
Group 1: European explorers.
These are companies with below average sales, primarily to European GP’s with a share of sales coming
from the rest of the world.
According to the analysis results, a relationship between sales level, geographic region, and coverage of
market segment can be found in our data set.
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Technicalities
The Cluster Analysis tool applies the squared Euclidean distance method.
Between-Group – Shows the dispersion between groups. The higher it is, the better the segmentation.
Within-Group – Shows the dispersion within groups. The lower it is, the better the homogeneity of groups.
Standardization – This means preliminary processing of data in each column by means of complete
standardization with the formula:
xi − x x
σx
Best partition is the highest of all ratios [Trace(B) / Trace(W)].
Euclidean distance between points x and y is found with the formula:
2
m
| x − y |2 = ∑ | xl − y l | .
l =1
Center of group Xi is found with:
ci =
∑x
∑1
x∈X i
x∈X i
Group capacity of group Xi is defined with the formula:
Pi =
∑1
x∈X i
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References to Cluster Analysis
Anderberg, Michael R.
Cluster Analysis for Applications.
Academic Press, 1973.
Calinski, T. and Harabasz, J.
A Dendrite Method for Cluster Analysis.
Communications in Statistics, 3, 1-27, 1974.
Everitt, Brian S.
Cluster Analysis.
Edward Arnolds, 1993
Lilien, Gary L. and Rangaswamy, Arvind
Marketing Engineering.
Myers, James H.
Segmentation and Positioning for Strategic Marketing Decisions.
American Marketing Association, 1996.
Punj, Girish and Stewart, David W.
Cluster Analysis in Marketing Research: Review and Suggestions for Applications.
Journal of Marketing Research. 20 (May), 134-149, 1983.
Smith, Wendel
Product Differentiation and Market Segmentation as Alternative Marketing Strategies.
Journal of Marketing, 21 (July) 3-8, 1956.
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12. Segmentation Tree
Segmentation Tree in a Nutshell
Advertising campaigns, direct marketing actions, and promotional plans are some of the activities that
require marketing managers to identify groups of people that are homogeneous in terms of given
characteristics. When the need arises, managers can use one of the segmentation techniques that in the
past 40 years have blossomed since William Belson’s original work on matching and prediction, such as AID
(Automatic Interaction Detection) and CHAID (Chi Square Automatic Interaction Detection), THAID (Theta
AID), and CART (Classification and Regression Trees).
MM4XL’s Segmentation Tree tool applies Belson’s original algorithm to a set of data that can be gathered,
for example, by means of a sample survey. Say we were interested in identifying the demographic factors
that most closely relate to the purchase of vitamin tablets, and a marketing research agency ran a sample
survey for us. We can use the data set for drawing a segmentation tree like the one below, which shows in
pictorial form the number of people belonging to one segment (tree leaf), and which variables relate most to
the use of vitamin in that group. In our example the first split is based on gender, followed by the area where
respondents reside. The size of the identified groups can be then inferred from the overall target population.
Repo rt fo r criteria Use vitamins
Sex
1017 100.0%
Sex
F
628 - 61.8%
252 - 40.1%
Sex
M
389 38.2%
A rea
City
A rea
Land
A rea
City
A rea
Land
418 - 41.1%
182 - 43.5%
210 - 20.6%
70 - 33.3%
255 - 25.1%
80 - 31.4%
134 - 13.2%
29 - 21.6%
A ge
'35-54
A ge
'<35 '+54
A ge
'35-54
A ge
'<35 '+54
A ge
'35-54 '<35
A ge
'+54
A ge
'35-54
A ge
'<35 '+54
151- 14.8%
71- 47.0%
267 - 26.3%
111- 41.6%
95 - 9.3%
36 - 37.9%
115 - 11.3%
34 - 29.6%
199 - 19.6%
69 - 34.7%
56 - 5.5%
11- 19.6%
55 - 5.4%
13 - 23.6%
79 - 7.8%
16 - 20.3%
A ge
'<35
140 - 13.8%
60 - 42.9%
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A ge
'+54
127 - 12.5%
51- 40.2%
A ge
'<35
63 - 6.2%
19 - 30.2%
A ge
'+54
52 - 5.1%
15 - 28.8%
A ge
'35-54
95 - 9.3%
34 - 35.8%
A ge
'<35
104 - 10.2%
35 - 33.7%
A ge
'<35
57 - 5.6%
12 - 21.1%
A ge
'+54
22 - 2.2%
4 - 18.2%
287
How To Run Segmentation Tree
Segmentation Tree is simple to run. In the MM4XL floating toolbar, click on this button to display
the window shown below. Define the basics of the analysis you want to run, then click on OK.
That’s it.
Note:
In the Input range field, select the area on sheet
where the data for the profiles to be investigated
are stored (read more concerning input data later
in the Technicalities section). In the Output range
field select the cell where you want to start printing
the report of the analysis. From the Select criteria
list box choose the discriminant criteria you want to
run the analysis for.
From the list box on the left side select the
Available factors you want to run the
segmentation with and click on the Add>> button.
The tool will partition all factors listed in the
Selected factors box. To move all factors at once
from the left to the right list box, select the Select
all checkbox, then click on Add>>.
The checkbox Show item group number, which is
active by default, prints in the first blank column on
the right side of the input range the group number
each item was assigned to.
Tip:
After the segments have been found, with the item
group numbers available, use the CrossTab tool
from the MM4XL menu to make contingency tables
that describe the items clustered in one group.
In the Tree frame select Show counts and Show % counts if you want the boxes in the tree chart to display
the number of individuals assigned to each group and their percentage size. This is useful feature that can
make trees rich in information or small in size depending on your needs. By default both checkboxes Print
table and Print tree chart are selected. Clear them if you do not want these items printed.
The default options in the Tree branches frame are set to display a full tree. However, you can use the
Branch(es) list box to select whether to draw both sides of the tree, or either the left or right branch only.
The N. of levels list box defines how many levels the tree shows, and the Font size option allows you to
rescale the text in the chart. These options are intended to help you draw readable trees, which can become
quite large when you are working with several variables.
In the Learning Center in the lower left corner of the form you can open the MM4XL online Reference
Manual, the Example sheet with test data, and other helpful utilities for learning the tool.
Click OK to run Segmentation Tree.
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288
Tip:
Depending on the amount of data you are working with, it can take from a few second to a few
minutes to run the analysis. Watch the Excel status bar to confirm that the tool is working.
Anatomy of a Segmentation Tree Report
Segmentation Tree prints by default a tree chart and a table of data that summarize the outcome of the
partition. You can choose to not print one or the other by clearing the Print table and Print tree checkboxes
on the user form.
The group number each item was assigned to can be printed in the first blank column on the right side of the
input range. Segments are counted from the lowest level only. For example, the sample tree shown in the
section Segmentation Tree in a Nutshell shows four levels and eight groups at the fourth level. The segment
Teens 2 or + on the left is group number 1 and the segment Teens 2 or + on the right is group number 8.
The Tree
A tree like the example shown below is a pictorial representation of the segmentation result. The example
refers to an exercise performed for a company investigating buyers of vitamins for European households
(active variable).
The tree shows four levels, although the original tree detected a fifth level not shown in the example, and it
accounts for four passive variables: gender, area, teens, and age. Each level is split into branches, and the
main information concerning the branch is stored in the squared boxes (leaves), which represent the final
groups. This tree tells us:
1. Gender is the variable most highly related to the purchase of vitamins for the household. Out of a
total of 361 (35.5% of 1017) buyers, 252 women (40.1% of 628 surveyed women) bought vitamins,
while only 109 (28.0% of 389 surveyed men) buyers were men. The Area where people live is the
second variable most highly related to the purchase of vitamins.
2. The left side of the tree shows a large group of 158 women buyers living in cities, with two or more
children. An analogous situation is shown on the right side, with males from the city aged below 45.
Large groups are often of interest to the marketing manager because they can be the targets of
communication activities.
3. The situation changes in the countryside where women and men split according to their age and the
number of children at home, respectively. This happens at the forth level and we still see groups of
appreciable size. When the split produces small groups the analysis must be handled with caution.
Sex
1017 100.0%
Sex
F
628 - 61.8%
252 - 40.1%
Sex
M
389 38.2%
A rea
City
A rea
Land
A rea
City
A rea
Land
418 - 41.1%
182 - 43.5%
210 - 20.6%
70 - 33.3%
255 - 25.1%
80 - 31.4%
134 - 13.2%
29 - 21.6%
A ge
'35-54
A ge
'<35 '+54
A ge
'35-54
A ge
'<35 '+54
A ge
'35-54 '<35
A ge
'+54
A ge
'35-54
A ge
'<35 '+54
151- 14.8%
71- 47.0%
267 - 26.3%
111- 41.6%
95 - 9.3%
36 - 37.9%
115 - 11.3%
34 - 29.6%
199 - 19.6%
69 - 34.7%
56 - 5.5%
11- 19.6%
55 - 5.4%
13 - 23.6%
79 - 7.8%
16 - 20.3%
A ge
'<35
140 - 13.8%
60 - 42.9%
A ge
'+54
127 - 12.5%
51- 40.2%
A ge
'<35
63 - 6.2%
19 - 30.2%
A ge
'+54
52 - 5.1%
15 - 28.8%
A ge
'35-54
95 - 9.3%
34 - 35.8%
A ge
'<35
104 - 10.2%
35 - 33.7%
A ge
'<35
57 - 5.6%
12 - 21.1%
A ge
'+54
22 - 2.2%
4 - 18.2%
The tree is made of single elements grouped together. To modify the shapes, right-click on the tree and
select Grouping>Ungroup. To change text in a box, click on the box and enter and format the text. As with
any other Microsoft Office object, you can copy and paste the tree between applications such as Word and
Power Point.
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The next section explains the various elements of the box.
The Table
With the Print table option selected, Segmentation Tree summarizes the outcome of the partition in a table
like the one below.
Rows 1 to 5 of the table report the basics of the user selection. Rows 6 to 22 concern the tree partitions.
Beginning from the left, in column A (cells 8 and 14) are shown the codes of the variable that was found to
be most related to the purchase of vitamins in our sample. Columns B, C, and D show the other levels
identified with the segmentation.
Column E shows values from the whole dataset used for the analysis (1017 cases as shown in cell E7) and
column G shows the number of people in each of the lowest clusters. The 71 people in cell F8, for instance,
can be found in the lowest left box of the tree shown above.
Column G shows the percentages for the values in column E. Cell G8, for instance, is 15%, which is found
by dividing 151 by 1017 (=E8/E7*100). Column H shows values computed on sample values from column F.
The value in cell H8 is obtained dividing 71 by 151 (=F8/E8*100).
Row 7 tells us that Gender is the variable found to relate most to the purchase of vitamins. There are 1017
people in our sample, and 361 of them have bought vitamins during the past 4 weeks.
In row 8 the tool has identified a group of 151 women (15% of 1017), living in cities, aged between 35-54:
47% of these (71 women) have bought vitamins for their households in the past 4 weeks. The same
information is available for all the identified segments, which are shown at the lowest level of the tree.
In general, you should be careful when dealing with groups of less than 20 units.
Tip:
Use Smart Mapping, another tool available in MM4XL, when you have several groups
of items and you want to quicklyfind out which of the groups is of interest to you. Give
it a try by plotting the values in columns G and H in the table above.
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Technicalities
The easiest way to understand how Segmentation Tree works is to think of regression analysis. Say we were
interested in finding which factors have the strongest relationship on the dependent variable Purchase of ice
cream (called Criteria in Segmentation Tree) and we used three independent variables in the model: air
temperature, availability of money, sense of craving. With multiple regression we can measure the degree
and form of relationship among the variables. With Segmentation Tree we can identify groups of similar
cases in terms of relationship to the dependent variable, and show them graphically in a tree diagram.
Segmentation Tree applies Belson’s segmentation method, which drove the development of AID (automatic
interaction detection) methods. The method iteratively splits sample data into two branches for each variable
and finds the highest discriminant value, which stands for the strongest relationship between the chosen
criterion and the sampled data. The procedure loops until all cases have been assigned to one branch.
Segmentation trees are heuristic models designed for finding homogeneous subgroups in sample data. The
starting point of the analysis is the selection of the independent (or passive) variables and the criterion of the
segmentation. In the previous example the criterion was Buyer of vitamins and the passive variables were
Gender, Area, Kids, and Age. There is no one standard method for selecting the relevant variables of a
model. Some researchers use regression and correlation, but these are not always applicable techniques.
Experience and taste play an important role when defining segmentation models.
Segmentation techniques require large samples in order to reach useful conclusions. When the
segmentation is run, what makes a variable important is the strength of its relationship (level in the tree) and
the number of cases it covers.
Assembling input data
A standard input table to
Segmentation Tree has column
labels and is arranged by rows.
The table here shows a data
set made of 14 columns (B:O)
and 1016 rows (2:1017).
There are two kinds of
variables. In this picture
segmenting
variables
are
shaded in yellow and the
discriminating variable is in
green. You can have several
discriminating variables in your
data set, but one analysis is run with one discriminating variable at a time only.
Segmenting variables can be either text or figures and they cannot show missing values. In general, we
recommend using as few codes as possible for each segmenting variable, and you should use meaningful
but brief descriptive codes. This is true for column labels as well: short labels take less space and result in a
more compact and more readable tree chart, while a few codes in a column help to keep clustered groups
large enough to make sense to marketers.
Discriminant variables are dichotomous, such as Yes-No, and are used to distinguish items with the
desired characteristic from items that don’t have it. In our example we use the number 1 in column O to
qualify the 360 interviewees out of 1016, who answered Yes when asked whether they had used any vitamin
supplements in the past 4 weeks (the data set is available in the sheet you can access using the Example
button in the tool form). Subjects without the characteristic (did not use vitamins) got a blank cell in column
O.
Input data to Segmentation Tree typically comes from survey studies, but also from other sources. We have
noticed an increasing application to web data, such as web site traffic, and also to databases such as those
of visitors to conferences or affiliates of associations.
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Known problems
When trying to cluster more than six variables, the tool warns you that the segmentation could reach useless
results, and suggests an alternative route. You can skip this if you like. However, be warned that using too
many variables at once may result in a weak analysis unless the database is large, say above 5000 input
rows.
When the analysis lasts several minutes, make sure that Excel does not collide with your screensaver. We
have heard of instances when the screensaver prevented Excel from completing its operations.
Finally, creating large trees may overload Excel’s resources and cause it to crash. To avoid this, you can
reduce the number of levels in the tree, plot only one side of the tree, or reduce the number of levels.
References
De Luca, Amedeo
Le Applicazioni dei Metodi Statistici alle Analisi di Mercato.
Franco Angeli, Milano, 1986.
Lilien, Gary L., Rangaswamy, Arvind
Addison Wesley, 1997.
Myers, James H.
Segmentation and Positioning for Strategic Marketing Decisions.
American Marketing Association, 1996.
SAS Institute Inc.
SAS User Manual
USA, 2000
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13. Proportion Analyst
Proportion Analyst in a Nutshell
Proportion Analyst is useful for determining if a significant difference exists between two proportions, which is
a recurrent question when interpreting such things as the results of a marketing survey study. When
investigating product acceptance, for instance, testing whether there are significant differences between
target segments is a basic step to correctly interpret the results of the study.
Applying a two-tailed Z test for homogeneity, Proportion Analyst tests equality and determines if any
difference exists in the proportion of successes in two samples. It interprets results and presents conclusions
written in plain language, both on the sheet and in the user form as shown below.
This tool is part of the Survey Analysis suite, which also includes Sample Manager, a tool for determining
sample size, and CrossTab, a professional tool for running complex contingency table elaborations.
Note:
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How To Run Proportion Analyst
On the MM4XL floating toolbar, click this button to display the window shown below.
All you need to do is enter the
values in the Core Data and
Hypothesis (Ho) frames. Results
are automatically shown in the
pane on the right side of the
window.
In the Hypothesis frame you can
alter the minimum Confidence
required
for
achieving
level
significance and can also change
Difference
between
the
proportions that is to be tested.
Technical notes which explain the
interpretation of results can be
found in the Technicalities section
later in this chapter.
Tip:
The Print report function starts printing at the currently selected cell in Excel. Be careful where your cursor
is placed before printing.
Note:
When working with the form, if you see the cursor change to a question mark, click on the label
and the Quick Online Help opens and displays a short description of the label.
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Anatomy of a Proportion Analyst Output Report
Based on the user input, Proportion Analyst states a hypothesis, tests its probability of occurrence, and
draws conclusions. All this information is summarized in the right-hand pane of the user form and can be
printed on sheet in the form of an output report.
User Form Summary
Visualization of
user input data
Hypothesis of the study
(alternative):
the two proportions differ.
Probability that the
proportions differ.
Required is user
defined while Achieved
is computed by
Proportion Analyst.
When Yes, there is evidence
that proportions are
significantly different.
Vice versa when No appears.
Output Summary Report
Clicking the Print report button generates the following output report below:
MM4XL - Comparison of proportions, two-tailed.
Hypothesis Ha: (Proportion 1 - Proportion 2) <> 0.000
Proportion 1
Proportion 2
Difference (1-2)
Value%
25.0%
21.9%
3.1%
Significance (required):
Probability (achieved):
p Value:
z Value:
95.000%
94.920%
10.160%
1.6372
Sample size
1005
998
If Probability > Significance
proportions differ significantly.
(= 5.080% * 2 tails)
Conclusion
NO, the difference between proportions is not statistically significant.
p Value is the two-tailed probability
of accepting or rejecting Ho.
z Value is the statistic against
which to test significance of results.
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Analysis results are interpreted
using plain language.
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Technicalities
Proportion Analyst applies the Z test for homogeneity of two proportions when investigating whether a
significant difference exists. It tests equality by running a two-tailed test that determines whether there is any
difference in the proportion of successes in the two samples. A one-tailed test is needed when determining
whether successes are higher in one of the two groups.
The null ( H 0 ) and alternative ( H a ) hypotheses Proportion Analyst sets are:
H 0 : p1 = p2 or the difference p1 − p2 = 0
H a : p1 ≠ p2 or the difference p1 − p2 ≠ 0
The test statistic, Z, is approximated by a standard normal distribution:
Z≅
(p
s1
)
− p s 2 − ( p1 − p 2 )
⎞
⎟⎟
⎠
⎛1
1
p (1 − p )⎜⎜ +
⎝ n1 n 2
Where:
p1 = Proportion of successes in sample 1;
ps = Sample proportion from population I;
i
ni = Size sample I;
p=
X 1 + X 2 = Pooled estimate for population proportion.
n1 + n2
The probability of accepting or rejecting Ho, called p Value in the output report, is approximated by a
standard normal distribution with mean 0 and standard deviation 1 (see formula NORMSDIST in Excel). The
equation for the standard normal density function is:
z2
⎛ 1 ⎞ −2
f (z;0,1) = ⎜
⎟e
⎝ 2π ⎠
The null hypothesis is rejected if the Z value lies
outside the critical values from the standard normal
distribution. This means that when the achieved
probability is higher than the user-stated
probability, the two proportions are recognized as
significantly different and the alternative hypothesis
H a is accepted.
p1 <> p2
Reject Ho
0.025
Do not
reject Ho
-Z
p1 = p2
p1 <> p2
Reject Ho
0.025
+Z
Significance 95%
References to Proportion Analyst
Mark L. Berenson, David M. Levine
Basic Business Statistics. Concepts and applications.
Prentice-Hall International, London 1996
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14. Sample Manager
Sample Manager in a Nutshell
How many people prefer brand A? How many households have a black and white TV? How many patients
made progress using drug X? What proportion of electors voted for candidate Y? These are all questions we
can answer by surveying samples of individuals with relevant characteristics.
In order to design a sample that
makes sense, one important thing is to
determine the number of required
interviews, how large the sample
should be. The answer can be found
quickly, accurately, and objectively
with Sample Manager. It is the
objectivity of probabilistic assumptions,
rather than ‘gut feeling’, which helps
companies to both perform reliable
survey studies and save money.
Sample Manager can extract random
samples from a dataset stored in MS
Excel, a must-have feature for
managers and analysts interested in
running fast and robust in-house data
analysis. Conference visitors, web site
visits, POS purchases, and survey raw data are just some of data sets a company might want to analyze inhouse.
Based on your input data, Sample Manager generates a sensitivity analysis which can be viewed online in
the user form or can be printed.
Sample Manager is part of the Survey
Analysis suite, which also includes
Proportion Analyst, a tool for testing
the significance of difference between
two
proportions;
CrossTab,
a
professional tool for running complex
contingency table elaborations; and
Variance Analyst, which tests whether
there is a significant difference
between groups of items, such as
sales results from a promotional action.
Note:
available. Click on the Start button in
Windows and select MM4XL –
Marketing Manager for Excel. The file
can be found in the Examples folder.
Alternatively, start the tool and click the
Example button.
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How To Run Sample Manager
On the MM4XL floating toolbar, click this button to display the Sample Manager window.
There are four values you can work with: Population size, Confidence level, Error level, and
Hypothesis of the study. More details about these parameters can be found in the Technicalities
section. Should you input a wrong value, don’t panic! Sample Manager warns you.
Click in the frame above the Quick Help button and the answer to your query appears in the white panel.
Note:
When working with the form, if you see the cursor change to a question mark, click on the label
and the Quick Online Help opens and displays a short description of the label.
How to Extract a Random sample
On the Sample Manager form click the Extract Sample button to display a new form. In the Input range
field select the range on the sheet containing the data you want to extract a sample from. In the Output
range field select a cell on the sheet where Sample Manager can start printing the sampled data. In the N
textbox enter the number of data rows you want to extract. From the listbox select the data rows to extract:
Extract N random data rows extracts the desired number of rows, applying an algorithm that randomly
picks the next rows up to N; Extract the last N data rows; or Extract the first N data rows.
Click OK. Sample Manager prints the output starting from the selected cell.
Tip:
The Print report function starts printing at the currently selected cell in Excel. Be careful where your cursor
is placed before printing.
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Anatomy of a Sample Manager Output Report
Sample Manager prints a succinct report that summarizes the user input data and provides a Sensitivity
analysis of sample sizes.
The sensitivity analysis covers the five percentage points immediately before and after the Confidence and
Error levels you input. Confidence uses intervals of one percentage point, and Error level . The example
below shows five intervals preceding 95%, the user input, and there are only four intervals above because
the highest value Sample Manager prints for Confidence is 99%. The same applies to the Error level with the
difference that intervals are made of half-percentage points beginning from 0.5%.
Printing several sensitivity analyses may help to depict a really viable sample size.
MM4XL - Sample Size: Sensitivity analysis
- Population size (N):
254700
- Confidence level:
95.00%
- Error level:
2.00%
- Hypothesis of the study:
0.5
- Sample size (n):
2378
Confidence level
90.00%
91.00%
92.00%
93.00%
94.00%
95.00%
96.00%
97.00%
98.00%
99.00%
0.5%
24458
25829
27357
29082
31060
33380
36186
39744
44635
52637
1.0%
6589
6989
7439
7951
8547
9255
10126
11253
12847
15573
1.5%
2971
3154
3361
3596
3871
4198
4602
5127
5875
7165
User input
summary data
Error level
2.0% 2.5% 3.0%
1680 1078
749
1784 1145
796
1901 1220
849
2035 1306
909
2192 1407
979
2378 1527 1063
2609 1676 1166
2910 1870 1301
3338 2147 1494
4080 2627 1830
3.5%
551
585
624
668
720
782
858
957
1100
1347
4.0%
422
448
478
512
552
599
657
734
843
1033
2,378 interviews are required for a
sample from a population of
254,700 at the 95% confidence
level, 2% error, and worst (0.5)
hypothesis.
4.5%
334
354
378
405
436
473
520
580
666
817
A Sample of 473 interviews,
however, would be equally useful;
only the error level would increase
to 4.5%.
This means it is not always wise to
buy large samples. Plan your
sample accurately, and you will
save money.
Answer to user input
Technicalities
The sample size has a high impact on the overall cost of a survey study. Fortunately, Sample Manager can
help you find an acceptable compromise between accuracy and cost. Let’s see how.
The software computes sample sizes using the following Bernoullian formula for finite populations:
n=
σ 2 ( p ⋅ q )N
e 2 ( N − 1) + ( p ⋅ q )σ 2
Where:
N = Population size
σ = Confidence level
e = Error level
p = Hypothesis of the study
The formula for finite population has the advantage of allowing you to shape the sample size according to
the population size the sample is drawn from. The formula for infinite populations is more popular among
MBA students and practitioners, and its results can be obtained using Sample Manager simply by setting the
population size N to an infinite value, say 1 million or above. The formula for random sampling from an
infinite population is:
n=
σ 2 ⋅ P ⋅Q
e2
The population of the study must be precisely identified. 18,700 nurses in Texas rather than 250,000 golf
players in Europe or 19 million households in Italy. Above 1 million units, populations are commonly treated
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303
as infinite, for results do not change significantly. For less than 500 units it is not recommended to use the
formulae above.
Samples can be designed in many ways. In marketing research, the most common sampling techniques are
quota and random. Quota sampling is a non-probabilistic method applied when the population cannot be
described in detail. Random samples assign to each member of the population the same probability of being
selected. Each of the 18,700 nurses in Texas has a probability equal to 0.00534% of being selected
randomly. And all 18,700 nurses could be part of a quota sample that includes other groups such as 6,732
doctors, 1,059 surgeons, and 3,997 clerks.
Samples are drawn to reproduce certain characteristics of the population they are drawn from. The more
important the answer we seek, the closer the sample should reproduce those characteristics under the
probabilistic assumptions. If we were to launch a new product we might desire accurate data, say with a 95%
Confidence level. This meansthat if we draw the same sample 100 times under the same conditions, 95
samples will show very similar values. The Confidence level of survey studies for the business environment
is usually set at 95%, but it is not unusual to find levels ranging from 90% to 99%. The higher the confidence
level, the larger the sample.
Tip:
It is not true that large samples are better than smaller ones, although they are certainly more expensive. It is
the way the sample is drawn that makes the difference in terms of accuracy. This means that randomly
selected individuals from one population will supply as accurate information as any other random, larger
sample from the same population But the level of disaggregation in the analyzed data can be an argument
for enlarging the size of the sample. For example, if you want to know the percentage of consumers of
instant coffee in the whole US population you may use a small sample drawn with accuracy; but if you want
to find out the percentage by US state you need a larger sample.
The Error level is the range within which values from a survey are allowed to vary. If we found that 53% of
respondents answered yes to a certain question and we operated with a 4% error level, the value is
interpreted as 50.8% <= yes <= 55.2%. When the range becomes wide you should be careful when
interpreting results. Read the Proportion Analyst chapter for a comprehensive description of the significance
of proportions obtained from sample surveys.
The fourth value Sample Manager requires as input is the Hypothesis of the study. This is important
because it can help to significantly reduce the cost of a study without impacting on its accuracy. In the
absence of other information, the hypothesis level is typically set at 0.5, which implies the largest sample of
its kind. Samples become smaller as we move away from this base value. For example, say we are
launching an editorial product by means of direct marketing using 1 million names from a list broker we trust.
From previous experience we know that some 200,000 prospects might contact us in response. To test the
feasibility of the concept we opt for an exploratory survey at the 95% confidence level, 1% error level, and
0.2 for hypothesis of the study (20% of prospects will contact us). This yields a sample of 6,109 individuals,
which would have been 9,512 interviews if the hypothesis level was set at 0.5.
This is what we mean by saying that Sample Manager can help to find acceptable compromises between
accuracy and cost. Comparing various levels of significance and error together with a robust hypothesis can
help you design very convenient samples that are still able to supply the relevant informative content you
seek.
Finally, it must be remembered that sampling in business is not exclusive to marketing research. Sales
analysis, promotional campaigns, direct marketing actions, and more can profit from the use of sampling
techniques.
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References to Sample Manager
Ulderico Santarelli
Un Campione. Di Quanti Casi? Guida pratica al progetto ottimale di ricerche e controlli statistici.
Franco Angeli, 1982, Milano, Italy.
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15. CrossTab (Contingency Tables)
CrossTab in a Nutshell
CrossTab produces contingency tables that are the joint distribution of two variables, described by a limited
number of distinct values. It can test:
•
•
•
proportions for significance (Z-test),
rows and columns for independence ( χ 2 test)
variables for correlation (R and R squared coefficient).
You can choose to have CrossTab add user-defined labels to row and column variable codes.
These are important features to business analysts. They speed up the process of data interpretation and
they help to focus on the relevant part of the data. An expert eye using CrossTab can attain the goal faster.
This powerful tool and its statistical measures allow you to
make a detailed and accurate exploration of any data set
by means of two-way contingency tables.
Note:
An example report of this tool is available. Click on the
Start button in Windows and select MM4XL – Marketing
Manager for Excel. The file can be found in the Examples
folder. Alternatively, start the tool and click the Example
button.
CrossTab is part of the Survey Analysis suite, which
includes Sample Manager for determining sample size,
and Proportion Analyst for testing for the significance of
the difference between two proportions.
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Language
Client Class
Class B
(c2)
34
18.3%
Class C
(c3)
62
English
%
33.3%
Signif
c2
14
25
Spanish
%
18.7%
33.3%
Signif
c2
12
24
French
%
22.2%
44.4%
Signif
c1c2
144
60
111
Sum
%
45.7%
19.0%
35.2%
Signif
c2c3
c2
Chi2 test on table, 95% conf., Ho: col's & rows indep't = TRUE
Pearson Corr Coef= 0.981 - Pearson² = 0.962
Proportions/Means: Columns tested (5% Risk level)
* Small base (<30)
** Small base (<6)
Class A
(c1)
90
48.4%
c2c3
36
48.0%
c2c3
18
33.3%
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How CrossTab Works
CrossTab produces contingency tables that are the joint distribution of two variables, described by a limited
number of distinct values. The frequency distribution of one variable is subdivided according to each distinct
value of the second variable. The intersection of one value from each variable defines a cell, the basic
element of any contingency table.
Variables
Two distinct values.
Three for Language.
Table heading
Sex
Female
Male
Sum
English
(c1)
37
149
186
Language
Spanish
(c2)
20
55
75
French
(c3)
6
48
54
Sum
Column identifiers
63
252
315
Cell
1. Two kinds of tables
CrossTab creates two different kinds of tables. A single table display looks like the table above, with the
column heading containing one variable only. A multiple table shows more than one column variable, and
looks like the one below.
Sex
Female
Male
Sum
English
(c1)
37
149
186
Language
Spanish French
(c2)
(c3)
20
6
55
48
75
54
Class A
(c4)
18
126
144
Client Class
Class B Class C
(c5)
(c6)
8
37
52
74
60
111
Sum
63
252
315
The kinds of questions (variables) CrossTab can treat also take two forms: closed-end and open-end. The
tree below summarizes the alternative possibilities (the tree was made with Decision Tree, another of
MM4XL tools). There is more later in this chapter about kinds of questions.
Close-end question
Single table
Open-end question
CrossTab Output Table
Close-end question
Multiple table
Open-end question
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2. Two kinds of questions
CrossTab can analyze variables coded from closed-end and open-end questions. In a survey study, for
instance, the researcher gathers 315 interviews using a semi-structured questionnaire. Data are edited,
coded and inputted in a database of 317 rows and 69 columns that looks like the one below (rows 11-312
and columns F-BL are hidden).
Closed-end
question label
Open-end
question label
Open-end
code label
2 rows of titles
required with
open-end questions
Title on one row for closed-end questions.
Answer
codes
Two rows required when treating
open- and closed-end questions at once.
Note:
In the range A1:E1 text is displayed in a different colour. This text is only needed when the data set we work
with mixes closed- and open-end questions. It is simply a copy of range B2:E2. When working with closedend data only the grey titles aren’t needed.
In the range A1:BQ317 all data gathered during this hypothetical survey are stored. 315 people were
interviewed. The responses of the first person interviewed are in the range A3:BQ3, row 3. The first interview
refers to:
•
•
•
•
a man (Sex code 2, column B), who
speaks English (Language code 1, column C),
belongs to Client Class 1 in our client ranking list (column D), and
lives in the North of the country (Region code 1, column E).
Columns A:E refer to closed-end questions. These are questions where all possible answers are prespecified. Closed-end questions that only allow single answers are stored in one column, such as the
variable vector B2:B317. CrossTab recognizes values in the first row as titles. Codes can be either numerical
or text values, and blank cells are skipped. Every unique code in the variable vector is identified and
displayed as a single class in the table. Multiple answers to closed-end questions are treated as described
below for open-end questions.
Tip:
operation the tool is performing at a particular moment.
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Open-end questions allow people to answer in their own words. Columns BM:BQ refer to the open-end
question “Why do you use Swiffer?”. Respondent 1 (row 3) answered with two reasons: to Remove dust (cell
BM3) and because it does a Quick job (cell BN3). CrossTab requires titles in two rows for open-end
questions. The first row hosts the question label (cell BM1) and the second row hosts code labels
(BM2:BQ2). Every unique code in the variable vector is identified and displayed as a single class in the table,
and blank cells are skipped.
3. Code range
CrossTab prints either coded tables or naïve tables. Coded tables have meaningful title labels, like those on
the table to the left. The labels of naïve tables, like those of the table to the right, are less self-explanatory.
Sex
Female
Male
Sum
English
(c1)
37
149
186
Language
Spanish
(c2)
20
55
75
French
(c3)
6
48
54
Sum
Sex
63
252
315
1
2
Sum
1
(c1)
37
149
186
Language
2
3
(c2)
(c3)
20
6
55
48
75
54
Sum
63
252
315
By applying a user-defined code range, such as A2:F7 in the picture below, CrossTab refines tables by
assigning meaningful title labels, which dramatically increase the readability of the table.
Code
values
Variable
titles
Code
meaning
Code ranges have code values in the first column, as in A3:A7, and code meanings in successive
columns, as in B3:F7. One column of the code range refers to one single variable of the input data range.
Variable titles are displayed in the first row, as in B2:F2, and they must match the first row of titles in the
input data range.
4. Data treatment
Depending on your selections, CrossTab can enrich tables that contain only counts with:
•
•
•
•
Proportions (%) of cell counts computed on either row, column, or table total;
Test of significance of difference between proportions at the desired significance level;
Chi squared test for independence of table at the desired significance level;
Coefficient R and R squared for testing correlation between variables
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How To Run CrossTab
On the MM4XL floating toolbar,
click this button to display the
form to the right.
The form contains three pages:
Data, Parameters, and Statistics. The
Data page, shown here, is where the
input parameters are defined. On the
second page you select the variables to
tabulate. The last page contains options
related to table totals and statistical
tests.
Data page
The fields of this page tell CrossTab
where to find the raw data to work with,
where to print the output, and, if
applicable, how to refine the tables by
assigning meaningful labels.
Enter a Job title or accept the default
title. In the Dataset range field select the range on the sheet where the input data is stored. The first row of
the range is automatically recognized as title labels. In the Output range field, select an anchor cell where
printing of tables should start. It does not matter whether you select one cell or more, printing will start at the
top left cell. Code range is not a required field, but if you want to assign user-defined labels to tables, select
a range formatted as described in the Code range section above.
In the Define Table(s) Outlook frame you specify the layout of the table and the kind of variables in the
input range. For Kind of table select either Multi Table Heading or Single Table Heading. For Kind of
variable select Closed-end question or Open-end question. See How CrossTab Works above for a
detailed explanation of these options.
Parameters page
The Parameters page defines how to
cross-tabulate the input data.
The From List panel contains a list of
variables in the selected data set range.
Select one or more variables from this
list and click on the appropriate Add>>
button to copy the selection to the To
Row or the To Column list on the right.
The codes of variables in the To Row
list will be shown in the tables as row
items. The listbox Sort row values is
set by default to Ascending order, but
row tables can also be displayed in
descending row order. Codes of
variables copied to the To Column list will be shown as column items. The selection above would produce
six tables printed in two blocks, each made up of three tables.
To remove variables from the To Row or the To Column list, select one or more entries and click the
applicable <<Remove button.
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Note:
The Add and Remove buttons are activated or deactivated depending on the currently selected list panel.
Statistics page
The Statistics page contains options related to table totals and statistical tests. When the Show %
computed on checkbox is selected, CrossTab computes count proportions (percentage) in one of three
ways.
The cross table to the right shows totals computed on Row totals,
which means cell counts are divided by the respective row total in
order to get percentage values. The option Column totals computes
proportions by dividing cell counts by column totals. If Table total is
selected, counts are divided by the table total (equal to 315 in the
example).
Tip:
Tables made up of either counts or percentages only can be used as
input to Brand Mapping, Smart Mapping, or Comparative Mapping.
Client Class
Class B
Class C
Sum
(c2)
(c3)
English
34
62
186
%
18.3%
33.3%
100.0%
Signif
c2
Spanish
14
25
75
%
18.7%
33.3%
100.0%
Signif
c2
French
12
24
54
%
22.2%
44.4%
100.0%
Signif
c1c2
Sum
144
60
111
315
%
45.7%
19.0%
35.2%
100.0%
Signif
c2c3
c2
Chi2 test on table, 95% conf., Ho: col's & rows indep't = TRUE
Pearson Corr Coef= 0.981 - Pearson² = 0.962
Proportions/Means: Columns tested (5% Risk level)
* Small base (<30)
** Small base (<6)
Language
Class A
(c1)
90
48.4%
c2c3
36
48.0%
c2c3
18
33.3%
The Show % computed on checkbox must be selected to activate the Test table and proportions option in
the Statistical Tests frame. CrossTab can test proportions for significance, and can test rows and columns
for independence as well as variables for correlation. Select the checkbox and either accept the default
percentage values for the tests or input your own numbers. The Technicalities section of this chapter
provides technical details about the tests and how they are performed.
Click OK to generate the CrossTab tables.
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Output Report
A CrossTab output report consists of one or more contingency tables like the ones shown here:
Cell D8
Counts of Clients in Class C, who
speak English.
Cell A8
Use a Code Range and replace
anonymous code values with
meaningful labels.
Cell B-D5
Closed-end question
with 3 codes.
Cell E6
Totals can refer to rows (as
in this example), columns,
and the whole table.
Cell D9
Proportion. 62/186=33.3%
of clients in Class C speak
Spanish.
Cell B20
χ 2 test for
independence. It
investigates for
dependencies in the
counts of an rxc
contingency table.
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Cell D10
Column Identifiers appear
when the difference between
two proportions is
significantly different, as
between D9 and C9.
Cell B21
Pearson Correlation Coefficient
(R) and Pearson2 measure
association between variables.
Cell B22
Proportions in this table have been
tested for significance at the 95%
confidence level (1-Risk level).
313
Technicalities
CrossTab can test:
•
•
•
proportions for significance,
rows and columns for independence
variables for correlation.
This is important to business analysts because it can speed up the process of interpreting the data and help
to focus on the relevant part of the data. We are not saying that it reduces the amount of attention you must
pay while reading and interpreting the data, just that an expert eye supported by CrossTab may get to the
goal faster.
Testing proportions for significance (Z-test)
When survey data tells us that 65% of the people interviewed answered Yes to a certain question and 23%
answered No, there is no doubt that there is a significant difference between the two values. But what about
when 46% answered Yes and 51% answered No? Can we still say that the data differ based on the
parameters used to draw the sample (for example, sampling with 95% confidence interval, 5% error level,
and hypothesis of the study set at 0.5)? To answer, we should employ an appropriate test statistic, and the
Z-test for comparing the significance of difference between two proportions from independent samples fits
the contingency table case.
Testing significance can prove very useful when screening large numbers of contingency tables, for example
from a marketing survey. With significance values available, you can quickly identify the data that is driving
the most substantial differences in the tables.
The table on the previous page shows in cell D10 that 33.3% of English speaking respondents belong to
Client Class C. The string c7 in cell D10 (indicating column 7, beginning from the leftmost column in the table
– in this example we use a table from a larger elaboration, hence the numbers beginning from c6 instead of
c1) tells us that the proportion 33.3% is significantly larger than 18.3% in cell C9, so we can safely conclude
that there are more English speaking clients in Class C than in Class B. Similarly, the string c7c8 in B13 tells
us that 48.4% differs significantly from 33.3% and 18.3%. Finally, when two proportions do not differ
significanly, CrossTab does not print any small caps letters.
The rows of text below each table show the level at which proportions are tested, which is typically set
between 90% and 99%. Cell counts smaller than 30 are considered * Small base and caution should be
used when interpreting these values. Counts below 6 are considered ** Very small base.
Statistically speaking, the null ( H 0 ) and alternative ( H 1 ) hypotheses CrossTab sets are:
H 0 : p1 = p2 or the difference p1 − p2 = 0
H 1 : p1 ≠ p2 or the difference p1 − p2 ≠ 0
The test statistic Z is approximated by a standard normal distribution:
Z≅
(p
s1
)
− p s2 − ( p1 − p 2 )
⎛1
1 ⎞
p (1 − p )⎜⎜ + ⎟⎟
n
n
2 ⎠
⎝ 1
Where:
p2 = Proportion of successes in sample 2.
ps = Sample proportion from population i.
i
ni = Size sample i.
p=
X 1 + X 2 = Pooled estimate for population proportion.
n1 + n2
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314
The probability of accepting or rejecting Ho is approximated by a standard normal distribution with mean 0
and standard deviation 1. The equation for the standard normal density function is:
z2
⎛ 1 ⎞ −2
f (z;0,1) = ⎜
⎟e
⎝ 2π ⎠
The null hypothesis is rejected if the Z value lies
outside the critical value from the standard normal
distribution. This means that when the achieved
probability is higher than the user-stated
probability, the two proportions are recognized as
significantly different, the alternative hypothesis
H 1 is true, and the Column identifier appears under
the significant value.
p1 <> p2
Reject Ho
0.025
Do not
reject Ho
-Z
p1 = p2
p1 <> p2
Reject Ho
0.025
+Z
Significance 95%
Testing tables for independence ( χ Chi squared)
2
Say that we want to find out whether there is a relationship between clients in the respective class and the
language they speak.
A χ 2 test can help us answer this question. This test involves working with categorical values, as from a
contingency table, as opposed to the test for proportions discussed above that involves continuous variables.
The χ 2 test tells us, at the given confidence level, if the table comes from a random sample or if there is any
significant effect affecting columns and rows. In other words it tells us whether the two variables are
independent or are related in some way.
Note:
The Chi squared test is asymptotically very good, but it may lead to incorrect conclusions when some cells
hold less than 5 elements.
From our example, the χ 2 test made with 95% confidence, TRUE, tells us that there is in fact a dependency
between the two variables Language and Client class. Respondents who speak English and Spanish are
more frequently in Class A, while French is more frequent in Class C.
The hypotheses CrossTab tests are:
Reject H 0 if χ 2 > χ 2 U ( r −1)( c −1) (variables are independent);
otherwise, do not reject H 0 (variables are related).
If H 0 is rejected, CrossTab prints FALSE in the first line of text below the table, together with the confidence
level. If H 0 is not rejected, CrossTab prints TRUE. The test statistic is computed as follows:
χ2 =
∑
allcells
( fo − fe )2
fe
Where:
f o = Observed frequency;
f e = Expected frequency.
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Tip:
In Excel you can use CHIVALUE(x,df) and CHIINV(x,df) for computing Chi square values.
Testing variables for correlation (Pearson)
Using both R and R 2 coefficients, CrossTab can test the correlation between variables of each table it prints.
The Pearson Product Moment Correlation Coefficient, R. R is an index ranging from -1.0 to 1.0 which
reflects the extent of a linear relationship between two data sets. Panels A, B, and C in the picture below
show the three different types of association between variables.
In panel A, R = 1 represents perfect positive association between variables, which means Y increases in a
perfectly predictable manner as X increases. In panel B, R = 0.8, showing a strong relationship as well, but of
a negative nature so that as X increases Y decreases. Finally, panel C, R = 0, shows two unrelated
variables.
The Correlation Coefficient, however, does not tell us much about the strength of the relationship between
variables, which can be measured with the Coefficient of Determination, R 2 . R 2 measures the proportion
of variation explained by the independent variable. The proportion 1- R 2 is the aspect of variation explained
by factors other than what is accounted for by the two variables we use. Panel B, for instance, could refer to
the part of variability explained by the model and referring to daily sales and number of clients served.
B
A
y
r = -.8
r2 = .64
y
C
y
r=1
r2 = 1
x
r=0
r2 = 0
x
x
Note:
CrossTab prints the correlation and determination coefficients only when the input data is numerical. They
are skipped when the data is in string (text) form.
From the table above we see R = 0.094 and R squared = 0.009. This means no association has been found
between the language clients speak and the class they belong to. So, unfortunately, we cannot use the
variable Language to predict the client’s class membership.
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References to CrossTab
Richard W. Madsen, Melvin L. Moeschberger
Statistical Concept With Applications to Business and Economics
Prentice- Hall.
SPSS Inc.
SPSS User Guide
McGraw-Hill, 1983.
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317
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318
16. Descriptive Analyst
Descriptive Analyst in a Nutshell
What is the typical [price] for a certain product? How many of these products fall within a certain [price]
range? What is an unreasonable [price] for this product category?
Questions such as these can be answered with the MM4XL tool Descriptive Analyst. The brackets around
the variable name price underline the fact that these questions can be asked for any variable that can be
expressed on a categorical or continuous scale. Answering these questions can provide useful insights for
the manager responsible for compiling performance rankings, looking into industry sector records, or
comparing product profiles rather than competitor performance.
Descriptive Analyst provides Pareto curve (ABC) analysis, descriptive statistics, and box-whisker plots, which
are tools typically used when exploring data to answer questions such as these.
Note:
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How To Run Descriptive Analyst
Descriptive Analyst performs two major tasks:
•
•
It draws Pareto charts, also known as ABC curve analysis,
It computes descriptive statistics and prints box plots.
Both analyses can be run simultaneously for one or more input data series (batch analysis).
On the MM4XL floating toolbar, click this button to display the window shown below.
In the Input range field select the range where the input data is
stored. There must be at least two rows of data and the range can
be one or multiple columns of data. Each column is analyzed
separately. In the Output range field specify the place on the
sheet where the report should be printed, beginning at the upper
left cell specified.
Tip:
From the MM4XL menu open the Descriptive Analyst example for
a description of input data range.
Select the Labels in first row checkbox if the first row of data is
column labels. The column label is then used to identify reports
and charts.
At this point you are ready to choose what analysis to run.
Page 1: Pareto Chart
On the form shown to the right, select the Pareto Chart tab. Here
you will define the Pareto analysis options.
By default a summary table of the input data and the Pareto
chart will be printed. Clear the checkbox if you do not want to
print one of these.
In the Data panel, indicate whether the input data should be
treated as Categorical or Continuous. Categorical data is
expressed in classes, such as yes or no, below 100, 100-200,
201-300, etc. Continuous variables show values expressed on
an infinite scale, such as sales, costs, temperature, etc.
If you are working with continuous data, all you need to do is
select the Automatic bin calculation checkbox, and enter the
Number of groups you want to shrink the input data to.
Tip:
Watch the Excel status bar in the lower left corner. Messages are
displayed which briefly explain the kind of operation the tool is
performing at a particular moment.
When working with categorical data, you need to indicate where
to find the Bin range, which is a vector of labels used to reduce
input data into classes. Items marked with the same label (upper-
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320
and lowercase sensitive) are counted together in the same group. For more information about bin ranges,
refer to the Descriptive Analyst sheet in the MM4XL Examples folder under the Windows Start button.
Click OK to print results on the sheet.
Page 2: Descriptive Statistics
Select the Descriptive Statistics tab. There are three checkboxes to select. When Print table is not
selected the other two options are deactivated. An example of the table is shown in the Output report
section.
A Box plot can be printed by selecting the checkbox. When working with series measured with different
scales, select the Rescale data checkbox to print the box plot(s) on a percent basis, otherwise the chart will
be difficult to read.
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Output Report
A full output report generated by Descriptive Analyst prints a table and a chart covering the Pareto analysis
and descriptive statistics.
Pareto analysis
When exploring data, two tools statisticians typically use are frequency
tables and histograms. Pareto analysis brings these together to look at
the spread of data over a range of values. For example, we might be
interested in analyzing sales from a list of 450 stores, rather than the
spread of prices, or any other descriptive characteristic.
In the example below we look at the selling price of 191 PC’s. The table
showing the range of possible values has been arranged in 15 classes
(Bin range) scaled equally and sorted in ascending order. The frequency
count of prices falling in each class is reported under the heading
Frequency. Twenty items fall into the class $2,418, with an average price
of $2,274. These represent 10.5% of the 191 items in the list, which adds
up to 11.5% in cumulative form (class one plus class two).
The Pareto chart shown below displays the Frequency and Cumulative%
from the table, which is a good aid for grasping the overall distribution
shape of the data we are interested in.
Frequency
70
87.4%
92.7%
94.8%
$4'355
$4'839
68.6%
47.6%
40
30
20
11.5%
1.0%
10
0
$1'934
$2'418
$2'902
Nbr of observations
mean
Geometric mean
Price
191
3159.9
FALSCH
Standard dev.
828.9
1 st Quartile
2600.0
Min
1450.0
Median
2950.0
Max
7260.0
3 rd Quartile
3510.0
Kurtosis
4.61
Skewness
1.76
Mode
2600.0
Sum
603545.0
From the frequency
table and chart we
can see at a glance
that 87.4% of prices
fall within $3,871. If
120%
99.5% 100.0%
99.0%
98.4%
96.9%
we were planning to
100%
buy a new PC for a
80%
price
between
$2,400 and $3,500,
60%
we see there are
40%
129 products that
20%
may be of interest.
0%
The same analysis
$5'323
$5'807
$6'292
$6'776
More
repeated on different
characteristics of the
same data set may
help
to
refine
refining the data and select only the products that exhibit
the profile most appealing to us.
Cumulative %
80
50
Descriptors
Frequency
Pareto Chart - Series: Price
60
Descriptive statistics report
$3'387
$3'871
Bin
Pareto chart report: Bin range.
Series Price: 1 of 1
Title row 3
Bin
Frequency
Group
Average
Frequency% Cumulative%
$
1'934
2
$
1'670
1.0%
1.0%
$
2'418
20
$
2'274
10.5%
11.5%
$
2'902
69
$
2'674
36.1%
47.6%
$
3'387
40
$
3'124
20.9%
68.6%
$
3'871
36
$
3'597
18.8%
87.4%
$
4'355
10
$
4'041
5.2%
92.7%
$
4'839
4
$
4'675
2.1%
94.8%
$
5'323
4
$
5'131
2.1%
96.9%
$
5'807
3
$
5'548
1.6%
98.4%
$
6'292
1
$
5'820
0.5%
99.0%
$
6'776
1
$
6'400
0.5%
99.5%
More
1
$
7'260
0.5%
100.0%
Total
191
$
3'160
100.0%
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Tip:
If you want to use an equally spaced bin range in value
that makes sense to you, for instance, from 0 to 10,000
scaled with intervals of $1,000, proceed as follows. Type
0 in cell A1 and 1,000 in cell A2. Select the range A1:A2,
position the pointer on the small black box in the lower
right corner of the selected range. Right-click and select
all cells to A10. Use the newly created range as the bin
range for Pareto analysis with categorical data.
322
Statistics
The price distribution of our example can be examined further with the aid of the Descriptive Statistics
Report, which is a summary table of measures of tendency (mean, median, and mode), measures of shape
(skewness and kurtosis), and measures of variability (standard deviation and variance, which is equal to
Standard deviation squared).
Box plots
The box plot is a very useful tool for viewing a distribution. It shows extreme and quartile values in a pictorial
representation as in the chart below. The box plot of our example was rescaled to percentage values. This is
a useful feature when working with multiple data series expressed with different measurement scales. For
instance, when looking simultaneously at three different vectors of sales in thousands of dollars, in units, and
in percentage.
Rescaled data for box Plot
1 st Quartile
35.00%
Min
23.00%
Median
61.00%
Max
100.00%
3 rd Quartile
87.00%
The table above displays %-rescaled values.
Max, largest value in the data
3rd quartile, 75% of
data fall below it.
Whisker
Median, the middle value
with sorted data.
Box
1st quartile, 25% of data
fall below it.
Min, lower value in the data.
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323
Technicalities
Known problems
References to Decriptive Analyst
Berk Kennet, Carey Patrick
Data Analysis with Microsoft Excel
Duxbury, 1995.
Tukey, J. W.
Exploratory Data Analysis
Addison-Wesley, 1987.
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17. Group Variation Analyst
Group Variation Analyst in a Nutshell
Think of a product manager dealing with two promotional offers a year. Twice every year the same decision
has to be made, and every time he is faced with the same question: What’s best? The problem escalates
when referred to a marketing manager coordinating seven product managers and 11 major brands, perhaps
running four promotions a year. In such cases a clear understanding of the results produced in the past by a
single promotional action or a category of actions may prove very useful for increasing brand success.
Variation Analyst is a very flexible tool. It applies the analysis of variance (ANOVA) method to a variety of
data and finds out whether a significant difference exists between the performance results of two or more
comparable groups, such as sales growth in areas with and without promotional action. It reports results in a
concise and comprehensible manner and draws easy to understand, yet very helpful, charts designed for
business decision-makers rather than statisticians.
With Variation Analyst, MM4XL makes available another powerful weapon in the hands of dedicated
managers aware of the importance of monitoring scenarios and of making informed decisions based on solid
facts and data.
Quadrant Analysis: Dash vs Dixan
Item 2
2.5%
Disappo int
Head to head
Dixan
Item 3
0.5%
Item 6
Item 1
-1.5%
-0.1%
Item 5
Item 4
To gh jo bs
Go t it
1.7%
3.5%
Dash
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327
How To Run Group Variation Analyst
On the MM4XL floating toolbar, select this button to display the window shown below.
In the Input range field select the range where the input
data is stored. In an input range there must be at least two
columns and two rows of data. Select the Labels included
checkbox if the first row contains text labels. In the Output
range field select the cell on the sheet where you want the
output report to begin. Finally, assign a Probability value
larger than zero and smaller than one. Setting a large value
for probability requires a large difference between groups in
order to be significant. In the next section you can read
more about the shape and kind of input data feasible for
analysis.
The tool prints by default a summary table showing the
result of paired tests between input items. The options in
the lower part of the form refine and enlarge the analysis
report. Select Print statistics if you want a table of
descriptive measures such as mean, standard deviation,
etc. of the input data. Select Input data chart to generate a
common line chart showing the user input data. The
Averages chart shows average and variance values for each group included in the analysis.
When the Quadrant analysis checkbox is selected, a summary table is printed that shows, for the pair of
input items selected in the list box below, the paired performance of each element of both groups and related
statistics.
More information concerning the meaning of the output report created with Variation Analyst can be found in
the section Anatomy of a Variation Analyst Report.
Note:
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Planning and Managing Business Tests
Why perform business testing? For several reasons. First, competitive scenarios get more complex as time
goes by, and the pragmatic way alone cannot guarantee long-term success. Second, companies operating
through organized marketing departments purchase large amounts of expensive business data containing a
lot of useful information, which is often not fully available to managers. Finally, a thoughtful business testing
plan helps reduce managerial risk and helps you make better informed decisions.
Effective testing is comparable, concise, repeatable, actionable, and focused on business. Large projects
should be scaled down. Test results should be stored and their trends should be analyzed from time to time,
in order to reach general conclusions concerning the overall benefit of the process for the business.
Arranging data for testing
The data is key, and the GIGO concept holds true: Garbage In, Garbage Out. Before looking at the
assumptions that must be met in order to run a reliable variation analysis, let’s discuss the form and kind of
data suitable for the analysis.
There are two main situations when we want to analyze performance:
1. To find out differences in internal and
external data. The former refers, for
instance, to our product only, and the latter
includes competitors as well.
2. To find out differences in spatial and time
data, such as several geographic areas or
time series.
The four tables to the right show hypothetical data
concerning sales performance of a product called
Dash in several situations. The upper-left table shows
measurements for the same product in three different
geographic areas: Areas 1, 2 and 3. Each area is
made up of six zones (or stores if you like), and the
data shows sales growth by zone. For instance, the value in cell B2 is obtained by dividing the sales value
for Dash in Zone 1 of Area 1 in August 2004 by the sales value in the same zone for July 2004 minus 1.
This test may be of great value to managers, for example when evaluating the effectiveness of promotional
actions. Say you want to increase sales in the short run by means of a promotional campaign, and you have
doubts concerning which of three concepts should be applied: price discount, increased quantity, or bundling
a convenience package. Surveying a sample of consumers could produce the data needed to make an
informed decision based on customer preference and profitability, because Variation Analyst supplies values
that make clear the advantage of one choice against the others.
You may have noticed there are missing values in two of the tables. Variation Analyst handles such cases
without requiring the user to take any action. Missing data is discussed further in the Technicalities section.
The tables show percent values, but units or monetary data can also be used. The important thing is that the
variances of the groups (columns) are equal or close. In this instance, Variation Analyst produces reliable
results. However, if one of the stability assumptions is unmet, it may produce unreliable and, therefore,
dangerous results. The Technicalities section provides information concerning the assumptions underlying
the data arrangement for this analytical tool.
Implementing a Marketing Testing Lab
For any given product, the information needs of a general manager are different from those of a marketing
manager, a product manager, a sales manager, or a sales rep. Nevertheless, all of them may find it
beneficial to measure and test the effectiveness of business decisions and actions. When testing is done in
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329
an ongoing fashion and complies with some simple accuracy and reporting rules, both the new and the
experienced manager may find it very useful for making future business decisions.
Business analysts play an important role in planning and running testing plans. They most often own the
data and know them well, they are a link to different products and managers, and they have (or are in the
position of developing) the required know-how for implementing reliable business test plans. Managers and
analysts should decide together what makes sense and should be tested on an ongoing basis, whether the
data are available and robust, how to summarize results, and everything should be wrapped together in a
shared document for future reference. Then, for each individual test, one introductory page should be written
before the test is run, that synthetically describes goal, copy strategy, expected results, targeted group(s),
direct competitor(s) and their expected reaction. After the test is run one summary page should report
synthetically on the results of the action. These two pages, attached to each test, make an invaluable
information base for managers keen on building success upon success rather than moving on randomly.
Finally, trends of test results should be analyzed from time to time, to draw general conclusions concerning
the overall benefit of the process for the business, and to suggest improvements.
Anatomy of a Variation Analyst Output Report
The tables and charts generated by Variation Analyst always look the same, although the way some
formulae are computed varies depending on whether the analysis is made with equal or unequal sample
sizes. The user is not required to take any action in either case, because the tool can detect automatically
which instance applies.
To illustrate the output report we use the data of the sheet Data Equal sample in the Example file that can be opened from the tool
form.
There are three groups in the data set: Dash, Dixan and Persil. The
values refer to sales growth performance in six geographic regions
where Dash ran a promotional action targeting Dixan. The manager
wants to know whether the action produced the expected result. Persil was included in the study as a control
group.
The critical output section of the Variation test is the Group Comparison Report, shown below. Column A
contains the pairs of groups, products in our examples, tested for the significance of differences.
Each row shows the result of one test, and there are n(n-1)/2 tests run in an analysis, in our case 3 tests =
3*2/2.
Column B is the key place to examine. Yes in cell B27 stands for “Yes, results measured for Dash are
statistically different from those measured for Dixan”.
The column Desired Probability indicates the probability level employed for the test, 95%. To its right,
Achieved Probability indicates the probability level the analysis found for each comparison of group pairs.
When the achieved probability is lower than the desired one we must conclude that the variation in the data
is not significant and it must be due to casual effect rather than to our promotional activity. Therefore, in
these cases column B will display No.
F-Value and F-critical contain the base values used by the analysis of variance method to test its
assumptions, and for which we refer the reader to any statistics book dealing with this well-known analytical
method. Read also the Technicalities section for more information concerning the F-value.
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Correlation shows the measure of association concerning the input data of the group-pair. The correlation
coefficient ranges from 1 to -1. Our example shows a positive association for Dash and Dixan. With
reference to the input data, this means when sales of Dash grow, sales of Dixan also grow, and vice versa.
On the other hand, in cell G28 we find a negative association between Dash and Persil, meaning that when
sales of Dash grow those of Persil shrink, and vice versa. These facts may be due to the peculiar distribution
system of the market or other reasons, and in both cases they contribute an extra piece of information useful
to frame the context in an appropriate manner.
In the Average Difference column we find the overall difference in mean value for the pair in analysis. The
value 0.02 in cell H27 stands for an average +2% sales growth for Dash against Dixan. A negative value
would have meant that Dixan had performed better in sales growth than Dash did. This value may be used
as a reference point for the measurement of the effectiveness of promotional activities (we remind the reader
that promotions are strategic activities offered for a short period of time and aimed at increasing sales
volume).
The Statistics table shows the most common descriptive
measures for each group. This information can help us
understand the shape of the data we are working with,
especially Mean and Variance values as we shall see.
The chart Input Data is a common line chart drawn with the
original values as input by the user.
The chart Average – Variance plots these two measures for each
group, and it can be very helpful to figure out what kind of products
(groups) we are dealing with. According to the input data of the
example, a high average value such as for Dash may be obtained
thanks to a few abnormally large observations only, which wouldn’t
necessarily indicate an overall positive impact of the promotion. For
this reason, the variance is plotted together with the mean. When the
variance is high, such as for Dixan, we may conclude there are spread
observations in the data ranging from very high to very low (indeed
Dixan has the lowest Min value of the three groups). Alternatively,
when the variance is low we may conclude most observations are
placed around the mean value, which in such a case may be seen as a
good estimator of the final promotion outcome (like Persil, which has
the smallest value, 0.026 or 2.6%, for the difference Max-Min).
Input Data
4.0%
3.0%
2.0%
1.0%
0.0%
-1.0%
-2.0%
1
2
3
Dash
5
A verage
6
Persil
Variance
0.02
0.00
0.00
The Quadrant Analysis is the last output element produced by
Variation Analyst, and it can prove very useful when dealing with
groups made of many rows, such as sales growth values concerning
200 micro-zones of a whole country, for example. But it may also be
very helpful with a smaller number of items, as we are going to see.
4
It e m s
Dixan
0.01
0.00
Dash
Dixan
0.00
Persil
Each item (geographic areas in our example) of the input data
for a selected pair of groups is assigned to one of four
categories. The labels in column A of the summary table refer to
the quadrant position in the chart. Top-Right, for instance, is the
quadrant of the chart hosting zones scoring high on the second
as well as the first product. In our example, there are two such
zones (2 and 3) for the pair Dash (product 1) versus Dixan
(product 2). For the product target of the analysis, Dash, the
input data for the two zones Sum up to 5.9% (cell C34) and they have an Average value equal to 3% (cell
D34). On average, items belonging to the Top-Right quadrant contribute +1.9% (cell E34) as compared to
the overall product average value of 2.1% (cell E37).
Looking at the quadrant chart may make it easier to understand the concept. The chart is a scatter plot with
on the x-axis the input values for the first product of the pair in analysis. In our example this is Dash, and the
length of the x-axis goes from -01% to 3.5%, respectively the min and max value for Dash input data (see
cells B17 and B18 of the Statistics table). Similarly, the y-axis ranges, in this example, from -1.5% to 2.5%,
which are the min and max values for Dixan (cells C17 and C18 of the Statistics table). For both axes the
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crossing point is set to the mid-point, which equals (Max-Min)/2. This way the chart splits in four quadrants of
equal size. Each quadrant has a meaning, and for ease of interpretation they have been labeled as follows:
1. Top-Left: Disappoint.
These are items where product 1 scored low and product 2
scored high. If we were analyzing the result of a promotional
action, areas placed in this region of the chart had reacted badly
to the offer of the target product. Typically, there shouldn’t be
items in this quadrant.
Item 2
2.5%
Disappo int
Head to head
Item 3
Dixan
2. Top-Right: Head to head
Items in this quadrant scored well on both products, which may
indicate a not very effective promotion on our part. Typically, we
should see a reduction in performance of the target competitor as
opposed to growth for the challenger one. When both grow one
may suspect the growth is due also to reasons independent of the
promotion itself. Financially speaking, items in this quadrant are
acceptable, but on the strategic side they are not. There shouldn’t
be too many items here.
Quadrant Analysis: Dash vs Dixan
0.5%
Item 5
Item 6
Item 1
-1.5%
-0.1%
Item 4
To gh jo bs
Go t it
1.7%
3.5%
Dash
3. Bottom-Left: Tough jobs
These are items where both products scored low. Winning space in these areas seems to be very difficult. In
order to have an effective action there should not be many items in this quadrant, although it is quite
common to have areas where the performance is lower than in others. The position is sustainable as long as
the x-axis doesn’t sink into negative values.
4. Bottom-Right: Got it
The optimal outcome of a promotional action is that our product sales grow and those of the target
competitor decrease, indicating that we drew market share away from the competitor. This is captured in the
lowest quadrant on the right of the chart. When running a promotion, we want to find as many items as
possible in this quadrant.
A note of caution is required. So far we have been discussing an example based on sales growth data.
Some of the statements made above might not apply when dealing with data sets where, for instance,
negative values are interpreted as a positive rather than a negative outcome, for instance, reduction in time
or savings on costs.
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Technicalities
It is frequently of interest to compare differences in results among several groups. When the outcome
measurements across the groups are continuous, and certain assumptions are met, a methodology known
as Analysis of Variance, or ANOVA, may be employed to compare the means of the groups. The term
Analysis of Variance may be misleading since the objective of the analysis is to compare means. However,
through an analysis of the variation in the data we will be able to draw conclusions about possible
differences in the group means.
Group Variation Analyst computes the one-factor ANOVA F-test for difference for pairs of group means
rather than for all groups at once.
The assumptions to be met in order for the ANOVA to produce reliable results are three:
•
•
•
Error terms must be random and independent. That is, the difference (or error) for one
observation should not be related to the difference for any other observation. Most often this
assumption is violated when data are collected over a period of time, because measurements made
at adjacent time points may be more alike than those made at very different time, for instance when
measuring air temperature.
Values in each group must be normally distributed. As long as the distributions are not extremely
different from a normal distribution (bell shaped curve), the level of significance of the ANOVA test is
fairly robust, particularly for large samples.
Homogeneity of variance. This means that the variance within each group must be equal (very
close) for all groups. This assumption is often violated when analyzing groups with different sample
sizes. Thus, for computational effectiveness, robustness, and power, there should be groups of
equal sample size whenever possible.
If the normality and homogeneity assumptions are violated, an appropriate data transformation may be used
for normalizing data and reducing the difference in variances.
In ANOVA the null hypothesis is that no difference exists in the
means of the groups. The test splits the total variation in Within
and Between group variation and it computes the test statistics
F. The F-value follows an F-distribution, and for a given level of
confidence we may reject the null hypothesis if the F-value
exceeds the F-critical, which is the upper tail of the Fdistribution.
Unequal sample size
Σ n (Y
t
Although we have written that there should be groups of equal sample size
whenever possible, we can still obtain a suitable test statistic when the sample
sizes are not all equal. Specifically, we use the following formula as a test statistic
and reject the null hypothesis when the computed value exceeds F-critical. See
Madsen pg 530 for details.
i
i =1
Σ Σ (Y
t
ni
i =1 j =1
i, j
i.
− Y.. ) / (t − 1)
2
t
2 ⎡⎛
⎞ ⎤
− Yi . ) / ⎢⎜ Σ ni ⎟ − t ⎥
i
=
1
⎠ ⎦
⎣⎝
Other ANOVA methods
The analysis-of-variance method we have discussed so far is the one-factor model. Two or more factors can
also be tested, and MarketingStat is willing to develop further methods as our clients make the request.
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References to Group Variation Analyst
Berk Carey
Duxbury, 1998
R. W. Madsen, M. L. Moeschberger
Statistical Concepts with Application to Business and Economics
Prentice-Hall International
Gary Smith
Statistical Reasoning
Allyn and Bacon, Massachusetts 1988
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Section 3: Charts & Maps
Present data in an effective way thanks to better charts and maps.
SMART MAPPING
DIFFERENTIAL SEMANTIC
4D MAP
STACKED CHARTS
BENCHMARK MAP
PROJECT (MIND) MAPPING
(8)
Analytical (8)
Analytical
Strategic(9)
(9)
Strategic
•CrossTab
•CrossTab
•SampleManager
Manager
•Sample
Manager
•Proportion
Manager
•Descriptive
•ClusterAnalysis
Analysis
•Cluster
•SegmentationTree
Tree
•Segmentation
•GravityAnalyst
Analyst
•Gravity
•VariationAnalyst
Analyst
•Variation
•BCGPortfolio
PortfolioMatrix
Matrix
•BCG
PortfolioMtx
Mtx
•McKinsey
•
Brand
Switch
•Brand Switch
•BrandMapping
Mapping
•Brand
•
Forecast
Manager
•Forecast Manager
•ProfileManager
Manager
•Profile
•QualityAnalyst
Analyst
•Quality
•DecisionTree
Tree
•Decision
•
Risk
Analyst
•Risk Analyst
CHARTS
&
MAPS
ANALYTICAL
STRATEGIC
(6)
Charts&&Maps
Maps(6)
Charts
•SmartMapping
Mapping
•Smart
Semantic
•Differential
•
4D
Map
•4D Map
•StackedCharts
Charts
•Stacked
•
Benchmark
Map
•Benchmark Map
•Project(Mind)
(Mind)Mapping
Mapping
•Project
Charting tools: Smart Mapping, Semantic Differential, 4D Chart, Stacked Charts
MM4XL charting tools help you get more information out of data, overcome the limitations of Excel’s chart wizard, and
present data in a more readable format. Charts and maps are easy to draw with MM4XL, and they are exportable to any
other Windows application.
- Smart Mapping
Æ Bubble maps and Quadrant analysis with labels, arrows, and more
- Semantic Differential
Æ Chart used for profiling purposes
- 4D Chart
Æ Add more information to one chart
- Stacked Charts
Æ One more trick for clearer charting
- Benchmark Map
Æ Compare product performance to market tendency, and more
- Project (Mind) Mapping Æ Draw mind maps, link files, record voice messages, use symbol icons to enhance project
management
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338
18. Smart Mapping
Smart Mapping in a Nutshell
Smart Mapping creates bubble maps. A bubble map is a scatter plot whose points have been enlarged to
bubbles, and the diameter refers to a third variable. Smart Mapping draws two basic kinds of maps: with
common bubbles and with normalized variables.
Bubbles = Price 98
Max = 24,6
Less than 16
More than 15
High
Sun Protection
50_VICHY
50_VICHY
Unit price
50_VICHY
30_DAYLONG
50_MICROSUN
100_WIDMER
100_WIDMER
100_DAYLONG
90_MICROSUN
200_WIDMER
150_VICHY
125_VICHY
125_VICHY
150_VICHY
Low
200_DAYLONG
200_WIDMER
150_VICHY
Low
150_VICHY
Sales growth 98
High
Notes:
Large packs tend to have low er unit price.
Keep an eye on the future perform ance of Vichy 50 and 150
Normalization, a statistical computation to allow comparison of different variables, subtracts from each item
of a series the mean of all elements of the variable. Normalized variables are useful for getting rid of the
scale-of-measurement effect and allowing you to interpret more quickly and effectively the variable
distributions, for they make evident the over- and under-representations existing in the data. The end result
is a map similar to the one above.
Excel provides the ability to draw bubble maps, but they are less refined than the bubble maps you can make
with MM4XL. In Excel labels cannot be displayed, arrows linking bubbles are not available, and changing the
color of single bubbles may be a very long and tedious process. Moreover, there is no way to automatically
rescale quadrants or set the horizontal axis to a mean or median value. MM4XL helps you to overcome
these and other limitations and to save a lot of time.
Note:
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18. Smart Mapping
339
How to run Smart Mapping
On the MM4XL floating toolbar, click this button to display the Smart Mapping user form.
There are two tabs in the user form. Use the Input Data
tab to select the relevant data ranges. The Options tab
provides controls for refining the maps.
Input Data Tab
When launched, the Input Data tab fields are displayed.
Place the cursor in the 1st dimension (horizontal) field
and select on the sheet the data to be displayed on the
X-axis of the map. Repeat this operation for the 2nd
dimension (vertical), and for the 3rd dimension
(bubble), the size of the bubbles.
Note:
To understand quickly how to prepare data for input to
Smart Mapping, study the example file you can open
from the user form by clicking on the Example button.
Use the Bubble groups (color) field to assign different
colors to bubbles. This is a very useful option to visually distinguish items belonging to different groups, for
example small, medium and large packages. In this field you can input any sign: number or letter. The
function is case-sensitive, so a capital letter is not equal to the same letter written in lowercase. In the
Output range field select a cell on the sheet where you want to print the map. In the Data labels field select
the item labels to be displayed on the map. This is a very helpful option, not available for common Excel
charts, which will save you a lot of work!
From the Quadrant type list box you can choose one of four options. The Common bubble chart option
creates basic charts. The remaining options offer three ways to rescale quadrants. More details on this
option can be found below in the section Why and How to Re-scale Quadrants.
Tip:
To run a dynamic analysis using the field Bubble Color,
input different values for the same items at two points in
time. For instance, market shares of products A, B and C
in 1998, and market shares for the same products in
2001. Give different labels to each item, and the products
belonging to each group will be colored accordingly.
Use the Chart title box to specify a title for the chart.
Options Tab
When all fields on the Input Data tab are filled, select the
Options tab. Here you can refine the map, as well as
enhance it with some very useful features such as
placing connecting arrows between bubbles and
changing label size.
Use the Chart title 2 and Footnote text boxes to enter
text that will be shown on the map. Remember that
placing too much text on a map can either make it too crowded or require enlarging it significantly. Changing
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340
Label size and Color may prove useful when working with maps crowded with items. Click on the Label
Color button to access the color palette.
Connecting Arrows enables you to display arrows between bubbles. To see an example of arrows placed
on a map, open the Example file using the button in the lower left area of the form. See the section Example
of Sales Tendency Analysis below for details on how to place arrows and how to format chart elements. The
Remove chart axes is useful when negative values are displayed and you do not want the axis lines to
display for reasons of neatness. Plot on new sheet is used to create the graph on a single sheet. Read
more concerning Hide intermediary sheets in the Tip below. Click OK when you are done and the following
lines appear starting at the cell you selected in Output range:
Tip :
Every time the analysis is run, a new sheet is created to store the original and normalized data. Clear the
Hide intermediary sheets checkbox on the Options tab if you are going to run the same analysis several
times with only slight differences in the data. You may want to find out which display best suits your
requirements, and get rid of sheets you no longer need (when the Hide intermediary sheets option is
selected use Format Sheet Unhide in the Excel menu and then Edit Delete Sheet).
As you click the OK button a scatter chart like the one to the right
appears on the sheet. The first dimension you select is displayed on
the horizontal axis, the X-axis or abscissa. The second dimension is
displayed on the ordinate axis, the Y one, and the third dimension
of data is used to compute the size of each bubble. Stretching the
graph in length makes it much more readable, and after a very few
seconds work, will look like the example. It is very easy to modify
the layout of a chart. Select each element and change it to
whatever you like. To change text or position of a single label, for
instance, click on it once, and all labels of one data series will be
selected. Wait a second and then click again on the label, and only
this one will be selected. Now, click on the label border and drag
and drop it.
Here is the same chart before and after the changes:
Bubbles = Price 98
Max = 24,6
Less than 16
More than 15
High
Sun Protection
50_VICHY
50_VICHY
Unit price
50_VICHY
30_DAYLONG
50_MICROSUN
100_WIDMER
100_WIDMER
100_DAYLONG
90_MICROSUN
200_WIDMER
150_VICHY
125_VICHY
125_VICHY
150_VICHY
Low
200_DAYLONG
200_WIDMER
150_VICHY
Low
Sales growth 98
150_VICHY
High
Notes:
Large packs tend to have low er unit price.
Keep an eye on the future perform ance of Vichy 50 and 150
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18. Smart Mapping
341
How to Interpret Normalized Smart Mapping
When a Quadrant type other than the Common bubble chart is selected
Smart Mapping produces a normalized chart split into four quadrants.
One item, say a product, located in the upper right quadrant, called A,
has high values on both variables. Items in quadrant B have high values
for X and low values for Y, while items in quadrant C have low values
for both variables. Quadrant D items have low values for X and high
values for Y. The meaning of the quadrants depends only on the
variables included in the analysis.
In our example, sales growth and unit price have been plotted. In the
upper right quadrant are products with a high price that won sales over
the past year. Below and to the left, are low priced products, which lost
sales. Analysts with experience can find reasons to explain each
product’s position within each quadrant, and can provide input to management based on facts, rather than
beliefs and intuition. Normalized values are obtained, subtracting from each value its mean:
(x i − µ x )
With this computation, the axes of the chart cross always at (0,0), x=0 and y=0, and the points stand out in
terms of over- and under-representation against the average. One item placed at (0,0), the origin of the map
– the point where the 2 axes cross – has values on both variables which correspond exactly to the mean
value of both variables. Thinking of products, Smart Mapping can help to:
•
•
•
•
identify groups of competitors that perform in a similar manner
look at the spread of sales among products
search for free and interesting market opportunities
find relationships and association among variables
The only limit on the ways of applying normalized Smart Mapping is the ingenuity of the analyst. A Smart
Mapping analysis can be run in a dynamic, static or hybrid context, with either absolute or indexed figures12.
The way the analyst treats the raw data makes the difference. Static values are computed at one moment in
time, for example, the price in March 2000 or total sales in 1999. Dynamic values are computed over two or
more different periods of time, for example, the increase in price between 1996 and 1999 or the market
share13 growth between May 1999 and January 2000.
⎡⎛ Market Share 99 ⎞ ⎤
⎟⎟ − 1⎥ ⋅ 100
Market Share Growth 99 / 96 = ⎢⎜⎜
⎣⎢⎝ Market Share 96 ⎠ ⎦⎥
12
There are four scales of variables: Nominal is qualitative data classified in categories (male - female, etc.); Ordinal are nominal
variables which can also be ordered (high - medium - low, etc.); Interval are ordinal variables which can be expressed on an interval
scale (price indexes, intelligence quotient, etc.); Proportional are interval scaled variables which also include the zero.
13
The market share is the relative frequency of the sales of one product divided by the total sales of all competitors in the market, as
depicted below:
⎛ Pr oduct Sales1999
⎜⎜
⎝ MarketValu e1999
⎞
⎟⎟ ⋅ 100
⎠
The sum of the market shares of all competitors in one market must equal 1 or 100%. For convenience, the market share can be
computed both in value or units, which can lead to different results. In this context, the definition of the market is one very basic aspect
of the Product Portfolio Analysis. Each competitor within a given market must be taken into account in order to make a plausible
estimate of the market growth.
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Why and How To Re-scale Quadrants
Smart Mapping offers three options for re-scaling quadrants (see the Quadrant type field description above):
Median, Mean and Equal size. The last option yields equally scaled quadrants and it is computed using the
formula:
⎛ Min x t + Max x t ⎞
⎟
X t − ⎜⎜
⎟
2
⎝
⎠
Median and mean correspond to the common statistics. The pictures below show what happens when the
same data is plotted using each of the three options. The position of the bubbles does not change, merely
the origin of the map changes position.
Bubbles = c
Max = 87
Bubbles = c
Max = 87
Mean
High
High
(Min+Max)/2
Median
High
Bubbles = c
Max = 87
D
D
b
D
A
A
C
W
Y
A
E
Low
a
Low
B
High
Z
C B
Low
E
Low
C
B
a
Low
W
Y
High
Z
E
a
Low
W
Y
High
Z
The Mean option is used when the data of each variable is homogeneous; i.e. there are no excessively high
or low figures within each variable. If there are abnormal values the Median option should be used. The
median value of a series is simply computed ordering all figures in an ascending order and selecting the midpoint value. If, for example, there were seven items in a list, say 1, 2, 3, 4, 5, 6, and 170 the median value
would be 4. With this computation we avoid computing a mean value of 27.3, which would certainly not be
representative of the dispersion in the variable.
Finally, the Equal size option (Min+Max)/2 is useful to simplify the visual inspection of normally distributed
values. In fact, the analyst has a clear picture of the space left above or below both tails of the variable.
With rescaled quadrants axis labels aren’t shown because they do not really make sense. For the
interpretation it is the position one bubble takes according to the four quadrants that is of interest rather than
its absolute coordinates. Moreover, the original coordinates are rescaled, and they may differ from the
original user input. Should you still want to display axis values, double-click on one axis and check the option
Low in the lower right frame of the first page in the form that appears.
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18. Smart Mapping
343
Example of a Structured CM in the OTC Market
The general manager of a hypothetical company pressures staff
to launch successful new products. The marketing manager asks
the product manager to provide a picture of the current skin care
market and come up with a proposal. The product manager asks
the marketing research manager for help, who assigns the
project to marketing analyst George. George suggests starting
with a picture of the market dimension and tendency among
segments, in order to identify business areas worthy of an indepth analysis.
The skin care market is split into 18 segments. Each segment is
measured on static and dynamic growth, computed on sales in
units as shown in the table to the right. The segments are then
plotted using the Common Bubble Chart option.
Most segments are plotted on the left side of the map, meaning
the skin care market has grown in the past at a faster rate.
However, four segments seem to be interesting enough and be
worthy of more detailed analysis. On the right side, Face
Creams, both day and night, Body Lotion and the Sun Protection
segments have grown in 1998 above the average segment.
Gain experience with the program. Try
drawing some maps using this data and
form your own conclusions.
B ubbles = Ums98
M ax = 15716412.5
Skin Care Market
2nd Quarter 2003
200%
Hand Care
Dynamic Market Growth 98/95
George and the PM agree to focus on
the Sun Protection segment, and the
data shown below is used to look at the
performance of the most relevant
competitors.
Sun Protection
150%
Band aid
100%
50%
Optical
Acne care
Lipsticks
Bath and Oils
0%
Hair
Babies
Body Lotion
Show er
Medical Cosmetics
Wounds
Anti-Mycotika
Night Face Creme
Day Face
Creme
Hair system
Feet
-50%
-20%
-10%
0%
10%
20%
30%
40%
Static Market Grow th 98
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Example of Sales Tendency Analysis
Managers find it useful to look at
sales tendencies over a given time
frame, for instance, product category
sales in the past three years.
Picturing data in this way makes
evident
the
sales
trend
characterizing each item, and this
information proves useful when
assigning targets or controlling
performance.
MM4XL makes the Connecting
Arrows function available with the
Smart Mapping tool. This feature is
very effective in highlighting item
shifts over time because, as you can
see in the chart to the right, the
arrows make clear the direction bubbles take. When working with graphics crowded with bubbles, arrows can
make interpretation much faster and easy to understand.
The table here shows how to arrange data for placing
arrows. Of course, the number of periods that can be
connected with arrows is not limited to three as in this
example, but it may vary according to your preference
and needs.
Data labels relating to time (column B) are listed from last
to first, so the arrow direction matches the time direction.
In column E, we can see the grouping variable stays
unaltered for all items in one group. As for our example,
data in columns C and D are used to plot item
coordinates on the chart, and data in column F are used
to enlarge bubble size.
On the Options tab of the tool form there are controls for
setting arrow appearance and color, as well as the size of
the labels displayed beside each item on the chart.
As the chart appears on the sheet you may want to change the appearance of some of its elements. When
arrows are shown, to resize the plot area you need to use the Tab key to select the plot area and resize it
using the mouse.
Note:
If you simply click on the plot area with the mouse it won’t stay selected. If, after you resize the plot area,
arrows no longer match the bubble positions, click once on the plot area and all arrows will be repositioned
correctly in the middle of the bubble they refer to.
In order to make charts more readable, and depending on the number of items shown on the chart, you may
want to make some changes to the default chart produced with Smart Mapping. Click on it and drag the
legend to a different position or double-click on it to open the Format Legend form that allows you to resize
the legend and change more of its look. Similarly, double-click on a chart axis to open the Format Axis form
where you can change axis font size, color, etc. Double-click on a bubble to open the Format Series form
where you can change bubble size proportionally across all bubbles (Options tab), bubble color and more.
Also, double-click on a chart axis and open the Format Axis form where you can change the minimum and
maximum axis value and more.
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Note on Scatter Plotting
A scatter diagram is an effective pictorial representation for investigating relationships among variables. It
can be effectively employed to investigate the following:
•
•
•
Segmentations occurring in the data set
Associations between dependent and independent variables
Predictions of future performance
When the scatter chart takes the form of a bubble chart, the picture is enriched by use of a third variable. In
the example in the Smart Mapping in a Nutshell section, the segmentation among products in terms of pack
size is quite evident. It also demonstrates the relationship between variables, in that where the price
increases the pack size decreases. Using a different data set we can show how to use scatter charts as
prediction tools.
Scatter Chart as a Forecast Tool
In the picture to the right, weekly sales are
plotted against the number of customers for a
hypothetical product. Each point shows the
level
of
sales
achieved
with
the
corresponding number of customers during a
given week. The blue line passing through
the dots in the chart was drawn using the
Add Trend line option built into Excel. The
equation displayed allows us to evaluate the
fit of the curve (trend line). It also makes
clear the parameters required when making
projections based on the charted data. It was
very simple to make projections using the
regression equation shown in our example.
Click the scatter chart, then select the menu
item Chart>Add Trendline. In the Type
section of the window that is displayed, select y = − 2E − 06 ⋅ 1800 2 + (0,0112 ⋅ 1800 ) + 2,5257 = 29166
Polynomial of Order 2 (refer to the Excel help
file for details) and in the Options section tick display equation on chart and Display R-squared value on
chart. Click OK and the trend line and equation are displayed. The trend line was computed using the
number of customers as the independent variable and the weekly sales as the dependent one. Given we
chose the order 2, the second variable was computed by elevating the number of customers to the power 2.
If, for example, we are going to start an advertising campaign
⎛ ∑ Weekly Sales ⎞
and assume the customers will increase to 1,800 in a certain
⎜
⎟
week, we might want to predict the weekly sales using the y = ⎜ Weekly Customers ⎟ ⋅ 1800 = 22070
∑
⎝
⎠
coefficients given in the regression equation. The formula is:
(
)
Therefore, if the advertising campaign is really going to bring 1,800 customers, we can assume that weekly
sales will increase to some 29 thousand dollars. The accuracy of the computation is quite high, as shown by
the R2, coefficient of correlation, and we can assume the computation is quite reliable. In fact, it yields a
much more reliable value (29,166 US$) than a computation based on averages (22,070 US$). The decision
to start the campaign can now be based on return on investment, rather than uncertainty of return.
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References to Smart Mapping
David Arnold
The Handbook of Brand Management
Berk Carey
Duxbury, 1998
R. W. Madsen, M. L. Moeschberger
Statistical Concepts with Application to Business and Economics
Prentice-Hall International
James H. Myers
Segmentation and Positioning for Strategic Marketing Decisions
American Marketing Association, 1996
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19. Semantic Differential
Semantic Differential Chart in a Nutshell
When investigating attitude, analysts typically use rating scales such as Likert’s one. Osgood’s
semantic differential scale goes one step further because it links the measurement to the
connotative meaning of words placed on a bipolar scale such as “Expensive-Cheap”, “Clean-Dirty”,
and so on.
The MM4XL tool Semantic Differential Chart draws attribute charts in the form of vertical lines as shown in
the one to the right.
This charting technique can be a great help to marketers when analyzing profiles, attitude, performance,
satisfaction, or any other dimension relevant for connotative analysis.
Product Attribute Comparison
2
Attributes
Ease of use
3
5
5
Useful w hen
travelling
1
3
I like the color
1
3
It smells good
1
Light w eight
1
3
5
7
Expensive
1
3
5
7
5
7
2
My husband likes it
too
2
0
P kt A
P kt B
P kt C
P kt D
1
2
4
6
4
6
4
3
7
4
5
6
7
8
Products
Note:
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How To Run Semantic Differential Chart
Select Semantic Differential Chart
in the MM4XL menu to display this
window.
The options are all quite selfexplanatory. Bear in mind you can
select the Input range before calling
the tool and the selected range will
be recognized as the input range to
use for charting. Values in the first
row of the input range are
recognized as column labels.
The three checkboxes in the Chart
options frame are used for refining
the chart. Show values plots figures
beside lines, as in our example
above. Vertical axis labels displays item labels, and Plot markers prints small symbols for differentiating
lines (diamonds, circles, squares, etc.).
You can assign Titles to chart and axes, and you can also display vertical and horizontal Gridlines by
selecting the applicable checkboxes.
The tool is equipped with a number of useful features that make its use more pleasant. Our thanks for the
development of Semantic Differential Chart go to Ing. Jon Peltier ([email protected]), Microsoft Excel
MVP.
Note:
The maximum number of attributes (rows) the tool can handle in one single series is 35. In certain
circumstances the number can be reduced by 1 row. The number of columns that can be used as input
varies with the series length. We were able to draw a chart with 116 columns and 7 rows.
Technicalities: The semantic differential concept
People adopt attitudes, hold opinions and express emotions with varying levels of intensity. To investigate
attitude and measure its intensity, investigators typically use rating scales. Psychologists Thurstone and
Likert pioneered attitude-measurement scaling methodologies with a type of differentiated scale: a scale that
would determine with acceptable accuracy a person’s attitude (towards an object or concept) along a
continuum. Likert, who also had great interest in corporate management, devised a summated attitude scale
that allowed for the summation and averaging of scaled responses. Here is an example of a Likert scale:
Strongly agree
Somewhat agree
Neither agree nor disagree
Somewhat disagree
Strongly disagree
There are many variations on this theme, but in general, Likert’s method involved attaching numbers to
levels of meaning. The Likert-type scale proved to be extremely robust, and continues to be widely used
today.
The scale types devised by Thurstone, Likert, and others, however, did not connect measurement with the
meanings of words. Charles Osgood in the early 1950s constructed a bipolar scale based on semantic
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350
opposites, such as "good-bad", "soft-hard", "fast-slow," "clean-dirty," "valuable-worthless," "fair-unfair," and
so on. Osgood called these scales "semantic differential" scales because they differentiated attitudinal
intensity based on a person’s subjective understanding of the connotative meanings of words. Osgood et al.
explored large numbers of attitudes to numerous words and phrases. The outcome was Osgood’s discovery
of "semantic space"—the existence of three measurable underlying attitudinal dimensions that everyone
uses to evaluate everything in their social environment, regardless of language or culture. These three
dimensions are Evaluation, Power, and Activity, known as EPA.
The semantic differential is a method for measuring the meaning of an object to an individual. It may also be thought of
as a series of attitude scales. The subject is asked to rate a given concept (for example, Irish, Republican, wife, me as I
am) on a series of seven-point bipolar rating scales. Any concept—whether it is a political issue, a person, an institution,
a work of art—can be rated . . . Subgroups of the scales can be summed up to yield scores that are interpreted as
indicating the individual’s position on three underlying dimensions of attitude toward the object being rated. These
dimensions have been identified by using factor-analytic procedures (factor analysis is a [statistical] method of finding the
common element or elements that underlie a set of measures) in examining the responses of many individuals
concerning many concepts or objects. It has been found that . . . three subgroups measure the following three
dimensions of attitude: (1) the individual’s evaluation of the object or concept being rated, corresponding to the favorableunfavorable dimension in more traditional attitude scales; (2) the individual’s perception of the potency or power of the
object or concept; and (3) the individual’s perception of the activity of the object or concept.
(Kidder, 1981)
Of the three dimensions of semantic space, Evaluation proved to be the most important. Evaluation is also
known as the connotative or affective dimension. Affective or affect is the term psychologists use when
referring to emotion, or more specifically, the emotion associated with an idea or set of ideas.
The problem with the semantic differential technique is that it does not distinguish beyond a single evaluative
continuum, with positive attitude at one end of the scale through to negative attitude at the other end. That is,
it does not actually identify any individual emotions.
References to Semantic Differential
Kidder, L. M.
Research Methods in Social Relations.
New York, Holt, Rinehart & Winston, 1981.
Osgood, Suci, and Tannenbaum.
The Measurement of Meaning.
University of Illinois Pr., 1967.
Oskamp, S.
Attitudes and Opinions.
Englewood Cliffs, NJ: Prentice-Hall, 1977.
Snider, J. G., Osgood Charles E.
Semantic Differential Technique.
A Sourcebook. Chicago, 1967.
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20. 4-Dimensional Map
4D Map© in a Nutshell
When relationships between numbers are far more important than the numbers themselves, 4D Map is the
chart you need. 4D Map draws a bubble plot in a 3D environment. We made this feature possible in Excel by
rotating the plane and distancing the bubbles from it.
4D Map is a mapping tool conceived for displaying a larger amount of data on the same picture than Excel
allows. This adjunctive data may help the acute analyst to identify relevant information apparently hidden in
the data itself. It is again the miracle of the picture being worth a thousand words.
My First 4D Map
My First 4D Map
453
453
653
653
853
853
X-axis
X-axis
1053
1053
1253
1253
1453
1453
1653
1653
Rows
Rows
Columns
Columns
600
600
Derma
Derma
Women's health
Others
Women's health Blood
Others
Metabolism BloodArthritis/Bone
Arthritis/Bone
CNS
Metabolism
CNS
Respiratory
Oncology
Respiratory
Antivirals
Diabetis
Oncology
Antivirals
Cardio
Diabetis
Cardio
Antiinfective
Antiinfective
Antiinflammatory
Antiinflammatory
Vaccines
Vaccines
100
100
Y-axis
Y-axis
Gastro
Gastro
-400
-400
-900
-900
-1400
-1400
Note:
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How To Run 4D Chart
On the MM4XL floating
toolbar, click this button to
display the window to the
right.
The Quick Selection tab enables you
to draw a map with little more than a
click. Put the input data in the
appropriate format. Select the input
range. Click OK and that is it. MM4XL
does the rest of the job.
Alternatively, you can click the Detail
Selection tab and enter in the
textboxes the single range addresses
for each variable. This feature is
useful when the data lie in separate
sections of the spreadsheet. All fields
but the Group Variable are selfexplanatory. This column of data is
used for coloring bubbles. Enter either
text or values in this vector. All equal strings will be assigned a unique color to the corresponding bubble.
This feature is case sensitive, so a lowercase letter is different from the same letter in uppercase.
If you want to plot axis titles put them in the first row of the
input range(s) and select the Columns with labels checkbox.
The Bubble Colors frame allows you to color the bubbles in
one of two ways. The option by Group colors them according
to the data in the Group Variable and the option by
Placement colors them according to the position the bubble
takes on the plane: bubbles below are red and bubbles above
the plane are green. Moreover, bubbles are distinguished by
other features that make them easier to read: points going
upwards have a solid line and a triangle at their basis, while
points going below the plane have a dotted line and a dash at
the basis.
The Gridlines listbox sets the grid to dotted lines, solid lines, or no gridlines at all. The Bubble size listbox is
used for re-scaling the size of the bubbles to large, medium, and small. This last feature is useful for making
crowded maps more readable.
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Technicalities
As for most visualization techniques, the drawing of 4D maps is made up of two elements: the space where
items are placed and the items to be represented in the space. Our 4D space is made of two parts:
•
•
plane
grid
while the items are displayed in the form of pin-bubbles and are made of three parts:
•
•
•
marker
whisker
bubble
Each of these is shown in the picture below. Before going into detail, however, you should be warned that rescaling coordinates shows pin-bubbles apparently in a wrong position. This is true in terms of the axes scale,
although the overall bubble spread is still correct. This annoyance is due to the fact that Excel cannot handle
3D spaces for charting, so we have found a way around this by re-scaling coordinates and drawing a custom
oblique grid. This way we are able to reproduce the 3D effect on a chart but, unfortunately, resizing axes
may be confusing when seeking for correspondence between bubble coordinates and axes scale. This is,
however, a negligible detail in most analytic situations drawn in 3D space. Indeed, it is the spread of the pinbubbles around, above and below the plane that should attract our attention rather than the quantification of
the coordinates.
Anatomy of a 4D Chart
1. PLANE
The X and Y coordinates are common to
Excel charts. The Z coordinate is represented
by the whisker length. Coordinates are scaled
in order to match the oblique orientation.
5. WHISKER
- Bubbles placed above the
plane have a solid line.
- Bubbles below the plane
have a dotted line.
2. GRID
It can be drawn with dotted
lines, solid lines, or not at all.
Y-Axis
X-Axis
3. MARKER
- Bubbles above the plane have a triangle.
- Bubbles below the plane have a dash.
4. BUBBLE
Can be colored:
- by Group according to a user-defined variable (Group Variable)
- according to the Placement above and below the plane
Their size is defined according to a user-defined values.
Green if the product wins, either from the upper product or from
the lower products. White if it has a neutral net balance.
Red otherwise.
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21. Stacked Charts
Stacked Charts in a Nutshell
Stacked Charts is another simple to run and useful tool that MM4XL offers to managers who are interested in
plotting charts that are easy to read. The peculiarity of stacked charts is that we see different data series
displayed on the same chart but each in its own portion of the plot area. In this way series never overlap and
a very clear picture of the information is provided.
Stacked Chart can also plot data expressed with different scales of measurement on the same chart in a
readable manner, such as a column of values referring to sales in value and a column of percentage
changes in market share.
When you share your work with colleagues and clients, Stacked Charts may help you make your point
clearer.
My Stacked Chart
1.00
0.75
1.37
0.88
0.81
0.72
0.50
0.25
0.27
0.26
1.00
Sales
Compet 2
334
0.75
0.50
112
0.25
1.00
Compet 1
123
93
54
23
0.84
0.81
0.75
1.01
0.92
1.02
0.50
My Sales
0.34
0.25
Sep. 03
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Okt. 03
Nov. 03
Dez. 03
Jan. 04
21. Stacked Charts
Feb. 04
357
How To Run Stacked Charts
In the floating toolbar, click on this button to display the window shown below. To create a chart,
select the ranges in the sheet where the data is stored, choose the kind of chart you want to draw,
and click OK. That is it!
Note:
available. Click on the Start button in
Windows and select MM4XL –
Marketing Manager for Excel. The file
can be found in the Examples folder.
Alternatively, start the tool and click
the Example button.
In the Input range select the row
labels and the data to be plotted. You
can include column labels in the
selection as well, in which case select
the Labels in first row checkbox.
In Output range select the cell where
you want to start printing the chart.
Select the type of chart from the Chart
type list box: Line, Bar, or Area. Examples of the three types are shown below in the section Anatomy of a
Stacked Chart. The default selection is a stacked line chart.
If you are working with data measured with different scales, select the Rescale data checkbox. The trick is
that data are all rescaled to units. To avoid mixing up the interpretation, select the Show original values
checkbox and the original data will be plotted on the chart.
A number of options enable you to refine the appearance of the chart. Enter a Job title, and titles for the X
axis and Y axis. You will find that short labels are most effective.
The list box Thickness of line is active with stacked line charts only. Use it to select a different thickness of
plot line. The default selection is medium thickness.
Select the Gridlines checkbox to display horizontal grids. Select One color for all series to plot series on
the chart without changing color across series. Select Show Y-axis labels to display labels on the vertical
axis.
Select the Example button to opens an Excel sheet with sample data, an example of analysis, and an
explanation of how to make field selections. Click OK to generate the chart.
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Anatomy of a Stacked Chart
Stacked Chart produces any of the charts shown below:.
My Stacked Chart
My Stacked Chart
1.37
1.00
0.75
0.88
0.50
0.25
1.00
0.75
0.50
0.25
1.00
0.75
0.50
Ser i
0.81
0.72
0.27
es 3
0.50
0.25
1.00
0.75
0.50
0.25
1.00
0.75
0.50
0.26
334
Ser i
123
112
0.84
23
1.01
0.81
es 2
93
54
1.02
0.92
0.34
0.25
My Stacked Chart
1.00
0.75
Ser i
0.25
es 1
Ser i es 3
1. 37
0. 88
0. 81
0. 72
0. 27
0. 26
334
112
123
0. 84
0. 81
54
23
1. 01
Ser i es 2
93
1. 02
0. 92
0. 34
1.00
0.75
Ser i es 3
0.50
0.25 0.88
1.00
0.75
0.50
0.25 112
1.00
0.75
0.50
0.84
0.25
1.37
0.72
0.81
0.27
0.26
334
123
Ser i es 2
54
23
1.01
0.81
93
1.02
0.92
Ser i es 1
0.34
Ser i es 1
P r oduct A
P r oduc t B
P r oduc t C
P r oduct D
P r oduct E
Pr oduct A
Pr oduct A Pr oduct B Pr oduct C Pr oduct D Pr oduct E Pr oduct F
P r oduct F
Ti me
Pr oduct B
Pr oduct C
Time
Pr oduct D
Pr oduct E
Pr oduct F
T i me
The range A1:D7 from the table below was used as input data for a default line chart:
The resulting charts are shown below:
My Stacked Chart
1.00
0.88
0.25
0.88
0.81
0.72
0.50
0.27
334
112
0.25
1.00
Compet 1
123
0.81
1.01
1.37
334
0.81
0.26
Series 3
93
Series 2
112
123
93
54
23
0.84
0.75
0.27
Compet 2
0.75
0.50
0.72
0.26
1.00
Sales
My Stacked Chart
1.37
Sales
0.75
0.92
54
1.02
0.84
My Sales
0.50
0.34
0.25
0.81
23
1.01
0.92
0.34
1.02
Series 1
Product Product Product Product Product Product
A
B
C
D
E
F
Time
Sep. 03
Okt. 03
Nov. 03
Dez. 03
Jan. 04
Feb. 04
In the chart on the left, the data has been rescaled. The chart on the right is drawn without rescaling the
data, and is not very helpful.
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22. Benchmark Analysis
Benchmark Analysis in a Nutshell
Benchmark Analysis is a simple and easy to run tool that can be used to draw a picture of the competitive
power of a company, a product portfolio, or a single product against its counterparts. The competitive power
in this case is taken as the function of the market growth, and of the product or company.
The map works this way:
•
•
•
Products below the diagonal grew more than the market, and therefore have won market share.
Products above the diagonal grew less than the market, and therefore have lost share.
Products within the dotted lines grew slightly more or less than the market – they retained share.
Benchmark Analysis can help managers to rank performance, investigate trends, or cluster groups. It can
compare any pairs of items, not just product versus market.
Competitive Dynamic Analysis
60%
Lose Market Share
Keep Market Share
Market Growth (%)
50%
40%
ABBOTT
LUNDBECK
ROCHE
30%
GLAXO
NOVARTIS
20%
10%
ZENECA
NOVO
NORDIS
HMR
P&UPJOHN
BAYER
0%
-10%
-10%
WYETH
SB
PHARMA
BMS
ASTRA
LILLY
MSD
SCHERING
SANOFI
PFIZER
JANSSEN
Win Market Share
0%
10%
20%
30%
40%
50%
60%
Product Growth (%)
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How To Run Benchmark Analysis
In the MM4XL floating toolbar, click this button to display the window below. Select the ranges in
the sheet where the data are stored, click OK, and the chart is drawn. That’s it.
Note:
Typically, the fields Product growth and Market
growth are filled with percentages, but other scales
of measurement can also return meaningful maps.
It is important that both variables are measured with
the same scale, for instance, both in percentage or
both in thousands. Growth values can be found, for
instance, by dividing the sales value this year by
last year’s sales value.
The Bubble size range indicates how large each
bubble should be. You can use a vector of sales
values here, or alternatively select one of the three
options in the list box.
The Product labels range attaches a text label to
each bubble and the Bubble color field assigns
different colors to bubbles. Alternatively, select one
of the three options in the list box.
Finally, the Output range indicates where to place
the map on the sheet.
Select the Labels in first row checkbox if the selected input data range includes a column label in the first
cell.
In the Report frame select the sections of the analysis to be printed. Read more about Report content later
in the section Anatomy of a Report. The Confidence Boundaries frame contains text boxes that indicate
where to place the boundaries around the main diagonal that separates growing products from stable and
declining ones. The confidence region is where product versus market growth is not broad enough to identify
a gain or loss of market share. Enter zero in the two boxes if you want to get rid of confidence boundaries
and work with the main diagonal only.
Click the Example button to open an Excel sheet with data, an example of analysis, and an explanation of
how to make field selections. Click the OK button to generate the chart.
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Anatomy of a Benchmark Analysis Output Report
Benchmark Analysis can print a map and a
report made of two parts: the summary report
of the analyzed data and a table showing the
difference between each product and market
growth. The example to the right analyzes 20
pharmaceutical companies using their overall
growth compared to the overall growth of the
market segments they compete in. Columns A,
F, G, and H are required fields while columns
B-E are shown for explanatory purpose only.
The Benchmark Map
The Benchmark Map looks like a common
bubble scatter plot with the peculiarity that both
X- and Y-axis have the same length (-10%;
+60% in the map below). Axes with equal
length show a squared surface that favors the interpretation of the distance of the bubbles from the diagonal
that splits the map in two equally sized triangular regions.
60%
Lose Market Share
Keep Market Share
Market Growth (%)
50%
40%
LUNDBECK
ABBOTT
GLAXO
30%
BMS
ROCHE
20%
10%
ZENECA
ASTRA
LILLY
NOVARTISNOVO NORDIS
MSD
SCHERING
SB PHARMA SANOFI
WYETH
P&UPJOHN
HMR
BAYER
0%
PFIZER
JANSSEN
Win Market Share
-10%
-10%
0%
10%
20%
30%
40%
50%
60%
Product Growth (%)
The lower triangle contains products that grew faster that their markets did. These are products that have
won market share. On the other side, the upper triangle contains products that grew less than the market,
and these have lost market share. The dotted diagonals are parallel to the main one and are set arbitrarily by
the user in order to identify a region of insignificant changes.
Tip:
Benchmark often initiates a broader competitive analysis. First, look at your company performance; then look
at your portfolio with BCG or McKinsey; finally, go in-depth by market segment (product) with Brand Mapping
and Brand Switch.
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The Tables
The tool can print two tables of data extrapolated from the user input data. The table below shows the overall
summary. In our example, we analyzed 20 products. The Average Market Growth of the analyzed
segments, 21.0%, was obtained by dividing the overall sum of market growths by the number of products.
Report
N.
Bubble size
Avg Market
Growth
TOTAL
Win Market Share
Keep Market Share
Lose Market Share
20
11
5
4
15.56
7.25
4.00
4.30
21.0%
24.0%
16.9%
18.1%
Avg Product
Average
Growth
Bubble Size
26.1%
38.8%
15.9%
3.8%
0.78
0.66
0.80
1.07
The Average Product Growth (companies in our case), 26.1%, is found by
dividing the overall sum of product growths by the number of products. The
Average Bubble Size, 0.78, is calculated by dividing the overall sum of
bubble sizes by the number of products. These values are given for the
overall data set, the row Total, and for each of the three regions on the map:
win, keep, and lose market share.
Tip:
The Average Bubble Size can highlight whether large competitors are
winning over smaller ones and vice versa. The average size of winners in
our example (0.76) tells us that medium size competitors are gaining share
at the expense of larger companies, while small firms are keeping their
positions. Why? Run portfolio analyses to find out.
Product
LUNDBECK
BMS
PFIZER
ABBOTT
MSD
LILLY
SCHERING
ASTRA
SANOFI
GLAXO
SB PHARMA
P&UPJOHN
ZENECA
WYETH
ROCHE
NOVO NORDIS
JANSSEN
NOVARTIS
BAYER
HMR
The second table the tool draws shows the Share Difference vector, which
tells us how fast the product (company) is growing. In the table to the right,
for instance, 38.6% for Pfizer was obtained by subtracting the growth of the
market Pfizer competes in (14.5%) from the overall company growth level (53.1%).
Change in
Market share
23.3%
21.4%
38.6%
5.9%
11.5%
14.3%
15.6%
10.1%
11.5%
-2.7%
6.4%
4.7%
-2.3%
1.5%
-13.4%
-2.5%
0.8%
-13.2%
-9.3%
-21.1%
References
A. C. Hax and N. S. Majluf
Strategic Management.
Prentice-Hall, 1984.
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23. Project Mapping
Project Mapping in a Nutshell
A project map is a synthetic roadmap designed to help business decision-makers when creating, managing,
and communicating ideas in situations such as:
•
•
•
•
Brainstorming sessions
Public presentations
Corporate meetings
Project planning
The main strength of project mapping is perhaps its function of structuring even very complex projects in a
clear graphical format, creating a strong visual impact. Project maps designed with MM4XL allow managers
to organize concepts in a visually appealing form. With a layout that stimulates creative thinking, project
maps assist in the monitoring of projects, and offer an effective solution for grouping together all projectrelated information stored in different formats (Word files, Power Point files, Adobe files, anecdotal
information, notes, hints, thoughts, etc.).
Project maps designed with MM4XL are enriched with powerful features:
•
•
•
•
•
•
You can attach pictures, symbols, shapes, and files to the map in order to maximize clarity and
group together all information relevant to a project.
You can modify fonts, shapes, and connectors in order to direct the attention of your audience.
You can collapse branches, enabling information to be concealed and then retrieved at the
appropriate point in time.
Maps can be linked and exported in a variety of ways: to PowerPoint, Word, Excel, or in image
format.
You can add hyperlinks to Internet addresses.
You can attach your own voice messages to maps, which can then be played back during meetings.
Project mapping can be used to organize a wide variety of business projects: survey studies, business plans,
media plans, product launch plans, product development studies, promotional plans, and every other
management project that needs to be split into phases.
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How is Project Mapping Useful?
Project mapping is an effective method of note-taking which helps managers to generate ideas, show
associations, and organize and communicate thoughts effectively. It stimulates visual thinking and fosters
creativity.
The project mapping tool available with MM4XL software provides users with a choice of two different
mapping formats:
•
•
Common mind mapping.
Process flow diagrams.
The difference between these two formats is that the mind mapping technique starts from a main idea in the
center, with the phases displayed in the form of child branches organized around the main idea in a
clockwise formation; whereas the process flow scheme has a start point and an end point, typically extending
from one side to the other. Both techniques, however, share the common function of visually representing a
complex structure; that being a project, an idea, a process, or any other activity that can be split into phases.
Project mapping provides the tools to draw a synthetic structure in a way that is not only visually appealing,
but also enhances the effectiveness of communication.
Mapping guidelines
Listed below are a few common suggestions to help maximize the speed and effectiveness with which your
project map communicates information:
•
•
•
•
•
Use keywords and clear fonts.
Use images, icons, shapes, and voice notes throughout the map.
Use colors and emphasis.
Show associations.
Inject your own personal style into the map.
Effective mapping involves creativity and order. Creativity requires a sense of flair, and a certain amount of
experimentation. There are hundreds of techniques which can be used to develop creative thinking, and a
comprehensive list of these can be found on the website www.mycoted.com. It is necessary to organize
thoughts and ideas in order to give the map a clear structure. Consideration of the 5 W’s—Who, Where,
Why, When, What (and also How)—can assist in achieving this. Transposing the SWOT analysis schema
used in business planning to the context of project mapping can also be useful in map structuring.
Tip:
When coloring maps it is good practice to give a unique meaning to each color. Typically in mapping, colors
are assigned the following meanings:
White:
Yellow:
Red:
Green:
Blue:
Black:
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Figures, facts
Logical, positive
Intuition, feeling, emotion
Creativity, proposals, alternatives
Overview, process, control
Judgment, caution
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The Working Environment
On the MM4XL floating toolbar, clicking this button to open the project mapping tool.
The drawing surface
It is important to understand that this is not MS Excel. The project mapping working environment works
alongside Excel, but not in it. Therefore, while working with project mapping, it is possible to switch back to
MS Excel (through the keyboard combination Alt+Tab, for instance) and work with it simultaneously.
Project maps can be constructed by accessing the functions and utilities on the drop-down menu, or by
selecting the appropriate button from the toolbar.
As well as a range of other functions, the Tools>Options menu command can be used to define the
background color of the drawing surface and to set the default map style when a new map is created.
Drop-down menu
The drop-down menu consists of six options. Clicking on File, or selecting the hot-key Alt+F, will display the
sub-menu options, as shown in the picture below. This list contains commands which are common to most
software applications. It is worth noting that the Save as command, which allows the active map to be saved
under a different name, is a useful feature when using template maps. The Print option exports the project
report containing all information embedded in the map. Additional information on printing reports and maps is
provided in the Project Mapping Output Report section.
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The Export option opens a form. Clicking Next will display another form, pictured below. Here you can select
a format for exporting the map (it is important to note that only the map will be exported). The options on the
left export the map, in the form of a bitmap picture, to the respective applications (Word, Excel, Powerpoint,
Outlook). The Clipboard option saves the map to the clipboard, from where it can be pasted (through either
using the Ctrl+V hot key or the Paste option) into Word or Excel, for example, or any other compatible
application. The BMP and GIF options save the map in a file with the respective extension. Once an option
has been selected, clicking Next will export the map.
The Edit submenu consists of commands useful for making changes to the shape of the map.
Select elements
To change the position or appearance of a shape, it must first be selected. One or more shapes can be
selected by clicking on a blank space on the map close to the shape(s) you want to modify, and then
dragging the mouse until the relevant portion of the map is selected. This process is illustrated in the picture
below.
Non-adjacent selections can be made using the keyboard’s Ctrl button—with the Ctrl button depressed, click
on the branches you want to select with the left mouse-button. The Select all option (or Ctrl+A) can be used
to select all the elements of a map.
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Move elements
To move the selected elements, click on one of the elements with the left mouse-button and drag the
selection to the desired place, then release the mouse button.
Cut, Copy, Paste and Delete
The Cut, Copy, Paste and Delete options work as one might imagine; with an active selection, click on the
appropriate command to perform the desired change.
Like
This command copies the appearance of a shape and applies it to a second shape. Say you want to copy
the appearance of Branch 1 to Branch 2, as illustrated in the picture below.
Click on the Like button on the toolbar, or select the branch and then the Like option from the drop-down
menu, then click the shape you want to copy the appearance from (Branch 1). Next, click the shape you want
to copy the appearance to (Branch 2). The result is displayed in the picture below.
Align
When the branches are not aligned, as in the picture below, you can align them together using the Align
option.
With the unaligned shapes selected, click on the Align option. A form will appear, listing a total of 16 options
in four different groups. Select the desired alignment option and click OK. Using the example in the picture
above, the Horizontal – Left side option aligns the two shapes (Branch 1 and Branch 2) in the format
illustrated in the picture below.
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The Tools submenu contains two options: Show legend and Options. The legend is illustrated in the
floating panel below, along with the meaning of the icons attached to the map. Information on how to attach
symbols, files, etc. to a map will be provided later in this chapter.
The Options command allows the selection of one of four alternatives relating to the default map displayed
when project mapping is started. The Basic map is the default option. The settings in the Scrollbars frame
determine the intervals at which the map will be shifted when the scrollbars on the right and bottom sides of
the working environment are clicked on. The Attach dir field is used to link files to a map stored in the same
directory. When a map is sent to other users of MM4XL software, they can restore the original map and its
links to files by simply copying the attached material to a folder with the same name as the original one.
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The Examples submenu lists template maps stored in the default directory \MiM\Examples, located in the
directory where the MM4XL software is installed. If maps are saved in this directory, they will be listed under
the Examples menu option.
Project mapping operates in all the languages listed in the Language submenu, plus the active one: English
in our example. Simply select your language preference and the tool will work accordingly.
Note
Do you want to work with project mapping in a language that is not available from the menu? Do the
translation yourself! From the directory \MiM\LNG, located in the directory where the MM4XL software is
installed, open the file labeled English.lng and save it under a new name—your language name, for
example. Once this has been done, open the file, translate all text after the equals sign (=), and then save
the file. Launch project mapping and you will find the new language option listed under the Language
submenu. Select it and the tool will work in your language.
Lastly, from the Help submenu, you can launch the online help file, connect to MarketingStat via the Internet,
and purchase MM4XL software online.
Toolbar menu
The toolbar menu contains buttons linked to most of the functions described in the Drop-down menu section,
as well as a number of other functions not available from submenus, like the Branch, Text, Connector, and
Zoom functions. These functions will be described in the next section, Working with Project Mapping.
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Working with Project Mapping
A map consists of three elements: the main shape (in the center of the map), the branches, and the
connecting lines, called connectors. Each part of a map can be modified, and the many available options
allow the creation, in only a few minutes, of widely varied map styles that not only enable the effective
communication of information, but also function as a comprehensive storage system for documents relating
to the same project.
Enriching Maps
The appearance and position of the elements in a map can be modified in two basic ways:
1. Right-mouse clicking on an element opens a pop-up menu with a few basic options.
2
1
2. Left-mouse clicking on an element opens a form, from which the
selected elements can be modified.
Formatting single elements
Left-mouse clicking on the main shape in the middle of a map (labeled Main Idea in the example pictured
below), will open a form where changes can be made to the appearance of the selected element. The form
consists of two pages: Settings and Additional. All available options are detailed below.
Settings page
There are two main sections to this
page: Branch and Appearance.
In the Branch frame, at the top of
the page, the Text box can be used
to add labels to branches—the text
will subsequently be displayed on
the map. When, as in this example,
the selected branch is the map’s
main branch, check the Is main
symbol option. The main branch is
the primary branch, from which all
other branches extend. This system
is required for the printing of clearly
organized reports. When active, the
Branch autosize checkbox sets the
branch size according to the length
of the text in the label.
The six buttons on the right side of
the frame (Cut, Copy, Paste, Delete,
Collapse, Add childs) act on the
map structure.
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Cut, Copy and Delete branches
To cut a branch, select the relevant branch, or group of branches, then left-click on the selection and choose
the Cut button in the Branch frame. The selected branches are then removed from the map. The Copy
button works in the same way but leaves the shapes on the map. The Delete button removes the shapes
from the map.
Paste and Link branches
After an element has been cut or copied, use the Paste option to place it in the desired position on the map.
This function is also available from the right mouse-click menu.
To connect a child branch to the parent branch, click on the Link button, then select the parent
branch. Click on the child branch again and a connector will be displayed. Clicking on the connector will bring
up a form, where formatting commands can be accessed.
Add children
To add one or more branches (with connectors) to a parent branch, use the Add childs button in the Branch
frame. A form will then appear, where you can make your selection.
As shown in the above picture, the placement and shape of a new branch can be selected, as well as the
quantity of new branches to attach to the selected parent branch. In order to choose the shape of the
branch, click on the button with the ellipsis points […] to access the form below, then select the desired
shape and click on the OK button.
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Collapse branches
The project mapping tool is very useful when describing complex and multifaceted projects. In such cases
maps can easily become unmanageably large, and risk losing their visual efficacy. To overcome this
problem, users can either click on the Magnify lens button on the floating toolbar (buttons 5 and 6 in the
toolbar from the left) or use the Collapse button—click on a branch containing sub-branches (collapse is not
active when the main shape is selected), then click the Collapse button. A small plus sign (+) will appear,
which indicates a collapsed branch. The branch still exists but is not visible to the user. Clicking on the plus
sign again reverts the branch to its original appearance. This option can be very useful in a number of
instances; for example, when presenting projects which require topics to be displayed only at a specific point,
encouraging the audience to focus on targeted portions of information only.
On the left side of the Appearance frame is a list of options for changing various elements of the branch,
such as font size, color, etc.
Raw branches do not have a shape attached. To attach a shape to an existing branch, select the Use shape
option, then click on the button with the ellipsis points […] to access the Select shape form previously
described in the Form page settings section. Select a shape and then click on the OK button.
Alternatively, you can attach a picture to a branch. Select the Use picture option and click on the button with
the ellipsis points […] to locate the file with the picture you want to attach. Most standard graphic formats are
supported.
On the left side of the Appearance frame, the Apply appearance to listbox allows the format of several
branches at different map levels to be changed simultaneously. The default selection is this child only.
There are a further three options which determine the extent of format changes: whole map, or to child or
parent branches only.
Additional page
The Additional page in the
main form provides a series
of options regarding map
content. There are seven
frames in this page:
•
•
•
•
•
•
•
Task description
Hyperlinks
Attachments
Vocal messages
Icons
Schedule tasks
Task budget
The Task description text
field works as a note sheet,
and is useful for attaching
hidden
information
to
branches. This information
can then be retrieved by
placing the cursor on the
icon resembling an open
book ( ) which appears
beside a branch that has a
description note attached to
it (see picture below). The
above form is accessed by
clicking on the ( ) icon.
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The Hyperlink field accepts Internet or file addresses. To open a hyperlink, right-click on the icon and select
Follow Hyperlink on the form that appears (as shown in the Working with Project Mapping section). If the
hyperlink is a web address, the project mapping tool connects with the default browser. If it is a file, the tool
opens it, given that the software required to open the file format is installed on your machine.
Attachments can be added to a branch by clicking on the Add button. An attachment can be a file of any
kind, and when added, appear as in the picture below. Place the cursor on a file icon to view the path and file
name. Click on the file icon to open the file in its own application. This feature makes the project mapping
tool a true repository of documents of all kinds. To remove attachments, click on the branch label, enter the
Additional page, then select the attached file to be removed and click on the Remove Button.
Tip
Complex maps can be split into chunks. Create a main map containing the issues central to your idea. Then,
in a separate file, create a new map describing, for instance, a sub-process relevant to a section (branch) of
the main map. Link the second map to the first using the Attachment option to any branch of the main map.
The attached map can then be opened with a simple mouse click.
Plug a microphone into your computer and take advantage of the great features in the Sound note frame.
Click on a shape, go to the Appearance page, then click on the Record button. You can then start talking in
the microphone; the message is recorded and linked to the selected branch, which will then show an icon
resembling a microphone. Click on the microphone icon and listen to the message. To remove the message,
click on the branch, not the microphone, then go to the Additional page and click on Delete. It is that easy to
record voice messages with the MM4XL project mapping tool, and you can share voice maps with your
fellow MM4XL users across the globe.
The Icons frame on the upper right side of the Appearance page shows the various icons that can be
attached to map elements. Each icon has a meaning, and they are used to enrich maps of incremental visual
information. Place the mouse on one icon for a second, without clicking, and the icon meaning appears in a
small pop-up box. The whole list of icons and their meanings is displayed in The Working Environment
section
In the Schedule task frame, a Start and End date can be assigned to the central shape (whole project) and
to branches (project phases). The Priority level can be assigned to branches only. The Task budget frame is
used to assign a value to a branch. This information is printed as a reminder in the Summary report.
The Help button in the lower-right corner of the main form launches the online reference documentation, the
file you are currently reading.
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23. Project Mapping
377
Project Mapping Output Report
The project mapping tool prints as output a map and a summary report. Together, these elements supply a
detailed and yet concise picture of a project.
The Map
To export a map, click the corresponding button on the toolbar, or select Tools Æ Export from the menu. On
the form that appears, click on Next, then select the file format you want to export the map to and click Next.
For MS Office files, select whether to export to an existing file or to a new one; for other formats, assign a
name to the export file. Click on Next and the map will be exported.
Tip:
Export the map to the Clipboard and it will be saved in memory. Go to any Microsoft application such as
PowerPoint, Excel, Word, etc., place the cursor where you want to paste the map, press Ctrl+V and the map
will appear.
The Summary Report
The Summary report lists all information concerned with each single branch of a map in a structured
manner. A map can contain a lot of information in several formats, such as text and symbols, time schedule
and budget value, attached files and their location, author notes, and vocal messages.
To print a copy of the report, select the Print option from the toolbar or press Ctrl+P, then select whether to
export to Excel, Word or WordPad on the form that appears. Pictured below is an example of a summary
report generated in the project mapping tool.
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Examples of Project Mapping
The only limit to the number of possible maps that can be created with project mapping is your creativity. The
following are just a few examples:
Common mind map:
Node map:
Flow diagram:
SWOT analysis:
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379
Tips & Tricks
Open the example map labeled Tips & Tricks from the Examples menu option in Project Mapping to find
suggestions on how to best use all available features.
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References
Tony Buzan and Barry Buzan
The Mind Map Book: How to Use Radiant Thinking to Maximize Your Brain's Untapped Potential.
Plume, 1996.
Nancy Margulies
Mapping Inner Space: Learning and Teaching Mind Mapping.
Zephyr Press, 1991.
Dilip Mukerjea and Tony Buzan
Superbrain: Train Your Brain and Unleash the Genius Within by Using Memory Building, Mind Mapping,
Speed Reading.
Times Academic Press, 1998.
Peter Russell's
The Brain Book
Dutton and Reissue, 1979.
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381
MarketingStat.com
382
Appendix: Detailed output
by tool
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Portfolio Analysis – BCG Share/Growth Matrix
Floating Toolbar
User Form
Detailed output by tool
a. Input Data
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b. Output Report
Portfolio Analysis
B ubbles = sales. M ax Sales: 1906.4
25%
Product 13
20%
Product 14
Product 16
15%
Market Growth (%)
10%
Product 2
Product 6
Product 15
Product 10
A
Product 3
B
Product 9
5%
Product 5
C
Product 17
Product 12
D
Product 7
0%
Product 20
Product 26
-5%
Product 19
-10%
Product 25
Product 4
Product 1
J
Product 8
L
Product 21
Product 18
M
N
Product 24
Product 11
P
Product 22
-15%
100
Product 23
10
1
0.1
0.01
Logarithm ic Relative Market Share
Summary table:
Financial Charts
Portfolio: Cash Flow (line) Vs Investments (col's)
Portfolio: Average Product Investment
6000
300
4956.2
5000
4000
3000
2000
1000
2859.4
1894.6
2961.0
262.0
250
200
166.2
150
1310.2
831.0
411.1
824.9
102.8
100
68.7
50
0
Cow s
Stars
Questions
0
Dogs
Cow s
Stars
Questions
Dogs
Segm ents: Cash Flow vs Investm ent
900
800
D
700
600
C
N
L
500
400
J
300
A
200
B
100
P
M
0
0
1000
2000
3000
4000
5000
C a s h F lo w
Market Segment Interpreter
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Verbal Report
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Portfolio Analysis – McKinsey Assessment Array
Floating Toolbar
User Form
Output Report
B ubbles = Revenue -- M ax = 4
Input Data
Invest & Gro w
McKinsey Portfolio Analysis
Selective gro wth
Selectivity
Competitive Advantage
Brain Tumor
Anticoagulant
Pain Selectivity
Gro wth Ho rmo ne
Contraception
Selective gro wth
Harvest / divest
Sleep Disorder
Haemostasis
Selectivity
Harvest / divest
Harvest / divest
Nasal Cold
High
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Market Attractiveness
Lo w
387
Brand Mapping: Strategy (Correspondence Analysis)
Floating Toolbar
User Form
a. Input Data
b. Output Report
Ulcer & Gastritis: 2003
Duodenal
gastritis
PANTOZOL
SEVERE
60%
ULCOGANT
Acut e gast rit is
Dolori addominali
Abdominal ulcer
MODERATE
40%
AGOPTON
Reflux
ZURCAL
Gastrite gastroduodenale
PANTOZOL
Dispepsia
Disturbi stomaco
Atrof ic gastritis
ZANTIC
Severe gast rit is
ZANTIC
ANTRA
Peptic ulcer
Duodenal ulcer
3-axis inertia = 95%
Inertia axis 1= 61%
Inertia axis 2 = 25%
St omach
disorders
ZURCAL
Gastrite acuta
ULCOGANT
Gastrite grave
Ulcera peptica
Ulcera duodenale
Gastrite atrofica
Dyspepsia
Abdominal pain
Esofagia
ANTRA
Ulcera addominale
AGOPTON
Dendrogram
0
200
400
600
800
1000
1200
* Contours traced according to a cluster ran with the first 3 coordinates of the Brand Mapping. See dendrogram.
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Brand Mapping: Supplementary Points
Floating Toolbar
b. Output Report
User Form
Eigenvalues
Values
Inertia %
Inertia cum. %
Mother
Father
Teeny
Ma&Pa
Profile A
Profile B
Prevention
Prescribed
I find it @ home
It's a good habit
This is my 1st time
Item 1
Item 2
Item 3
1
0.1512
55%
55%
Mass
250
250
250
250
0
0
340
150
175
285
50
0
0
0
2
0.1068
39%
93%
3
0.0186
7%
100%
Coordinates
1
2
3
Inertia Inertia ‰
77
279
231
500
-76
34
122
-294
65
211
67
241
-450
-201
-155
99
358
513
-364
19
-945
-209
-716
148
58
-400
26
94
109
219
-127
102
370
521
-641
-7
92
331
-674
-247
91
29
104
126
248
154
28
101
-670
-115
-313
-464
-121
-317
-7
73
152
-195
174
98
Contributions
1
2
3
88
585
77
143
10
597
334
95
321
435
310
5
Squared Cosines
1
2
3
172
809
19
639
32
330
758
152
90
665
335
1
27
270
525
30
148
157
398
867
157
802
153
577
100
164
6
295
0
78
365
262
630
602
117
607
24
212
0
16
235
174
Explained variance (3-axis inertia) = 100%
Brand Mapping: Vitamins Usage
Axis 2 - Explained variance = 39%
Mother
Prevention
It's a good habit
Father
Item 3
Item 2
This is my 1st time
Profile B
Item 1
Teeny
Profile A
I find it @ home
Ma&Pa
Prescribed
a. Input Data
Filter: Have used vitamines in the past week.
Question: Why have you taken vitamines during the past week?
Yellow shaded area = supplementary rows & columns.
Mother Father Teeny Ma&Pa Profile A
14
Prevention
50
26
30
30
5
Prescribed
5
7
12
36
23
I find it @ home
3
28
32
7
15
It's a good habit
39
34
15
26
This is my 1st time
3
5
11
1
38
14
33
8
Item 1
12
24
Item 2
22
27
17
20
16
Item 3
37
45
34
19
45
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Profile B
43
18
3
26
14
27
33
9
389
Brand Mapping: Missing Data
Floating Toolbar
User Form
a. Input Data
Filter: Have used vitamines in the past week.
Question: Why have you taken vitamines during the past week?
Product Product Product Product Product Product
E
F
A
B
C
D
Mother
101
52
60
60
Father
64
53
14
36
Cousin
4
8
17
2
Neighbour
10
14
24
73
Teeny
6
56
65
14
48
54
Ma&Pa
79
69
30
52
32
67
Friend
6
10
22
2
91
18
b. Output Data
Eigenvalues
Values
Inertia %
Inertia cum. %
Mother
Father
Cousin
Neighbour
Teeny
Ma&Pa
Friend
Product A
Product B
Product C
Product D
Product E
Product F
Mass
462
281
53
204
0
0
0
202
143
130
192
167
167
1
0.0947
64%
64%
2
0.0450
30%
95%
Inertia
11
29
33
74
Inertia ‰
75
199
226
500
34
16
37
61
0
0
230
110
248
411
0
0
3
0.0079
5%
100%
1
-112
-236
-74
598
-54
-170
-41
-377
-267
90
535
0
0
2
61
-201
769
-59
507
-111
309
-116
-77
523
-174
0
0
3
-87
92
195
19
413
102
66
-115
191
-15
-12
0
0
1
62
165
3
771
2
38
254
693
16
3
438
301
252
10
1
530
531
9
989
2
155
388
932
10
3
315
81
60
1
302
108
11
579
0
0
61
19
790
130
0
0
335
658
4
3
0
0
841
628
29
903
408
408
80
52
971
96
68
68
78
320
1
0
524
524
Explained variance (3-axis inertia) = 100%
Brand Mapping: Vitamins Usage
Cousin
Teeny
Product C
Friend
Mother
Product F
Product B
Neighbour
Product E
Product A
Ma&Pa
Father
Product D
www.mm4xl.com
390
Brand Switch Analysis
Floating Toolbar
User Form
a. Input Data
Sales $
Year 1925
Year 1926
Year 1927
Year 1928
Year 1929
Year 1930
Year 1931
Year 1932
Year 1933
Year 1934
Year 1935
Year 1936
Year 1937
Year 1938
Year 1939
Year 1940
Year 1941
Year 1942
Year 1943
www.mm4xl.com
Camel
24310.1
23459.0
21656.0
19559.6
17487.3
16179.5
15919.8
14116.8
13434.0
16434.3
18593.2
19588.4
19636.5
18473.0
18011.4
17828.7
17208.4
16958.4
15751.5
Lucky Strike
9750.9
9130.7
10751.0
14612.0
17386.3
19800.0
21276.1
21627.1
19271.1
15871.7
14487.0
13972.5
14179.3
15362.1
16145.8
16828.6
17564.2
18516.2
18631.6
Chesterfield
14020.6
15491.9
15674.6
13910.0
13208.0
12102.1
10885.7
12337.7
15376.5
15775.6
15001.5
14520.6
14265.8
14246.6
13924.4
13424.4
13309.0
12607.0
13698.4
391
b. Output Report
B r a n d S wi t c h
Luc k y
St r i k e
( T o- Fr om) :
- 0. 004
C a me l
( T o- Fr om) :
0. 006
C he s t e r f i e l
d
(To-Fr om):
0.053
C he s t e r f i e
ld
( T o- Fr om) :
- 0. 002
C a me l
(To-Fr om):
0.047
Luc k y
C he s t e r f i e
St r i k e
(To-Fr om):
-0.047
ld
(To-Fr om):
-0.051
Sw itch values in original units: LUCKY STRIKE
Luc k y
St r i k e
(To-Fr om):
0.051
C a me l
(To-Fr om):
-0.053
Loyalty Rate vs Sw itch Rate: LUCKY STRIKE
40%
35%
35%
30%
30%
Loyalty Value
40%
25%
20%
15%
10%
1.2%
1.0%
27.5%
30.2%
28.9%
33.5%
31.6%
33.6%
0.8%
0.7%
0.6%
25%
0.5%
0.4%
20%
0.2%
0.1%
15%
0.0%
0.0%
10%
5%
-0.2%
5%
Fro m Camel To
Fro m Chesterfield To
To Camel Fro m
To Chesterfield Fro m
-0.4%
-0.4%
Year 1943
Year 1942
Year 1941
Year 1940
Year 1938
-0.6%
Year 1939
0%
Year 1943
Year 1942
Year 1941
Year 1940
Year 1939
Year 1938
0%
1.0%
Switch in Minus Switch Out
Lucky Strike
Lucky Strike
Switch In(new) - Out(dislo yal)
Correlations of Sw itch
Values in Original Units:
LUCKY STRIKE
100.0%
80.0%
60.0%
40.0%
20.0%
0.0%
-20.0%
-40.0%
-60.0%
Fro m Camel To
-80.0%
Fro m Chesterfield To
-100.0%
Lucky Strike
To Chest er f ield
From
To Camel Fro m
To Camel Fr om
Lucky St r ike
Fr om
Chest er f ield To
www.mm4xl.com
392
Gravity Analysis
Floating Toolbar
User Form
a. Input Data
City A
City H
City I
City C
City D
City F
City G
City E
City B
Data Label
Place B Town A
Place C Town B
Place D Town C
Place E Town D
Place F
Place G
Place H
Distance from city A
0
0
0
135
34
122
187
59
156
128
56
98
76
123
76
78
36
22
34
25
234
65
673
345
128
2
265
98
34
Population
124
785
54
6253
1233
9856
654
5987
795
76
357
b. Output Report
Gravity Analysis
City C
Gravity Analysis
Gravity Analysis
City I
Size : 345
Dist : 57.8=45%
Size : 673
Dist : 69.4=37%
Tow n C
Place E
Place D
Size : 654
Dist : 17.0=30%
City D
Place F
Size : 128
Dist : 43.7=57%
City F
Size : 2
Dist : 69.6=92%
City G
Size : 795
Dist : 34.8=28%
234
City B
City E
Size : 265
Dist : 17.4=48% Size : 98
Dist : 20.6=61%
www.mm4xl.com
Place B
124
Place C
Size : 54
Dist : 20.5=60%
City H
City A
Size : 65
Dist : 88.4=65%
Place H
Size : 34
Dist : 18.1=72%
Size : 9856
Dist : 34.3=22%
Size : 1233
Dist : 14.2=24%
Tow n A
785
Tow n B
Size : 357
Dist : 8.2=37%
Place G
Size : 76
Dist : 43.7=56%
Size : 6253
Dist : 31.9=26%
Tow n D
Size : 5987
Dist : 26.1=27%
393
Cluster Analysis: Ward’s Method
Floating Toolbar
User Form
a. Input Data
b. Output Report
Dendrogram
Novo Nordisk
Sanofi
Basf
Boehring I.
Bayer
Warner L.
AHP
Lilly
J&J
Abbott
Schering-P.
SKB
BMS
Pharmacia
Pfizer
Aventis
Roche
Novartis
Glaxo
AstraZeneca
Merck
Levels histogram
Index
1
3
5
Knot
7
13
15
17
0
200
400
Index
www.mm4xl.com
9
11
600
800
1000
19
0.0
200.0
400.0
600.0
800.0
1000.0
394
Cluster Analysis: K-Means Method
Floating Toolbar
User Form
a. Input Data
b. Output Report
Item Dispersion Around Group Center
A straZeneca
Ro che
J&J
Lilly
No vartis
B ayer
BM S
P harmacia
P fizer
A HP
Sano fi
Glaxo
A ventis
M erck
A bbo tt
Schering-P .
Warner Lambert
www.mm4xl.com
B o ehring I.
SKB
B asf
No vo No rdisk
395
Segmentation Tree
Floating Toolbar
User Form
a. Input Data
b. Output Report
Sex
1017 100.0%
Sex
F
628 - 61.8%
252 - 40.1%
A rea
City
A rea
Land
A rea
City
A rea
Land
418 - 41.1%
182 - 43.5%
210 - 20.6%
70 - 33.3%
255 - 25.1%
80 - 31.4%
134 - 13.2%
29 - 21.6%
A ge
'35-54
A ge
'<35 '+54
A ge
'35-54
A ge
'<35 '+54
A ge
'35-54 '<35
A ge
'+54
A ge
'35-54
A ge
'<35 '+54
151- 14.8%
71- 47.0%
267 - 26.3%
111- 41.6%
95 - 9.3%
36 - 37.9%
115 - 11.3%
34 - 29.6%
199 - 19.6%
69 - 34.7%
56 - 5.5%
11- 19.6%
55 - 5.4%
13 - 23.6%
79 - 7.8%
16 - 20.3%
A ge
'<35
140 - 13.8%
60 - 42.9%
www.mm4xl.com
Sex
M
389 - 38.2%
109 - 28.0%
A ge
'+54
127 - 12.5%
51- 40.2%
A ge
'<35
63 - 6.2%
19 - 30.2%
A ge
'+54
52 - 5.1%
15 - 28.8%
A ge
'35-54
95 - 9.3%
34 - 35.8%
A ge
'<35
104 - 10.2%
35 - 33.7%
A ge
'<35
57 - 5.6%
12 - 21.1%
A ge
'+54
22 - 2.2%
4 - 18.2%
396
Profile Manager
Floating Toolbar
User Form
a. Input Data
b. Output Report
Profile chart
Estim ated share
Price
28.0%
27.6%
Price deal
27.0%
25.0%
23.5%
24.0%
23.3%
23.0%
28% 31%
25%
A
Pack
25%
Quality
21%23%
25%
B
C
31%
D
Shelf space
22.0%
21.0%
19% 22%
Premium
25.6%
26.0%
24%
27%
24%
25%
A
B
C
D
Adv
29%
21%
14%
18%
Store display
24%
22%
36%
36%
25%
0%
10%
20%
30%
40%
Market Share
Adv
20.0%
Quality
20.0%
Pack
18.0%
Store display
15.0%
Shelf space
8.0%
Price
8.0%
Premium
6.0%
Price deal
5.0%
18.5%
28.5%
38.5%
Attribute effect on m arket share
Sensitivity Analysis: Product A
www.mm4xl.com
397
Descriptive Analyst
Floating Toolbar
User Form
a. Input Data
b. Output Report
Pareto chart report: Bin range.
Frequency
Pareto Chart - Series:%Error
Cumulative %
120%
16
14
84.1%
Frequency
12
87.3%
93.7%
100.0%
100%
74.6%
80%
10
52.4%
8
6
4
60%
31.7%
6.3%
40%
15.9%
20%
9.5%
2
0
0%
-15.6%
-11.8%
-8.1%
-4.3%
-0.6%
3.1%
6.9%
10.6%
14.4%
M o re
Bin
Descriptive statistics report
Box plot
20%
18.1%
15%
10%
5%
3.2%
0%
-1.1%
-5%
-5.9%
-10%
-15%
-20%
-19.3%
-25%
%Error
www.mm4xl.com
398
Smart Chart (Bubbles with labels)
Floating Toolbar
User Form
a. Input Data
b. Output Report
B ubbles = Est. Sales -- M ax = 252.7
Class A
Class B
Class C
Project Analysis
B ubbles = Est. Sales - M ax = 252.7
Class A
Quadrants: Equal Size
250
Class C
Project A
Project A
Project F
Cost of Project
Project B
150
Project D
100
Project I
Project G
48
Project H
-2
Project D
Project C
Project G
Project E
Project J
-102
-89
0
50
100
150
11
Quadrants: Split to Mean
144
139
111
Class A
Class B
Class C
Class A
Class B
Class C
Quadrants: Split to Median
61
Time to go
Legend:
P ut yo r no tes here
94
89
Project A
Project A
Cost of Project
Project F
39
Project B
Project I
Project H
-11
Project G
Project D
Project B
Project I
Project H
-6
Project G
Project D
-56
Project E
Project J
Project E
Project J
-21
Project F
44
Project C
Project C
-61
Legend:
P ut yo r no tes here
-39
200
Time to go
-111
-71
Project I
Project C
-52
Project E
Project J
0
Cost of Project
Project B
Project H
50
Project F
98
Cost of Project
200
www.mm4xl.com
Class B
148
29
79
-106
-77
129
Legend:
P ut yo r notes here
Time to go
-27
23
73
123
Time to go
399
User Form
c. Input Data
b. Output Report
B ubbles = P ro duct P ro fit (B ubble) - M ax = 321.7
Day Face Creme
Hair system
Hand Care
Bubbles with Arrows
Lipsticks
5.0
Night Face Creme
Sun P ro tectio n
2003
4.5
2001
2001
Mkt Growth (Ver)
4.0
2003
2002
2002
2002
3.5
2001
2002
2001
2003
3.0
2003
2002
2.5
2.0
1.5
550
2003
2003
2001
2002
2001
750
950
1150
1350
1550
1750
1950
Sales Value (Hor)
www.mm4xl.com
400
Semantic Differential
Floating Toolbar
User Form
a. Input Data
b. Output Report
My Left Shoe
These are Alta Moda shoes
10
I have seen the advertisement
57
I have seen them in a w indow
5
User Statement
Good quality/price relationship
I bought the brand before
25
35
They are status symbols
22
7
11
Many VIP's w ear them
69 74
36
26
37
36
0
9
24
20
29
84
45
78
44
7983
46
56
59
52
40
P roduct A
P roduct D
www.mm4xl.com
76
46
14 21
This shoe lasts longer than others
This is the shoe for myself
62
18
These shoes recall me of French
4
69
47
25
4 8
76
56
32
22
21
18
3
65 71
44
60
P ro ductB
P ro duct E
80
100
P ro duct C
401
4-D Map
Floating Toolbar
User Form
a. Input Data
b. Output Report
Coord X
4D Chart
Gastro
Oncology
Women's health
Diabetis
Coord Y
CNS
Respiratory
Others
Cardio
Antiinfective
4D Chart
Coord X
Gastro
Oncology
Women's health
Diabetis
Respiratory
Others
Coord Y
CNS
Cardio
Antiinfective
2
www.mm4xl.com
1
3
402
Stacked Charts
Floating Toolbar
User Form
b. Output report
My First Stacked Chart
1.07
0.79
0.75
0.43
0.62
0.38
Series 4
1.37
0.88
0.81
0.72
0.27
112
123
0.84
0.81
0.26
334
93
1.02
54
23
1.01
0.92
0.34
Product
A
Product
B
Product
C
Product
D
Product
E
Series 3
Series 2
Series 1
Product
F
My first stacked chart
1.00
0.75
0.50
0.25
1.00
0.75
0.50
0.25
1.00
0.75
0.50
0.25
1.00
0.75
0.50
0.25
1.00
0.75
0.50
0.25
1.00
0.75
0.50
0.25
a. Input Data
0.35
0.3
0.88
0.72
1.07
0.79
0.88
0.72
112
123
0.84
0.81
Product A
Product B
0.75
0.3
0.43
0.43
0.75
0.75
1.37
0.27
Series 2
0.81
0.06
0.84
0.81
0.38
0.62
0.81
1.01
Series 3
Series 2
54
0.92
Product C Product D
Series 4
0.26
334
23
Series 5
93
1.02
0.34
Product E
Series 1
Product F
My first stacked chart
1.00
0.75
0.50
0.250.35
1.00
0.75
0.500.88
0.25
1.00
0.75
0.501.07
0.25
1.00
0.75
0.50
0.250.88
1.00
0.75
0.50
0.25112
1.00
0.75
0.500.84
0.25
Product A
www.mm4xl.com
0.3
0.72
0.79
0.72
0.75
0.3
0.43
0.43
0.75
0.75
1.37
0.27
Series 2
0.81
0.06
0.84
0.81
0.38
0.62
0.81
Series 3
0.81
1.01
Product B
Product C
Series 2
54
23
0.92
Product D
Series 4
0.26
334
123
Series 5
93
1.02
0.34
Product E
Series 1
Product F
403
Benchmark Map
Floating Toolbar
User Form
a. Input Data
b. Output Report
61%
Lo se M arket Share
Keep M arket Share
51%
Market Growth (%)
ABBOTT
41%
BM S
ROCHE
M SD
31%
GLAXO
NOVARTIS
11%
LUNDBECK
LILLY
HM R
21%
BAYER
SCHERING
SB
NOVO ZENECA
ASTRA
PHARM A
NORDIS
P&UP
SANOFI
WYETH JOHN
PFIZER
JANSSEN
1%
Win M arket Share
-9%
-9%
1%
11%
21%
31%
41%
51%
61%
Product Growth (%)
www.mm4xl.com
404
Project (Mind) Mapping
Floating Toolbar
User Form
b. Output Report
www.mm4xl.com
405
www.mm4xl.com
406
Forecast Manager
Floating Toolbar
User Form
a. Input Data
www.mm4xl.com
407
b. Output Report 1: Forecast
506
Input - Forecast
456
406
356
306
Forecast t+4
Jul '00
-5%
Oct '00
Jan '00
Fo recast
Special Events Analysis - Series: Appliance Shipments
Cumulative Sum Control Chart (CuSum)
Series: Appliance Shipments
Apr '00
Jul '99
Oct '99
Jan '99
Observed
Forecast t+1
B est Fit:
B ro wn's Linear Expo nential Smo othing
M SE: 118.111
M A P E: 2.8%
M A D: 9.155
R-squared: 87.9%
Theil's U: 0.254
Durbin-Watso n: 0.112
Apr '99
Jul '98
Oct '98
Jan '98
Apr '98
Jul '97
Oct '97
Jan '97
Apr '97
Jul '96
Oct '96
Jan '96
Apr '96
256
+5%
Special event s summar y:
- Favor able: 1.0%or 2.9
4.0%
- Adver se: -0.5%or - 1.7
F a v or a bl e Ev e nt s
60
- Tot al: 0.4%or 1.2
Won: 1.0%
or 2.9
3.0%
Upper Limit +2 SD
% Forecast Error
Cumulative Forecast
Error
40
20
0
-20
2.0%
ULim +2SD
1.0%
ULim +1SD
0.0%
LLim -1SD
-1.0%
LLim -2SD
-2.0%
-40
-3.0%
Lo wer Limit -2 SD
-60
1
4
7
www.mm4xl.com
10
13
16
19
22 25 28
31 34 37
Tim e
40 43 46 49
52 55 58
Lost : 0.5%
or 1.7
A d v e r se Ev e nt s
-4.0%
1
4
7
10
13
16
19
22
25
28
31 34
37
40
43
46
49
52
55
58
Tim e
408
Hidden Sheet
www.mm4xl.com
409
c. Output Report 2: Forecast Special Events
Forecast Chart - Series: Sales
14929
12929
Input - Forecast
10929
8929
6929
4929
Green: values above
2929
Max Conf Int
Observed
Special events summary table
Coefficient:
Average values
Smoothing met Quadratic trend
Kind of
Input
event
value
Time period:7
Time period:8
Time period:16
Time period:17
Time period:21
www.mm4xl.com
Promo -15
Comp action
Promo -15
Comp action
Promo -20%
10780
870
11020
1090
1510
Forecast
-5%
Smoothe
d value
Event
effect
Event
Event
effect % coefficient
1317.0
1327.6
1328.4
1326.9
1448.7
9463.0
-457.6
9691.6
-236.9
61.3
718.5%
-34.5%
729.6%
-17.9%
4.2%
Forecast t+4
Forecast t+3
Forecast t+2
Dec '00
Best Fit :
Holt 's double exponent ial smoot hing
M SE: 7543.128
M APE: 4.2%
M AD: 56.160
R-squared: 99.9%
Theil's U: 1.048
Durbin-Wat son: 2.541
Forecast t+1
Oct '00
Nov '00
Sep '00
Jul '00
Aug '00
Jun '00
Apr '00
May '00
Mar '00
Jan '00
Feb '00
Dec '99
Oct '99
Nov '99
Sep '99
Jul '99
Aug '99
Jun '99
Apr '99
May '99
929
+5%
724.0%
-26.2%
4.2%
410
CrossTab (Contingency Tables)
Floating Toolbar
User Form
a. Input Data
Code Range
Client
Sex
Language Class
1 Female English
Class A
2 Male
Spanish
Class B
3
French
Class C
4
5
Region
North
Center
South
Why using Swiffer?
Remove dust
Quick job
Friend suggestion
Curiosity
Others
b. Output Report
Open-end question
Closed-end question
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411
Sample Manager
Floating Toolbar
User Form
a. Output Report
MM4XL© - Sample Size: Sensitivity analysis
- Population size (N):
- Confidence level::
- Error level::
- Hypothesis of the study:
- Sample size (n):
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412
Proportion Analyst
Floating Toolbar
User Form
b. Output Report
MM4XL© - Comparison of proportions, two-tailed.
Hypothesis Ha: (Proportion 1 - Proportion 2) <> 0.000
Significance (required):
95.000%
Probability (achieved):
88.139%
p Value: 23.723% (= 11.861% * 2 tails)
z Value: -1.1819
Conclusion
NO, the difference between proportions is not statistically significant.
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413
Variation Analyst
Floating Toolbar
User Form
a. Input Data
b. Output Report
Method: ANOVA - One-factor analysis of variance
User Input Data: Statistics
Input Data
300.0
250.0
200.0
150.0
100.0
50.0
0.0
1
2
3
4
5
6
It e m s
3x2
Discount
7
Quantity
Group Comparison: Report
A verage
Variance
167.8
130.8
114.1
1906.5
1277.3
854.3
Discount
3x2
Quantity
Quadrant analysis: Discount vs Quantity
Quadrant analysis:
Discount vs Quantity
137.0
Disappo int
Item 7
Head to head
Item 3
Item 1
Item 2
Item 4
103.6
Item 5
70.3
92
Item 6
To ugh jo bs
141
Go t it!
190
D is c o unt
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414
Quality Manager
Floating Toolbar
User Form
www.mm4xl.com
a. Input Data
415
www.mm4xl.com
416
Decision Tree
Floating Toolbar
User Form
a. Input Data: Multiply Path
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b. Output Report: Multiply Path
417
a. Input Data: Maximize / Minimize Utility
Path
Week 2
FALSCH
-190.785
744.1
23.0%
849.1
39.0%
509.2
0.0%
614.2
0.0%
MM4XL - Decision Tree Risk Profile Report
Tree: Tree #1 of Decision Tree.xls
Created on 30.05.2003 at 12:35:42
Risk Profile
Profile #
1
2
3
4
Mean
Minimum
Maximim
Week 4
FALSCH
-215.67
FALSCH
-240.555
Probability
20.00%
18.00%
23.00%
39.00%
Optim um Path: Tree #1
39.00%
40%
719.2
0.0%
824.2
0.0%
30%
23.00%
20.00%
18.00%
20%
What quantity?
724.2
Week 3
Value
534
639
744
849
724
534
849
50%
10%
200 Items 20.0%
700
230 Items 18.0%
805
Items sold?
674.4
260 Items 23.0%
910
290 Items 39.0%
1015
200 Items 20.0%
700
230 Items 18.0%
805
Items sold?
649.5
260 Items 23.0%
910
290 Items 39.0%
1015
484.3
0.0%
589.3
0.0%
0%
534
639
744
849
Value
694.3
0.0%
799.3
0.0%
459.4
0.0%
564.4
0.0%
Optim um Path (scatter)Tree #1
50%
40%
Probability
Best Order
WAHR
-165.9
534.1
20.0%
639.1
18.0%
Probability
Week 1
200 Items 20.0%
700
230 Items 18.0%
805
Items sold?
724.2
260 Items 23.0%
910
290 Items 39.0%
1015
200 Items 20.0%
700
230 Items 18.0%
805
Items sold?
699.3
260 Items 23.0%
910
290 Items 39.0%
1015
b. Output Report: Maximize Utility Path
39.00%
30%
18.00%
10%
669.4
0.0%
774.4
0.0%
23.00%
20.00%
20%
0%
0
200
400
600
800
1000
Value
120%
Cum ulative Probability: Tree #1
Cumul Probability
100%
80%
60%
40%
20%
0%
518
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550
581
613
644
676 707
Value
739
770
802
833
865
418
Risk Analyst
Floating Toolbar
User Form
a. Input Data: Sheet Model
MarketingStat.com
419
b. Output Report: Preview
c. Quick Help
www.mm4xl.com
420
www.mm4xl.com
421
www.mm4xl.com
422
Index
3
3D environment 353
A
ABC analysis 319
abnormal error size 105
Acceptance curve 151
Acceptance sampling 119
accuracy 66
Accuracy and reporting rules 330
accuracy coefficients 104
accuracy of forecast 110
accuracy of random numbers 191
accuracy report 104
Achieved Probability 330
active points 71
Activity 351
acute angle θ 63
Additive seasonality 110
Additive trend 110
adjunctive data 353
adjunctive information 274
adverse events 106
advertising awareness 69
affective dimension 351
AID 291
algorithm re-iteration 278
allocate resources 41, 53
alternative hypothesis 298, 314, 315
amount of risk 191
Analysis of variance 327
Analysis of Variance 333
analysis of variation 333
Analysis Toolpak 109
angle θ 63
ANOVA 327, 333
answer report 80
answer variable 218
approximation for the mode 175
approximation of unknown values 112
array formula 216, 219, 225
array formulae 102
association 61, 63, 65, 66, 316, 342, 346
association between variables 316
assumption of independence 192
assumptions 163, 190
ASTM 156
ASTM manual 216
asymmetrical distribution 192
Attachments 377
attitude 277, 349, 350
attitude scales 351
attitude toward risk 265
attitude-measurement scaling 350
attitudinal dimensions 351
attribute charts 349
Attributes characteristics 119
autoadaptive optimization’ 112
autocorrelation of error terms 104
automatic interaction detection 291
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Autoregressive models 109
Average Difference 331
Average method 101
Average outgoing quality 119, 154
average profile 61, 63
avoid risky ventures 266
avoiding risk 264
awareness data 70
Axes with equal length 363
axis orientation 66
B
bar chart 179
basic roots 62
batch analysis 320
batch forecast 98
battle for the mind 71
BCG 33, 34, 36, 37, 38, 39, 41, 43, 47, 51, 53
BCG Interpreter 37
behavior 277
Belson’s segmentation method 291
Benchmark Analysis 361
Benchmark Map 363
BEP Siehe Break Even Point
bernoullian formula 303
best curve 99
best fitted curve 102, 109, 172
Best partition 284
best-fit coefficient 112
best-fitted model 103
Beta distribution 175, 223, 238
Between group variation 333
Between-group inertia 282
bi-modal distribution 175, 193
bin range 322
Binomial distribution 164, 196, 206, 211, 220, 222,
233, 238, 241
Binomial probability distribution function 133, 139, 150
bipolar scale 349, 350
black-box 97, 98
blank tree 259
Boston Consulting Group 33
box plot 178
boxplot 323
box-whisker plots 319
braces brackets { } 102
Brainstorming sessions 367
Branches 374
brand awareness 70
brand differentiation 70
brand image 69, 70
Brand Loyalty Index 77
brand personality 64
brand preference 77
brand probability purchase vector 95
brand switch behavior 77
brand switch matrix 81
brand switching behaviour 91, 95
brand-switching 79
Break Even Point 195
break point 274
Brown’s linear exponential smoothing 113
423
bubble diameter 59
bubble distribution 63, 68
bubble map 339
bubble maps 198
bubble size 68, 274, 282
building models 188
Business analysts 330
Business test plans 330
C
calibration phase 178
Capability 147
Capability ratio 148
cascade charts 80
cash absorbers 40
cash cows 35, 36, 37, 38
cash flow 33, 36, 37, 38, 39, 40, 41, 42, 52, 53
cash generators 40
Categorical data 320
categorical scale 319
causal models 109
C-chart 126
cell comment 102, 104
Center of group 284
Centering standardization 279
central item 272
central tendency 174, 196
Central tendency 128
Centroid method 277
certainty equivalent 266
CFD Siehe Contributing Factor Diagram
Chance nodes 261
chance of failure 195
change in slope 106
Chart limits 128
chart readability 341
Chi squared distance 61
Chi squared statistic 61
chi squared test 307, 315
Chi squared test for independence of table 310
Chi2 distribution 224, 230, 231, 238, 239, 240, 243,
244
CHIINV() 316
CHIVALUE() 316
classes of product portfolios 42
classification 280
Clipboard 370, 378
closed-end questions 309
cluster analysis 277, 280
cluster configuration 280
code meanings 310
code values 310
Coded tables 310
Coefficient of Determination 115, 316
Coefficient of variation 115
Coefficient R 310
CoF Siehe chance of failure
Collapse branches 376
Coloring maps 368
Common mind map 379
communication effort 71
compact summary 181
company utility function 265
comparable products 77
comparative analysis 35
compare means 333
competing products 77
Competitive Advantage 47, 48, 49
competitive condition 52
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competitive environment 53
competitive marketing mix matrix 93, 95
competitive power 361
competitive structure 61
competitive weaknesses 77
Competitiveness maximization 38
Complete standardization 279
complex markets 70
Components of switch behavior 83
concept development 93
conditional probability 189
Confidence 303
confidence interval 104, 314
Confidence level 302, 304
Conjoint Analysis 91
Connecting Arrows 341
Connectors 374
connotative analysis 349
connotative dimension 351
connotative meaning 349
Consistency of Performance 103, 116
Consolidated pictures 80
Consumer risk 150
contingency table 60, 307
continuous distribution 170, 172, 192
continuous scale 319
continuous variables 320
Continuous variables 192
Contributing Factor Diagram 163, 189, 202, 205, 209,
Siehe Contributing Factor Diagram
Contribution 62
coordinate 62, 72
coordinates on the McKinsey grid 49
CORREL() 279
correlated variables 197, 219
correlation 63, 307
Correlation analysis 279
correlation coefficient 183, 219, 279, 316
Correlation coefficient 331
correlation matrix 219
correlation of residuals 116
correlation values 179
Correlations of Switch Values 84
correspondence analysis 57, 61, 279
cost of studies 304
cost of survey studies 303
COUNTIF() 115
Coverage of the campaign 107
Cows 42
Cp 148
Cpk 148
CpL 148
CpU 148
Cr 148
creative thinking 257
Creative thinking 367
Criteria 291
critical values 298
cross-sectional data 60
Ctrl+Shift+Enter 216, 219, 225
cumulative distribution 182
cumulative error 105
cumulative error 116
cumulative probability of occurrence 249
Cumulative Sum chart 104, 105, 116
custom variables 191
customer preference 91
customer retention 77, 84
CuSum chart 104, 105, 116
424
D
decision analysis 256, 264
Decision nodes 260
decision problems 259
Decision tree branches 267
decision trees 259
Decision trees 253
decision trees, building 257
decisional model 163
Decision-makers 264
decision-making 119
decrease in sales 107
default number of bins 216
defects in a sample 233
Defensive marketing warfare 67
defining R 265
Demonstrated excellence 148
dendrogram 280
dependence techniques 279
dependency 315
dependent variable 109, 291
describing variables 279
Descriptive Analyst 174
descriptive statistics 124, 319
Desired Probability 330
detecting correlation 198
diameter of the circles 43
difference between two proportions 314
difference in variance 333
differences in the group means 333
differentiation 61, 64, 69, 70, 277
dimensions of attitude 351
direct competition 84
direct competitor 34, 36, 40, 41, 61, 84, 101
discrete distribution 170, 172, 192
discriminant value 291
Discriminating variable 291
discriminating variables 291
dispersion 342
dispersion between groups 284
Dispersion chart 280
dispersion within groups 284
distance 63
Distribution Functions 167
divest 52
dogs 35, 36, 37, 38, 40, 42
dotted whiskers 274
Double moving average 114
dual display 65
Durbin-Watson coefficient 104, 116
dynamic analysis 35, 340
dynamic data 60
Dynamic Loyalty Analysis 83
dynamic maps 69
dynamic markets 40
dynamic model 190
Dynamic values 342
E
earnings 47
educated guess 163, 205
educated guesses 41
educated guessing 93
educational community 111
Effectiveness of business decisions 329
eigenvector 62, 64
elapsed time 172
emotions 350
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EMV Siehe Expected Monetary Value
End nodes 261
EPA 351
equal probability 190
Equal sample sizes 330
equally scaled quadrants 343
equally spaced bin range 322
Equilibrium 42
Erlang distribution 228, 230
Error Function 226
Error level 302, 303, 304
Error summary 100
error term 110, 116
Error terms 333
estimate the missing values 72
estimated share chart 93
Euclidean distance 284
Evaluation 351
evaluative continuum 351
even nodes 261
Event Coefficients 107
Event Effect 107
Examples of Project Mapping 379
Excel settings 98
exceptional events 108
EXP 236
Expected 263
expected boundaries 105
expected monetary value 264
Expected monetary value 266
Expected Monetary Value 254
expected monetary values 189
expected utilities 265
Expected utilities 266
expected utility maximizers 266
expected value maximization 263
exploring data 319
Exponential distribution 193, 227, 229, 235, 239, 240,
243, 248
Exponential smoothing 113
exponential utility 265
extract a sample 302
Extract N random data rows 302
extract random samples 301
Extreme Values distribution 190, 228, 235, 248
F
F9 key 175
failure region of the distribution 195
failure time 226, 247
False signals 106, 116
favorable events 106
F-critical 330
F-distribution 333
finite population 303
finite populations 303
first minimum 112
first order Markov process 81
fit analysis 171
Fit Index 171
fit of the curve 346
fitted curve 103
Fitted Distributions 171
fitted line 101
fitted model 102
Fitting tool 170, 226
Fix costs 43
Flanking marketing warfare 67
Flow diagram 379
425
flow diagrams 189
forecast algorithm 100
forecast horizon 98, 109
Forecast Manager 174
forecasting 77, 109
forecasting errors 105
frequency distribution 182, 308
Friedman’s method 112
F-test 333
Full accuracy report 104
Function Wizard 186
functional distance 275
functional know-how 77
future special events 102
F-Value 330
G
Gamma distribution 220, 222, 224, 227, 228, 230, 238,
239, 240
Gaussian distribution 238
GE/McKinsey portfolio matrix 48
General Electric 47
Geometric distribution 232, 237
GIGO concept 329
goodness of fit 104, 171
goodness-of-fit 149
Gradient method 112
gravity 271
gravity model 275
Group capacity 284
grouped charts 80
growing markets 38
growth rates 36
growth trends 67
Guerrilla marketing warfare 67
Gumbel distribution 229
H
help online 98
Help with distributions 185
hidden report 103
hidden sheet 52, 102
hierarchical methodology 281
Hierarchical methods 277
histogram chart 178, 179, 216
Holt’s double exponential smoothing 113
Holt-Winter’s additive seasonality 114
Holt-Winter’s multiplicative seasonality 114
homogeneity assumptions 333
homogeneity of clusters 283
homogeneity of groups 284
Homogeneity of variance 333
homogeneous groups 277
homogeneous subgroups 291
horseshoe shape 68
hybrid models 109
Hypergeometric distribution 223, 241
Hypergeometric operating characteristics curve 119,
152
Hypergeometric probability distribution function 152
Hyperlink 377
hypothesis 297
hypothesis level 304
Hypothesis of the study 302, 304, 314
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I
identifiers for the variables 178
Image format BMP 370
Image format GIF 370
incoming quality 154
increase in sales 107
independence 307
independence techniques 279
Independent random numbers 191
independent variables 109, 110, 291, 315
indifference value 265
individual emotions 351
inertia 61, 66
Inertia level 278
infinite populations 303
infinite scale 320
influence diagrams 189
input variables 167
integer distributions 192
Integer Uniform distribution 175
Intensity of the event(s) 107
interdependence statistical techniques 277
intermediary sheets 341
intermediate computations 102
intermediate data 111
Intermediate-term forecast 109
intersection 308
Inverse Gauss distribution 211, 238
invest & grow 52
Investment level 37
Investments 53
investor profiles 254
item dispersion chart 282
J
Johnson Type VI distribution 240
joint distribution 308
K
Kaizen 124
K-means clustering method 277, 281
Kolmogorov-Smirnov statistic 171
Kolmogorov-Smirnov test 149
Kotler, Philip 91, 93, 95
Kurtosis 174
L
lack of memory 228, 233
latent structure 57, 60, 85
Law of Retail Gravitation’ 271
leader products 38
Left-mouse click 374
less is better 193
levels of meaning 350
lifetime expectancy 247
limits report 80
linear optimization 97
linear regression 101
linear relationship 316
linear relationships 198
Linear trend 114
Listen to the message 377
logarithmic market share 34, 43
logarithmic relative market share 36, 40
Logarithmic Relative Market Share 36
426
logarithmic scale 36, 43
logarithmic utility 266
LogNormal distribution 211, 230, 238
Lomax distribution 240
longitudinal data 60, 68
Long-term forecast 109
lot size 152
low dimensional space 61, 62
Low investors 42
Lower capability index 148
loyalty rate 85
loyalty values 83
M
Macro-environmental 47
macro-factors 48, 49, 52
MAD 99, 115
Main shape 374
management processes 123
Manual on Presentation of Data and Control Chart
Analysis 156
map orientation 69
MAPE 99, 115
marginal utility 264
Market Attractiveness 47, 48, 49, 50, 51
market elasticity of adoption 86
market gaps 61
market growth 33, 34, 35, 36, 40, 41, 342, 362
Market growth 362
market leaders 36
market scenarios 92
market segment 41, 64, 85
market segmentation 279
market share 33, 36, 37, 40, 41, 42, 43, 52, 62, 77, 79,
81, 84, 85, 86, 342, 362
market share behaviour 91
Market share forecast 80
Market share matrix 79
marketing principles 67
marketing response vector 93, 95
Marketing Warfare 67
Markov processes 79, 81, 87
mass 68
mass value 59, 62, 66
matching moments 171
matrix of correlation coefficients 219
matrix of transition probabilities 86
mature market 38
Max time 79
maximize competitiveness 38
Maximize EMV 258
maximize incoming cash 52
McKinsey 47
McKinsey Summary Report 51
Mean 343
Mean Absolute % Deviation 115
Mean Absolute Deviation 115
Mean expected value 262
Mean Square Error 115
meaning of an object 351
meanings of words 350
measure its intensity 350
measure of central tendency 196
measure of success 189
measurement scale 323
measures in SPC 119
Measures of association 84
measures of dispersion 196
measures of fit 99
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measures of shape 323
measures of tendency 323
measures of variability 323
measuring the process 124
median 36, 343
Medium investors 42
Meeting facilitations 367
Micro-environmental 47
micro-factor 48, 49, 52
Mind mapping technique 368
minimization problem 263
Minimize EMV 258
Missed signals 106, 116
missing values 329
mmBETA 201, 220, 221
mmBETAGEN 201, 220, 221
mmBINOMIAL 169, 179, 196, 201, 223
mmCHI2 201, 224
mmCORREL 197
mmCORRELATE 167, 200, 209
mmDISCRETE 201, 202, 225
mmERF 201, 226
mmERLANG 201, 227
mmEXPON 201, 228, 233
mmEXTVAL 229
mmEXTVALUE 201
mmGAMMA 201, 230
mmGAUSSINV 201, 231
mmGEO 201, 228, 232
mmHISTO 167, 178, 179, 190, 191, 200, 216
mmHYPERGEO 201, 211, 233
mmINTUNI 201, 234
mmLOCK 167, 168, 178, 184, 199, 202, 215
mmLOGISTIC 201, 235
mmLOGNORMAL 201, 230, 236
mmNAME 167, 168, 178, 180, 183, 199, 207, 214
mmNEGBIN 201, 237
mmNORMAL 168, 170, 172, 197, 201, 214, 219, 230,
238
mmOPTNUM 165, 167, 175, 200, 206, 218
mmOUTPUT 167, 168, 180, 199, 213
mmPARETO 201, 239
mmPARETO2 201, 240
mmPOISSON 201, 241
mmRANDBETWEEN 169, 190, 191, 201, 242
mmRAYLEIGH 201, 243
mmSTUDENT 201, 244
mmTRI 190, 191, 201, 211, 215, 245
MMULT() 81, 87, 95
mmUNIFORM 201, 212, 246
mmWEIBULL 201, 247
modal value 175, 191, 196
mode 196
mode of a Pdf 175
model, refreshing 188
modeling assumptions 163
modeling scenarios 180
modelling interaction effects 95
monetary payoff 264
Monitoring projects 367
mono-modal distribution 193
Monte Carlo technique 188, 192
more is better 193
most likely value 190
Moving average 114
MSE 99, 112, 115
Multi Table Heading 311
multi-item analysis 273
multi-modal functions 112
multiple time series 111
427
multiplicative formulae 258
multiplicative seasonality 110
multiplicative tree 259
multiplicative trend 110
multiplying matrixes 95
multi-series forecast 98
N
naïve tables 310
naïve trees 259
Nature of the campaign 107
negative attitude 351
Negative Binomial distribution 223, 232
Negative saldo 42
nested equations 112
new brand usage 72
new competitors 72
new product development 91
Node map 379
non-leader products 38
Normal distribution 172, 193, 206, 219, 220, 222, 223,
224, 226, 235, 236, 238, 241, 243, 244
Normal variate 164
normality assumptions 333
Normalization 339
normalized variables 342
normalizing data 333
normally distributed variables 149
NORMSDIST() 298
nP-chart 137
NPD Siehe New Product Development
null hypothesis 298, 314, 315, 333
number of attributes 350
number of axes 59
number of clusters 277, 281, 282
Number of simulations 174
number of trials 175, 178
O
object of the risk assessment 195
objective of the analysis 188
oblique grid 355
obtuse angle θ 63
occurrence of extreme values 229
Offensive marketing warfare 67
old products 38
one-factor ANOVA 333
one-tailed test 298
open-end questions 309, 310
Operating characteristics curve 119, 150
optimal solution 79, 86, 112
optimization 79
optimization algorithm 98, 100
optimization process 112
optimized unknown 112
optimizing models 112
Optimum 42
Optimum path 261
order of data entry 278
Ordinates 281
orientating the axes 72
orientation of the map 60
orientation of the principal axes 62
origin of the map 62
Osgood’s semantic differential scale 349
Outgoing quality 154
outlier points 61, 66
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Output cells 168
output result 167
Output variable 183, 188, 189, 213
over-representation 115, 342
overwrite existing data 173
P
p Value 298
Paired performance 328
panel study 68
Pareto Chart 320
Pareto curve 319
Pareto distribution 228, 229, 235
Pareto distribution, class 2 240
partition 65, 278, 281
Partitioning methods 277
partitioning technique 281
Pascal variate 237
passive point 60
passive variables 291
payoff 265
Pbar 139
P-chart 133
P-chart with fixed 134
P-chart with variable lot 134
Pearson Product Moment Correlation Coefficient 316
Pearson’s Correlation Coefficient 279
PERCENTILE 178
percentile interval 221
percentile values 178
performance 277
performance ranks 319
peripheral items 272
philosophy of war 67
Picture of a project 378
pin-bubbles 355
Poisson distribution 223, 224, 233, 237, 238, 241
Poisson probability distribution function 126
Pooled estimate 314
population 274, 303
population size 272, 302
Portfolio Analysis 33, 34, 35, 37, 41, 43, 44, 47, 49, 53,
54, 342
portfolio evaluation 39
portfolio management theory 39
Portfolio Matrix 36
portfolio optimization 42
portfolio performance 42
portfolios 51
positioning 61, 64, 70, 71, 277
positioning maps 61, 71
positive association 316
positive attitude 351
positive correlation 165
Potential capability 148
Power 351
Preceding value 101
Precision 79
Predictions 346
preference 77
preference data 60, 70, 72
principle of distributional equivalence 72
prior knowledge 57, 61, 64, 66, 81, 85
probabilistic assumptions 301
probabilistic trees 260
probabilities of occurrence 264
probability distribution functions 192
probability functions 249
probability of acceptance 153
428
Probability of Acceptance 151
probability of an event 220, 221
probability of occurrence 191, 193, 249, 297
Probability of Rejection 151, 153
probability of retention 87
probability values 267
process capability 147
process capability analysis 119
Process flow schemes 368
Producer risk 150
product acceptance 295
product concepts 61
Product growth 362
Product of two arrays 87
product opportunities 61
Product Portfolio Analysis 34
product portfolio in equilibrium 42
product portfolios 33
product positioning 61, 67, 69, 70
product preference 69
product typologies 41
products not yet on the market 47
profile 63, 71
Profile chart 93
Profile Manager 91
profit maximization 38, 42
profit-maximizing portfolio 42
Project Mapping 367
Project planning 367
Projecting market share 87
projections 346
promotional action 101, 105
promotional actions, effectiveness 329
promotional campaign 107, 329
Promotions 331
Property Functions 167
proportions 295
Public presentations 367
Q
Quadrant analysis 328
Quadrant Analysis 331
Quadrant type 340
quadrants 342
quadrants of the share/growth grid 40
quadratic model 79
quadratic problem 86
quadratic programming 79
Quadratic trend 101, 114
qualitative models 109
Quality 63
Quality Manager 119
quality of fit 99
quality of fitted curves 99
quality of forecast 110
quantitative fit 109
quantitative models 109
quartile values 323
question marks 35, 36, 37, 38, 40, 42
queue analysis 240
Quota sampling 304
R
R 307
R squared 99, 112, 115, 307
Random numbers 175, 176, 191, 196, 246
Random samples 304
random sampling 303
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random selection 304
range 193
range spread 194
rating scales 349, 350
Rayleigh distribution 243, 248
Read sheet 169
real-life issues 192
recalculation mode 175
recessive markets 38
Record vocal message 377
Rectangular Continuous distribution 246
Rectangular Discrete distribution 234
Rectangular distribution 228, 234, 246
rectangular table 60
reducing risk 41, 53
regression analysis 291
regression models 109, 110
related variables 315
relationships 280, 342
relationships between numbers 57, 353
relative attractiveness 95
relative awareness 95
relative importance 93
relative market share 36, 40, 43
reliability measures 99
reliability of forecasts 110
rescale quadrants 339
Rescale the axis 64
rescaled axes 67
re-scaling coordinates 355
rescaling data 359
re-scaling the quadrants 343
residual curve 116
residuals 116
retention rate 77, 80
Right-mouse click 374
risk 188
risk analysis 188
risk analysis process 167
Risk Analyst Wizard 167
Risk attitude 255
Risk attitude index, R 265
risk averse 254
risk in management 191
risk neutral 254
risk premium 266
Risk Profile 262
Risk scenarios 162
risk taker 254
Risk Wizard 186
risk-adverse 193
risk-taker 193
risky distribution 193
RMSE 99, 115
rolling back method 263
Root Mean Square Error 115
R-squared 346
S
sample 301
sample of products 119
sample size 152, 303
sampling 314
sampling plan 154
sampling plans 232
sampling techniques 304
SBU 33
scale of measurement 115
scale-of-measurement effect 339
429
scales of measurement 357
scales of variables 342
scatter diagram 346
Scenario modeling 190, 191
scenario simulation 264
Scheuer-Stoller method 197, 219
Seasonal coefficients 114
seasonal periods 114
Seasonal regression 114
seasonality 100, 110
Seasonality table 104
second order Markov process 87
security level, Excel 267
segmentation 60, 61, 65, 67, 68, 70, 277, 279, 280,
281, 282, 284, 346
segmentation variables 279
Segmentations 346
segmenting items 277
segmenting variables 291
Segmenting variables 291
segments 279
selective growth 53
selectivity 52
semantic differential 351
semantic opposites 351
semantic space 351
semi-structured questionnaire 309
sensitivity analysis 95, 301, 303
Sensitivity analysis 303
sensitivity report 80
sequential analysis 231
series characteristics 108
shape 174
shape of the distribution 164, 178, 179, 193
Sheet mode 175
Sheet Unhide 52
short-term forecast 97, 109
short-term policies 38
Show mode 175
Show preview 175
Show random numbers 175
Sigma 128
significance 307
significance of differences 330
significant difference 295, 314
Significant difference 327
Simulated data 138
simulation 188
simulation technologies 109
Single Table Heading 311
single-bullet model 162
size in squared feet 274
size of the bubbles 39, 49, 340, 354
skewed distribution 172, 230
Skewness 174
slope of the actual curve 106
slow growing markets 38
slow markets 40
smoothed value 107
Smoothing Method 116
soft knowledge 109
solicited awareness 70
Solver 78, 79, 80, 86, 87, 88, 97, 100, 111, 112
Solver reports 80
Solver User Manual 79
source of abnormality 108
sources of uncertainty 163
spatial and time data 329
SPC, Attribute Charts 126
SPC, Variable Charts 140
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Special event coefficients 116
Special event summary table 107
special events 97, 98, 101
special events chart 105, 116
special events chart 104
spike distribution 165
Spontaneous brand awareness 70
spread 174
spread of income 239
spread of risk 164
square table 219
squared angle θ 63
squared cosines 61, 62, 66, 69
squared Euclidean distance method 284
squared residuals 86
stability assumptions 329
stabilize the mean value 165
stable series 109
Stacked Charts 357
standard deviation of the mean 218
standard normal density function 315
standard normal distribution 314
standardization 279, 284
standardizing variables 279
stars 35, 37, 38, 42
start seed 278
static modeling 190
Static values 342
Stationary data additive seasonality 113
Stationary data multiplicative seasonality 113
Statistical process control 119
statistical quality control 123
Statistical quality control 119
Statistical Quality Control 120
steady point 77
Strategic Business Unit 33
strategic decisions 41
strategic interest 52
strategic portfolio management 52
strategic reasoning 57, 61, 64
strategic thinking 61, 67, 77, 81, 85
strength of leadership 40
strength of the relationship 316
Strong investors 42
Student’s t distribution 223, 224, 238, 244
SUMIF() 115
Summary statistics 173
supplementary columns 70
supplementary points 69, 71
supplementary rows 70
Survey Analysis suite 295
switch matrix 84
switch percentages 79
switch rates 77, 86
switch values, estimation 79
switch-in rate 77, 80
switch-out rate 77, 80
SWOT analysis 368
SWOT analysis map 379
symmetrical distribution 172, 192
system resources 80, 87, 111
systematic error patterns 110
systematic errors 105
T
tails of the distribution 190
target group 85
TCoS Siehe Total Cost of Success
technical performance 84
430
Tendency for one brand 84
test correlation 314
test independence 314
Test of significance of difference between proportions
310
test proportions for significance 312
test significance 314
test statistic 314
test statistics F 333
Test, summary page 330
Test, trend 330
testing 329
testing correlation between variables 310
testing plan 329
Theil’s U 104
time between events 227, 228, 230
time series 68
Time series charts 180, 214
Time series forecasting 107
time to fail of a component 243
time to perform some work 243
time to reload models 184
Tolerance 79
top of mind 70
tornado chart 94
Total Cost of Success 195
tracking study 68
transition probabilities 86
Translation of Project Manager 373
tree root 260
tree settings 258
trend 68, 77, 83, 100, 106, 110
trend line 346
trend pattern 109
trends 330
Triangular distribution 164, 171, 193, 205, 211, 215,
245
Triple exponential smoothing 113
truncated distribution 193
Trust Access To Visual Basic Project 267
Trusted Sources 267
Turning-Point diagram 106
Turning-Point Performance 116
turning-points 100, 109
two-tailed Z test for homogeneity 295
Type I risk 150
Type II risk 150
U
U-chart 130
unattractive industries 52
unbalanced portfolio 42
uncertainty 163, 188, 205, 207, 253, 263
undefined mode 175, 193
under-representation 115, 342
Unequal sample size 333
Unequal sample sizes 330
ungrouped charts 80
Uniform distribution 163, 191, 193, 205, 226, 242
uni-modal equations 112
unit of measurement 115
unknown values 112
unknown variables 112
unstable series 111
Upper capability index 148
U-statistics 115
utilitarian comparison 255
utility assessment 265
utility function 265
Utility functions 167, 189
utility of money 266
V
value decomposition 62
value of money 266
value of special events 102
variability 61
variable cell assessment 167
Variable characteristics 119
Variable costs 43
variance 61, 65, 71
Variances 329
Variation 124
variation explained 316
Variation test 330
verbal report 40
visual inspection 110, 280, 282
visualization techniques 355
Voice maps 377
W
waiting-line theory 227
Wald’s distribution 231
Ward’s clustering method 277, 281
weak estimator 198
Weibull distribution 228, 229, 243, 247
Weighted moving average 113
weighting 48
Weights 49
Within group variation 333
Within-group inertia 282
X
Xbar Chart 142, 145
X-R charts 140
X-R charts, assumptions 140
X-Range Chart 142
X-S charts 144
X-Sigma Chart 145
Y
years to failure for a business 247
Z
Z 128
Z test for homogeneity of two proportions 298
Z-test 307, 314
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Index
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MM4XL User`s Guide

Transcription

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