The condition under which the variance of the difference is constant between any two estimated factor level means in an analysis of variance, but one that is less restrictive than compound symmetry. As with compound sphericity (of which sphericity is a more general form), it is important in the analysis of variance of repeated measures or longitudinal data. Whether or not this condition has been met can be examined by means of the Mauchly test. It is violated when the variances of the differences among all combinations of groups are unequal, with the result that the F-ratio is inflated.
See Analysis of variance (ANOVA), Compound symmetry, Greenhouse-Geisser epsilon, Hunyh-Feldt epsilon, Mauchly test, Mixed-effects models, Repeated measure analysis of variance, Sphericity assumption