StatReason

Repeated Measures ANOVA Calculator

Compare three or more measurements taken on the same subjects, such as scores before, during, and after an intervention, using each subject as their own control across every condition.

Every subject needs the same number of conditions (3 or more), with no missing values.

What this answers

This test answers "do these related conditions differ, using each subject as their own baseline?" rather than comparing separate independent groups. Removing between-subject variability this way often gives more statistical power than a one-way ANOVA on the same number of total observations spread across independent groups.

How it is calculated

Total variability is split three ways: variability between subjects (how different people's overall averages are, regardless of condition), variability between conditions (the effect of interest), and leftover error variability. The F statistic compares the condition variability to the error variability, each divided by its own degrees of freedom. This calculator reports the standard, uncorrected F, which assumes sphericity (that the variances of the differences between every pair of conditions are roughly equal); a Greenhouse-Geisser correction is a well known alternative for when that assumption looks doubtful, not computed here.

Worked example

For 3 subjects who each show the exact same relative pattern across 3 conditions (even though their absolute values differ substantially from subject to subject), the between-subject variability is fully absorbed and removed from the error term, leaving a clean, undiluted condition effect and typically a much larger F than a one-way ANOVA treating the same numbers as independent groups would produce.

Assumption audit

Calculated from your data: the sum of squares for subjects, conditions, and error, the resulting F statistic and p-value, and partial eta squared as an effect size.
Evidence to review: whether the differences between each pair of conditions have roughly similar variance across subjects (the sphericity assumption); strong violations can make the reported p-value too liberal.
You must verify: that every row genuinely represents the same subject (or matched unit) measured under every condition, not independent groups, and that every subject has a complete set of measurements.

What this result does not mean

A significant result means the conditions are not all equal on average, not that every pair of conditions differs; identifying which specific conditions differ requires a dedicated post-hoc procedure. This test also does not correct for sphericity violations on its own, unlike some software's default output.

Limitations

This calculator requires complete data: every subject must have a value for every condition, with no missing values and no partial dropout supported. If sphericity is a serious concern and you would rather avoid that assumption entirely, the Friedman Test answers a similar question using only ranks.