Repeated Measures ANOVA calculator

Compare means of the same group across three or more conditions. Calculate spherical residuals, F-ratio, and p-value online.

What it does

Compares 3+ measurements on the same subjects across time/conditions, modelling within-subject correlation.

Cautions

• Assumes sphericity (equal variances of all pairwise difference scores). The result tests this with Mauchly and, when it rejects, marks a Greenhouse–Geisser or Huynh–Feldt corrected row as Recommended — read that row rather than the uncorrected one. Mauchly is itself weak on small samples, so a borderline uncorrected result deserves the corrected p quoted beside it.
• Classic RM-ANOVA listwise-deletes any subject with a missing timepoint — a linear mixed model would retain them if missingness is nontrivial.

Alternatives

• Friedman — ordinal or non-normal outcome

How to read the output

F-statistic, df (treatments) and df (error)

The between-occasion variation against the subject-by-occasion variation left over. Subject-to-subject differences are removed first, which is what makes the design efficient.

Sphericity, Mauchly and the correction rows

The test assumes the variance of the difference between any two occasions is the same for every pair. Mauchly's test checks that; when it rejects, the table recommends Greenhouse–Geisser if ε is below 0.75 and Huynh–Feldt otherwise, each shrinking the degrees of freedom by ε. Use the row marked Recommended. The uncorrected line is shown for comparison and is exactly the one that is too liberal when the assumption fails. Mauchly's test is itself weak on small samples, so an uncorrected result that only just reaches significance deserves the corrected p quoted beside it.

N (subjects)

Only subjects complete on every occasion are used. Check the excluded-rows warning. One missing occasion removes the whole subject, so a small amount of scattered missingness can remove a great deal of the sample — the reason a mixed model is often the better tool.

p-value

How surprising a difference at least this large would be IF the groups really were identical on this measure. A small p means the data would be surprising under that assumption. It is not the probability that the result is due to chance, and not the probability that the groups are the same — those read the conditional backwards. It also answers 'would this be surprising?', never 'is this big enough to matter?': with a large sample a trivial difference returns a small p, and the result looks identical to an important one.

How this calculator is validated · Which statistical test should I use?