Lab3: writing up results and ANOVAs with within and between factors 1

Transcription

Lab3: writing up results and ANOVAs with within and between factors 1
Lab3: writing up results and ANOVAs
with within and between factors
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Should be able to answer:
• What are the independent and dependent
variables?
• Are the conditions of application met?
– Compound symmetry?
– Sphericity?
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Conditions of application
• Normality:
– fully balanced design, all subjects in all conditions,
all cells filled so probably safe
• Compound symmetry:
– Smallest covariance: .147, Largest covariance: 39
• Sphericity:
– p>.05, fail to reject hypothesis that pairwise
variances differ
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Should be able to answer:
• Are there main effects?
– Contrasts: to learn about others, p. 371
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Summary of results
• A significant main effect of coil was observed, suggesting that the fMRI
signal varies for coils with different numbers of channels (F1,11)=37,
p<.001), while collapsing across (or irrespective to) acceleration level.
Means reveal that signal was greater for the 32 channel as predicted.
• A significant main effect of acceleration was found, suggesting that MRI
signals differ for different levels of acceleration (F2,22=13.6, p<.001), when
collapsing across coils.
• Contrasts revealed that acceleration of a factor of 2 or 3 both differenced
significantly from no acceleration (2factor: F1,11=6.1, p<.05; 3factor:
F1,11=57.1, p<.001). In addition, a significant linear contrast was observed
(F1,11=57.1, p<.001) with a non-significant quadratic contrast (F1,11=0.0,
p>.1), suggesting that signal changes linearly with acceleration. Graphs
reveal that the linear relationship is such that MRI signals decrease with
increasing acceleration. This is consistent with our hypothesis.
• When reporting F, need degrees of freedom, first one is for
the factor and is number of levels -1, second one is for error,
which is (number of subjects -1) X (number of levels-1)
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Should be able to answer:
• Are there main effects?
• Interactions?
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Summary of results
• However!! There was a significant interaction of coil and
acceleration (F2,22=9.9, p<.01).
• We therefore investigated the effect of acceleration
separately for each coil.
• 12 channel: There is a significant main effect of acceleration
using the GG (F1.25, 13.8=18.1, p<.001).
Contrasts reveal that acceleration of a factor of 2
(F1,11=11.3, p<.01) and 3 (F1,11=131.1, p<.001) both differ
from no acceleration.
• 32 channel: There is again a significant main effect of
acceleration (F2,22=4.1, p<.05). However, contrasts revealed
that only acceleration of factor 3 differed significantly from
no acceleration (F1,11=7.9, p<.05). This suggests 32 channel
coil is less affected by acceleration than 12 channel, as
hypothesized.
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Interpreting interactions via contrasts
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12ch
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32ch
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25
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5
5
0
0
a2
32ch
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10
a0
12ch
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a0
a3
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Writing an abstract
• Background
• Objective
• Methods. May include:
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(Sample size calculation / power)
Instruments
Procedure
Sample description (or may be in results)
Analysis (or may be in results)
• Results
• Discussion
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Abstract format
Background: Advances in MRI hardware have led to coils with greater numbers of channels, while
software improvements have allowed MR data to be collected faster.
Objective: Here, we set out to test whether more channels are better, and how MRI acceleration
techniques might affect signal strength.
Methods: Twelve subjects underwent fMRI with both a 12 (12ch) and a 32 channel (32ch) coil.
For each coil, three levels of acceleration were tested (none, 2factor and 3factor). Average MR
signal was extracted and used as the dependent measure in a repeated measures ANOVA.
Results: There was a main effect of number of channels (F1,11)=37, p<.001), resulting from greater
signal from the 32ch versus the 12ch. There was a main effect of acceleration (F2,22=13.6,
p<.001), with signal decreasing as acceleration increased. In addition, there was an interaction
between number of channels and acceleration (F2,22=9.9, p<.01). To investigate the interaction,
repeated measure ANOVAs were performed for the simple effects. They revealed a significant
main effect of acceleration for both the 12ch, where the Greenhouse-Geisser correction was
used (F1.25, 13.8=18.1, p<.001), and for the 32ch (F2,22=4.1, p<.05). Simple contrasts revealed that
for the 12ch, signals decreased significantly for both 2factor (F1,11=11.3, p<.01) and 3factor
(F1,11=131.1, p<.001) acceleration. However, for the 3ch, signals decreased significantly for only
the highest level of acceleration (F1,11=7.9, p<.05).
Discussion: This suggests that signals are greater when collected with more channels, and as the
amount of acceleration increases, signals decrease. This was particularly true for the 12ch data.
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Next up: mixed design ANOA
• What if you have both within and between
subjects factors?
• No worries, ANOVA can handle it 
• What are between subject factors?
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Mixed design: conditions of application
1. Normality within each factor level or group
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Robust to violations as long as fully factorial -> no levels
missing (like having only 2 of the three levels of
acceleration for 32 channel data or group).
This can also be tested via histograms and tests for
normality (see chapter 4??)
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2. Homogeneity of variance:
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Replaced by compound symmetry or sphericity in RM
ANOVA
But now need to check for between subject factors with
Levene’s test
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Tests the null hypothesis that the error variance of the
dependent variable is equal across groups -> want nonsig
need to be careful because can be positive from small deviations
with large sample sizes
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Practical differences
• Must define between subject variables
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Practical differences
• Can use posthoc tests to investigate
differences: Scheffe
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Practical differences
• Making plots
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Practical differences
• Levene’s test
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New output
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Now you try!
• Expansion of MRI methods study from last week.
• Again tested two different MRI coils (12 channel
and 32 channel coils), and 3 levels of acceleration
(a0,a2,a3). Same hypotheses as before:
– Signal should be larger for 32 than 12 channel coil
– Signal should decrease with increasing levels of
acceleration
• In addition, half of the subjects (12) were
scanned with a resolution of 2mm (voxels
2x2x2mm) and half (12) with 3mm.
– Hypothesize that large voxels result in more signal.
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Should be able to answer:
• What are the independent and dependent
variables? Are they within or between?
• Are the conditions of application met?
– Sphericity?
– Homogeneity of variance?
• Are there main effects?
• Interactions: investigate with simple effects and
the contrasts
• What can you conclude: try writing up an abstract
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