Transcript Repeated Measure Final

Repeated Measures Analysis
Christopher R. Seemann
The New School for Social Research
T-Tests
T-Tests & Repeated Measure T-Tests
• Independent sample T-Test
– H0: The difference between groups = 0
– H1: The difference between groups ≠ 0
• Repeated measure T-Test
– H0: The change between measurements = 0
– H1: The change between measurements ≠ 0
Within and Between Subject Variables
• Between Subject Variable Definition: A factor
that is analyzed between subject groups
– Independent Sample T-Test
• Within Subject Variable Definition: A factor
that is analyzed within a single subject group
– Repeated Measure T-Test
ANOVA & Repeated Measure ANOVA
• ANOVA: between subject variables
• Repeated Measures ANOVA: within subject variables
• Mixed ANOVA: combination of between and within subject variables
• Problems:
– Violations of Sphericity:
• Too much change in correlation between variables
• Too much change in SD
– Missing Data
– Crossover Effects
Crossover Effects
A solution: Multivariate ANOVA
• MANOVA definition: a type of ANOVA where
there are 2 or more dependent variables
– Allows for a test of Sphericity
• Analyzes the variance and covariance between
dependent variables
– for repeated measures treats each of the
measurements as related measures
Mixed Linear Modeling:
A Better Approach
• Utilizes regression analysis to compute
predicted values
• After regression analysis comes an ANOVA
that tests against predicted values
Why We Use MLM
• Missing data
• Data cleaning
– Crossover effects
– Data that poorly matches the regression model
through an analysis of the residuals
• Modification of covariance structure
The Attentional Network Task and Dissociation
LIVE EXAMPLE
Methods and Hypothesis
• Methods
– Collected Heart Rate and RSA during a resting baseline and
during each of the three blocks of the Attentional Network
Test
– The Attentional Network Task is a computerized task that
measures the efficiency of the alerting, orienting,
executive control of attention.
• Hypothesis
• H1: There is change in the physiological measures
during the experimental procedure.
• H0: There is no change in the physiological measures
during the experimental procedure.
Mixed ANOVA
• RSA: To test the hypothesis that there would be a change in RSA we used a
4(RSA: Baseline, ANT1, ANT2, and ANT3) by 2(Trauma: No or Yes) mixed
ANOVA with RSA as a repeated within subject factor and Trauma as a
between subject factor. The only significant result was the main effect of
RSA with F(3, 48) = 3.28, p = .03, and η2p = .17. Simple effects using a
bonferroni adjustment suggest that this effect was driven by a statistically
significant increase from the first and second blocks of the ANT, with p =
.025.
• HR: To test the hypothesis that there would be a change in heart rate we
used a 4(HR: Baseline, ANT1, ANT2, and ANT3) by 2(Trauma: No or Yes)
mixed ANOVA with HR as a repeated within subject factor and Trauma as a
between subject factor. There was a failure to meet the sphericity
assumption, with a Mauchly’s W = .37, chi2 = 21.39, and p = .001, so the
Greenhouse-Geisser adjustment was used. The only result approaching
significance was the interaction between HR and Trauma, with an adjusted
F(1.87, 43.09) = 1.69, p = .09, and η2p = .07.
Repeated Measure MANOVA
• RSA: To test the hypothesis that there would be a change in RSA we
used a ) by 2(Trauma: No or Yes) MANOVA with RSA (Baseline,
ANT1, ANT2, and ANT3) as a repeated dependent variable and
Trauma (Yes or No) as a between subject independent variable. The
model violates the homogeneity of covariance so the Wilk’s Lambda
adjustment is used. The multivariate analysis suggested that there
were no significant differences with F(4, 13) = .77, p = .57, and η2p =
.19. As the model never reached significance, the univariate
ANOVAs were not explored.
• HR: To test the hypothesis that there would be a change in HR we
used a ) by 2(Trauma: No or Yes) MANOVA with HR (Baseline, ANT1,
ANT2, and ANT3) as a repeated dependent variable and Trauma
(Yes or No) as a between subject independent variable. There was
a multivariate effect of trauma at a trend level, with a Pillai’s Trace
F(4, 20) = 2.22, p = .10, and η2p = .31. As the model never reached
significance, the univariate ANOVAs were not explored.
There is a Solution,
But First: Data Structure
Wide Data Structure
Long Data Structure
Measureme
nt
Reading
Measurement
Reading1
Reading2
Reading3
S1
1
x
S1
X
X
X
S1
2
x
S2
X
X
X
S1
3
x
S2
1
x
S2
2
x
S2
3
x
Mixed Linear Modeling
•
RSA: To test the hypothesis that there would be a change in RSA we used a 4(RSA:
Baseline, ANT1, ANT2, and ANT3) by 2(Trauma: No or Yes) mixed linear model with
RSA as a repeated within subject factor and Trauma as a between subject factor. In
addition to this, Trauma was used as a grouping variable while the model used a
compound symmetry covariance structure and a restrict maximum likelihood
estimation of variance and covariance. The only significant effect was for the main
effect of RSA where F(3, 59.75) = 3.23, and p = .03. RSA was lower during the
baseline than the second ANT block, with an estimated Mdiff = -.45, SE = .15, and p
= .02.
•
HR: To test the hypothesis that there would be a change in heart rate we used a
4(HR: Baseline, ANT1, ANT2, and ANT3) by 2(Trauma: No or Yes) mixed ANOVA
with HR as a repeated within subject factor and Trauma as a between subject
factor. In addition to this, Trauma was used as a grouping variable while the model
used a autoregressive covariance structure with a time lag of 1 and a restrict
maximum likelihood estimation of variance and covariance. There was an
interaction between HR trial and Trauma with F(2.62, 71.26) = 2.62, and p = .06.
Effect slices would have been explored if the sample size was large enough (I tried,
I am sorry).
Summary
• MLM resolves issues:
– Data cleaning
– Sphericity
– Covariance structure
• Be careful with your data structure
– Plan your datasets based on the types of analysis
you will use
– Wide vs. long distinction
Are there any questions?
Thank you Jon for your data.