Mathematics and Statistics Support

Repeated measures ANOVA (and Friedman)

Dependent (outcome) variable: Continuous/numerical/scale (some disciplines also test ordinal data)
Independent (predictor/explanatory) variable: Time or condition (3+ levels)

Use: Tests the equality of means in 3 or more groups. All sample members characteristics must be measured under multiple conditions i.e. the dependent variable is repeated. This is the equivalent of a one-way ANOVA but for repeated samples and is an extension of a paired-samples t-test. It is used to analyse (1) changes in mean score over 3 or more time points (2) differences in mean score under 3 or more conditions.
Example: Test the effectiveness of a margarine for reducing cholesterol by comparing participants cholesterol before a trial to their cholesterol after 4 weeks and again after 8 weeks of using the margarine.

Assumptions: The dependent variable (or residuals) should be approximately normally distributed at each level . If a histogram or QQplot suggests the residuals are vey skewed or the dependent variable is ordinal, a Friedman test (which is based on ranks rather than the raw data) should be used. Some people use parametric tests for ordinal data if there are quite a few categories but be careful when interpreting differences

Data notes Ensure there is one row per participant with a different column for the dependent variable for each condition/time point.

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R Sheet

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Repeated measures ANOVA
Friedman test (Non-parametric repeated measures ANOVA)

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