Constant variances and constant covariances of the dependent measure across the levels of a factor in analysis of variance (i.e., the variances and covariances are equal between pairs of variables, but not necessarily between variances and covariances). This property of the variance-covariance matrix is present when the main diagonal elements of a set of multivariate data are equal to one another, which must also be the case for the off-diagonal elements. Compound symmetry is a stricter requirement than sphericity, and consequently if compound symmetry is met so is sphericity. As with homogeneity of variance, compound symmetry is rarely met exactly. Thus, a rule of thumb is that if observed covariances and variances are roughly equal, then one can assume that compound symmetry has not been violated. It is a condition that is important in the analysis of longitudinal data.
See Analysis of variance (ANOVA), Compound symmetry, Longitudinal studies, Mauchly test, Patterns of variances and covariances, Repeated measures analysis of variance, Sphericity, Sphericity assumption, Variance-covariance matrix