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Repeated Measures Analysis Christopher R. Seemann The New School for Social Research

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T-Tests

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T-Tests & Repeated Measure T-Tests Independent sample T-Test – H 0 : The difference between groups = 0 – H 1 : The difference between groups ≠ 0 Repeated measure T-Test – H 0 : The change between measurements = 0 – H 1 : The change between measurements ≠ 0

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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

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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

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Crossover Effects

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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

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Mixed Linear Modeling: A Better Approach Utilizes regression analysis to compute predicted values After regression analysis comes an ANOVA that tests against predicted values

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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

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LIVE EXAMPLE The Attentional Network Task and Dissociation

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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.

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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 η 2 p =.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, chi 2 = 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 η 2 p =.07.

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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 η 2 p =.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 η 2 p =.31. As the model never reached significance, the univariate ANOVAs were not explored.

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There is a Solution, But First: Data Structure Wide Data Structure Measureme nt Reading1Reading2Reading3 S1XXX S2XXX ReadingMeasurement S11x 2x 3x S21x 2x 3x Long Data Structure

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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 M diff = -.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).

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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

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Are there any questions? Thank you Jon for your data.

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