Mediation Analysis - JuliA Renberg`s Portfolio

Mediation Analysis - JuliA Renberg`s Portfolio

Results #3
EDRS 821
Julia and Luis
Determine if perceived teacher competence is a mediator between effort and overall amount learned.
First, bivariate correlation was conducted to check if there is significant correlation between a) IV
and M; b) M and DV. In this case, there is significant correlation for a) effort and teacher
competency (r = .40, p < 0.05) and b) teacher competency and overall amount learned (r = .64, p <
0.05). Additionally, although not required, there was significant correlation between IV (effort) and
DV (overall amount learned) with r = .37, p < 0.05.
Effort 1s
Effort 1s
Pearson Correlation
Sig. (2-tailed)
N
Pearson Correlation
Sig. (2-tailed)
N
Pearson Correlation
Sig. (2-tailed)
N
Overall Amount Learned 1s
Teacher Competency 1s
Overall Amount Learned 1s
.366**
.000
430
1
1
431
.366**
.000
430
.399**
.000
430
430
.642**
.000
430
Teacher Competency 1s
.399**
.000
430
.642**
.000
430
1
430
**. Correlation is significant at the 0.01 level (2-tailed).
To establish mediation effect, Baron & Kenny’s causal step approach was followed.
Step 1: We ran regression model to see if there was an association between effort (IV) and
mediator - teacher competency (DV).
Model Summary
Model
1
R
.399a
R Square
.159
Adjusted R Square
Std. Error of the
Estimate
.158
.67040
a. Predictors: (Constant), Effort 1s
Model
1
Standardized
Coefficients
Beta
Unstandardized Coefficients
Std. Error
B
(Constant)
1.579
Effort 1s
.426
a. Dependent Variable: Teacher Competency 1s
.151
.047
t
Sig.
10.483
9.012
.399
.000
.000
Step 2: We checked whether the association of independent and dependent variable reduced
significantly (partial mediation) or disappear (full mediation) when the mediator was added.
Model Summary
Model
R
R Square
Adjusted R Square
1
.366a
.134
.132
b
2
.653
.426
.424
a. Predictors: (Constant), Effort 1s
b. Predictors: (Constant), Effort 1s, Teacher Competency 1s
Model
1
(Constant)
Effort 1s
2
(Constant)
Effort 1s
Teacher Competency 1s
Std. Error of the
Estimate
.74882
.61016
Unstandardized Coefficients
B
Std. Error
1.279
.168
.430
.053
.254
.154
.153
.047
.649
.044
Standardized Coefficients
Beta
Repeated work via Processor:
MATRIX procedure:
***************** PROCESS Procedure for SPSS Release 2.13 ***************
Written by Andrew F. Hayes, Ph.D.
www.afhayes.com
Documentation available in Hayes (2013). www.guilford.com/p/hayes3
**************************************************************************
Model = 4
Y = AmtLe_1s
X = Effrt_1s
M = TComp_1s
t
.366
.130
.590
7.601
8.129
1.653
3.255
14.753
Sig.
.000
.000
.099
.001
.000
Sample size
430
**************************************************************************
Outcome: TComp_1s
Model Summary
R
.3993
R-sq
.1595
MSE
.4494
F
81.2085
df1
1.0000
df2
428.0000
p
.0000
Model
constant
Effrt_1s
coeff
1.5793
.4263
se
.1507
.0473
t
10.4829
9.0116
p
.0000
.0000
LLCI
1.2832
.3333
ULCI
1.8754
.5193
**************************************************************************
Outcome: AmtLe_1s
Model Summary
R
.6528
R-sq
.4262
MSE
.3723
F
158.5865
df1
2.0000
df2
427.0000
p
.0000
Model
coeff
.2541
.6490
.1529
constant
TComp_1s
Effrt_1s
se
.1537
.0440
.0470
t
1.6528
14.7526
3.2552
p
.0991
.0000
.0012
LLCI
-.0481
.5625
.0606
ULCI
.5562
.7355
.2452
************************** TOTAL EFFECT MODEL ****************************
Outcome: AmtLe_1s
Model Summary
R
.3657
R-sq
.1338
MSE
.5607
F
66.0844
df1
1.0000
df2
428.0000
p
.0000
Model
constant
Effrt_1s
coeff
1.2790
.4296
se
.1683
.0528
t
7.6008
8.1292
p
.0000
.0000
LLCI
.9483
.3257
ULCI
1.6098
.5334
***************** TOTAL, DIRECT, AND INDIRECT EFFECTS ********************
Total effect of X on Y
Effect
SE
.4296
.0528
t
8.1292
p
.0000
LLCI
.3257
ULCI
.5334
Direct effect of X on Y
Effect
SE
.1529
.0470
t
3.2552
p
.0012
LLCI
.0606
ULCI
.2452
Indirect effect of X on Y
Effect
Boot SE
TComp_1s
.2767
.0355
BootLLCI
.2173
BootULCI
.3593
Normal theory tests for indirect effect
Effect
se
Z
p
.2767
.0360
7.6775
.0000
******************** ANALYSIS NOTES AND WARNINGS *************************
Number of bootstrap samples for bias corrected bootstrap confidence intervals:
1000
Level of confidence for all confidence intervals in output:
95.00
NOTE: Some cases were deleted due to missing data.
The number of such cases was:
Questions
Please give complete but concise responses to the following questions regarding the
analyses you have conducted.
1
Explain any differences between the B&K approach and the PROCESS output.
The Baron and Kenny approach does not require testing of the indirect effect of the mediator. Their
four step analysis (although many reduce them to two steps, as we did) to establish mediation
requires that:
1) The causal variable is correlated with the outcome;
2) The causal variable is correlated with the mediator;
3) The mediator affects the outcome variable;
4) To establish that M completely mediates the X-Y relationship, the effect of X on Y controlling for
M (path c') should be zero for full mediation (or reduced to a very small amount for partial
mediation).
SPSS program provides us with necessary information to test for significance of indirect effect, but
does not actually performs any tests. PROCESS output does essentially B&K steps, but also runs the
Sobel test and a more superior bootstrapped test. Similarly, ROCESS calculates indirect effect of the
mediator (in this case, .2767), where as SPSS program only provides us with calculated coefficients
for paths a and b and we have to manually calculate the combined effect as ab (.426 x .649).
2
Write a short (1-2 sentence) summary of your model finding (write in terms of
constructs). What does your model suggest?
The present model suggests that teacher competency is a mediator, because when entered into the
model it partially “takes over” or “wipes out” the direct effect of effort on the overall amount learned
(still significant), reducing the unstandardized coefficient from .43 to .15. Therefore, effort affects
teacher competency, and teacher competency affects the overall amount learned.
3
What is the bootstrapped CI for the indirect effect? Is it significant?
Indirect effect of X on Y
Effect
Boot SE
TComp_1s
.2767
.0355
BootLLCI
.2173
BootULCI
.3593
According to the PROCESS output, the bootstrapped CI for the indirect effect (see above) ranged
from .22 to .36. This result indicates that the indirect effect of the mediator was significant because
there is no zero included in this range.
4
Conduct a Sobel test using your SPSS output—is it significant?
To test for significance of indirect effect (in other words, whether or not the total effect of X on Y is
significantly reduced by the addition of a mediator to the equation), the Sobel test was performed
(entering unstandardized coefficients and standard errors from the SPSS output for a path (IV to M)
and b path (M to DV) into the Sobel test calculator on Kristopher Preacher’s website). The result
was significant with the t value exceeding 1.96 - t (430)=7.69, p<0.05. These results are the same for
the PROCESSOR output:
Normal theory tests for indirect effect
Effect
se
Z
p
.2767
.0360
7.6775
.0000
5 Add a second mediator (perceived teacher caring) to your model using
PROCESS. Draw a picture of this model filling in path coefficients. Write 3-5
sentences explaining the model.
Run MATRIX procedure:
***************** PROCESS Procedure for SPSS Release 2.13 ***************
Written by Andrew F. Hayes, Ph.D.
www.afhayes.com
Documentation available in Hayes (2013). www.guilford.com/p/hayes3
**************************************************************************
Model = 4
Y = AmtLe_1s
X = Effrt_1s
M1 = TCare_1s
M2 = TComp_1s
Sample size
430
**************************************************************************
Outcome: TCare_1s
Model Summary
R
.3776
R-sq
.1425
MSE
.7029
F
71.1519
df1
1.0000
df2
428.0000
p
.0000
Model
constant
Effrt_1s
coeff
.9714
.4990
se
.1884
.0592
t
5.1558
8.4352
p
.0000
.0000
LLCI
.6011
.3828
ULCI
1.3417
.6153
**************************************************************************
Outcome: TComp_1s
Model Summary
R
.3993
Model
R-sq
.1595
MSE
.4494
F
81.2085
df1
1.0000
df2
428.0000
p
.0000
constant
Effrt_1s
coeff
1.5793
.4263
se
.1507
.0473
t
10.4829
9.0116
p
.0000
.0000
LLCI
1.2832
.3333
ULCI
1.8754
.5193
**************************************************************************
Outcome: AmtLe_1s
Model Summary
R
.6654
R-sq
.4427
MSE
.3624
F
112.8032
df1
3.0000
df2
426.0000
p
.0000
Model
constant
TCare_1s
TComp_1s
Effrt_1s
coeff
.3221
.1711
.5007
.1307
se
.1529
.0482
.0602
.0468
t
2.1072
3.5513
8.3123
2.7963
p
.0357
.0004
.0000
.0054
LLCI
.0216
.0764
.3823
.0388
ULCI
.6226
.2657
.6191
.2226
************************** TOTAL EFFECT MODEL ****************************
Outcome: AmtLe_1s
Model Summary
R
.3657
R-sq
.1338
MSE
.5607
F
66.0844
df1
1.0000
df2
428.0000
p
.0000
Model
constant
Effrt_1s
coeff
1.2790
.4296
se
.1683
.0528
t
7.6008
8.1292
p
.0000
.0000
LLCI
.9483
.3257
ULCI
1.6098
.5334
***************** TOTAL, DIRECT, AND INDIRECT EFFECTS ********************
Total effect of X on Y
Effect
SE
.4296
.0528
t
8.1292
p
.0000
LLCI
.3257
ULCI
.5334
Direct effect of X on Y
Effect
SE
.1307
.0468
t
2.7963
p
.0054
LLCI
.0388
ULCI
.2226
Indirect effect of X on Y
Effect
Boot SE
TOTAL
.2988
.0363
TCare_1s
.0854
.0267
TComp_1s
.2135
.0340
(C1)
-.1281
.0492
BootLLCI
.2339
.0382
.1528
-.2312
BootULCI
.3779
.1421
.2891
-.0353
Normal theory tests for specific indirect effects
Effect
se
Z
p
TCare_1s
.0854
.0262
3.2537
.0011
TComp_1s
.2135
.0351
6.0897
.0000
Specific indirect effect contrast definitions
(C1)
TCare_1s
minus
TComp_1s
******************** ANALYSIS NOTES AND WARNINGS *************************
Number of bootstrap samples for bias corrected bootstrap confidence intervals:
1000
Level of confidence for all confidence intervals in output:
95.00
NOTE: Some cases were deleted due to missing data.
16
The number of such cases was:
------ END MATRIX -----
Teacher
Caring
.50
.17
Overall
Amount
Learned
.13
Effort
0.
.43
Teacher
Competency
.50
The presented above regression model is statistically significant and explains about 44% of variance
of our criterion “overall amount learned” (R2 adj = .44, F (3, 426)= 112.80, p<0.05). The model shows
that the direct effect of our causal variable (effort) on the dependent variable (overall amount
learned) is replaced by two mediating variables (teacher caring and teacher competency). The
cumulative mediating effect of these variables is only partial, as the effect of IV on DV is reduced
from (unstandarized coefficient changed from .43 to .13), but remained significant. The Sobel and the
Bootstrapping tests indicate the indirect effect for both, teacher competency (t (430)=6.09,
p<0.05;[.15, .28] and teacher caring (t (430)=3.25, p<0.05;[.04, .14] were significant. The indirect
effect of teacher competency (.21) was stronger that of teacher caring (.09).
Write up
Note: Write up your results using the Baron & Kenny method describing what steps you
took and the results of your analysis (APA format). Include a diagram of the proposed
model.
You should include the following:
 Hypotheses that correspond to the above question.
 Results: Divide this into two sections.
o Descriptive statistics: Table of the correlations among all variables
in the study.
Correlations
Overall Amount Learned 1s
.366**
.000
431
430
**
.366
1
.000
430
430
.378**
.571**
.000
.000
430
430
**
.399
.642**
.000
.000
430
430
Effort 1s
1
Effort 1s
Pearson Correlation
Sig. (2-tailed)
N
Overall Amount Learned 1s Pearson Correlation
Sig. (2-tailed)
N
Teacher Caring 1s
Pearson Correlation
Sig. (2-tailed)
N
Teacher Competency 1s
Pearson Correlation
Sig. (2-tailed)
N
**. Correlation is significant at the 0.01 level (2-tailed).

Teacher Caring 1s
.378**
.000
430
.571**
.000
430
1
430
.739**
.000
430
Teacher Competency 1s
.399**
.000
430
.642**
.000
430
.739**
.000
430
1
430
o Hypothesis testing: results of the hypotheses tests.
Discussion: Include a brief discussion of your results. Be sure to explain
clear the mediational relationship.