Sphericity is one of the assumptions underlying repeated measures analysis of variance. Box discovered a parameter called epsilon that reduces the degrees of freedom to adjust for violation of sphericity. Because the routine use of the epsilon-adjusted F-test does not guarantee the most efficient test for repeated-measures treatment effects, a preliminary test of the sphericity assumption appears to be prudent. After addressing the problems with the existing sphericity tests, the use of empirical critical values of Box's epsilon as criteria for testing sphericity is proposed. First, tables of empirical critical values of Box's epsilon were generated. Then, the Type I error rate of the proposed empirical epsilon test was examined. Finally, the relative power of the empirical epsilon test was compared with Mauchly's test, the most widely applied sphericity test, under normal population conditions with repeated measures designs
