ANOVA and Friedman Test Explained: Repeated Measures Analysis

Overview

Osmosis explains Analysis of Variance (ANOVA) as a parametric test used to compare means across three or more groups, outlining key assumptions: random sampling, independent observations, and adequate sample size or normality for small samples. The video distinguishes repeated measures ANOVA, which tracks the same subjects over time, from one-way ANOVA across different groups at a single time point.

Takeaways

It emphasizes that ANOVA tests for differences among means but does not specify which groups differ. The method yields an F statistic by comparing mean squares between and within groups, and results are interpreted via a P value with a typical 0.05 threshold. The video also covers when Friedman non-parametric tests are appropriate as an alternative when parametric assumptions fail.

Introduction to ANOVA and Repeated Measures

Analysis of Variance (ANOVA) is introduced as a parametric test for detecting differences among three or more group means. Three core population assumptions are highlighted: random sampling to ensure external validity, independence of observations, and a sufficiently large sample size or normal distribution for smaller samples. The video distinguishes between repeated measures ANOVA, where time is the independent variable and the same individuals are observed across multiple time points, and the traditional one-way ANOVA that compares different groups at a single time point.

Hypotheses in ANOVA

Typically there are two hypotheses: the null hypothesis claims that all group means are equal, while the alternative claims that at least one group mean differs. Importantly, ANOVA does not tell which groups differ or the direction of the difference.

Step-by-Step SIX Steps of ANOVA Calculation

The video walks through a concrete example with group means of 138, 132, and 130, and a grand mean of 133. Step 1 computes the grand mean and group means. Step 2 computes the between-group variation, SSB, yielding 350. Step 3 computes the within-group variation, SSW, totaling 905. Step 4 separates within-group variation into the sum of squares of subjects and the sum of squared error; for repeated measures the subject term is removed, leaving SSE of 35 and SSS of 870. Step 5 calculates MST and MSE, giving MST = 175 and MSE ≈ 1.94. Step 6 computes the F statistic as MST divided by MSE, approximately 90.2, and compares it to a critical value (3.55 in the example). When F exceeds the critical value, the null is rejected.

Interpreting Results and Alternatives

The video notes that a P value provides the probability of obtaining the observed F statistic under the null hypothesis. If P < 0.05, the null is rejected, indicating that at least one group differs. It also discusses non-parametric alternatives, specifically the Friedman test, which compares medians when parametric assumptions are not met. Software often reports P values, making critical-value lookups unnecessary.

Key Takeaways

ANOVA helps determine if group means differ but does not indicate which groups differ. Repeated measures designs control for subject variability, and Friedman offers a robust alternative when assumptions fail. The video emphasizes the importance of assumptions for external validity and the preference for parametric tests when appropriate.