Repeated measures analysis of variance must display the variance pattern of sphericity for proper application (i.e., population variances of the differences between all possible pairs or levels of the independent variable are equal). This assumption is always met when there are only two levels of a repeated measures factor. Sphericity is both a necessary and sufficient (pre)condition for carrying out repeated measures F tests (assuming normality) whereas compound symmetry is a sufficient but not necessary condition. This distinction is not often recognized by statisticians.
See Analysis of variance (ANOVA), Compound symmetry, Greenhouse-Geisser epsilon, Hunyh-Feldt epsilon, Mauchly test, Mixed-effects models, Necessary sufficient conditions, Repeated measures analysis of variance, Sphericity