A repeated measures ANOVA tests whether the means of three or more conditions differ when the same participants are measured in every condition. Because each person acts as their own comparison, the design removes the variation between individuals from the error term, making it far more sensitive than comparing separate groups. It is the go-to test for within-subjects designs such as measuring an outcome before, during, and after an intervention on the same people.
What a repeated measures ANOVA is used for
Use it whenever the same units are measured under several conditions or at several time points: a pre-test, mid-test, and post-test on one cohort, or the same panel rating three product designs. It extends the paired-samples t-test from two measurements to many, just as the one-way ANOVA extends the independent t-test. The shared logic is that pairing the observations within a person strips out stable individual differences, which is exactly the noise that makes between-groups designs less powerful.
How it differs from a two-way ANOVA
This is a common point of confusion. A two-way ANOVA has two independent factors, each made up of different groups of participants, and tests their main effects and interaction. A repeated measures ANOVA has one factor whose levels are all measured on the same participants. The two are not rivals: you can have a two-way design where one factor is between-subjects and the other is repeated, called a mixed ANOVA. The defining feature of the repeated measures version is that the levels share participants, which changes the error structure and the assumptions.
| Design | Participants across conditions | Key assumption |
|---|---|---|
| One-way ANOVA | Different in each group | Equal variances |
| Repeated measures ANOVA | Same in every condition | Sphericity |
The sphericity assumption
The distinctive assumption of a repeated measures ANOVA is sphericity: the variances of the differences between every pair of conditions should be equal. Mauchly's test checks it, and when it is violated the F test becomes too liberal. The fix is a correction to the degrees of freedom, the Greenhouse-Geisser or Huynh-Feldt adjustment, which most software applies automatically. Reporting which correction you used, and why, is part of a defensible analysis rather than an optional footnote.
Interpreting and reporting the result
A significant within-subjects F tells you the condition means are not all equal, but not which ones differ, so follow up with pairwise comparisons using a correction such as Bonferroni. Report the F statistic, the (possibly corrected) degrees of freedom, the p-value, and an effect size such as partial eta-squared, following APA reporting conventions. If your design adds a continuous covariate or a second between-subjects factor, the analysis moves toward analysis of covariance or a mixed model, and choosing between them is exactly the kind of decision the test-selection guide is built for.