Sphericity (Mauchly's test)

With repeated measures, the analysis of variance assumes that all differences between any two time points vary equally (sphericity). Mauchly's test checks this: W near 1 and a p value above .05 do not indicate a violation of sphericity. If it is violated, the F test comes out significant too often; the degrees of freedom are then reduced by ε. With two time points there is only one difference, so sphericity always holds.

Example: Mauchly W = .70, p = .086, ε (Greenhouse-Geisser) = .77: the test shows no violation, but ε is clearly below 1, so a correction is applied.

Caution: Mauchly's test is weak with few people and responds even to small departures with many. That is why Statable always reports the Greenhouse-Geisser correction, not only when p is below .05.