I'm running a repeated measures ANOVA and I've read that one important assumption is the compound symmetry. I've read a litte and I just understood the difference between compound symmetry and sphericity. I've also read that compound symmetry implies sphericity but not the opposite. The thing is I remember in Uni, we used to run Mauchly's test for spherecity when doing repeated measures.
Why did we use to do that if we're really interested in the compound symmetry assumption ? Are the two assumptions equivalent ?