Mauchly's sphericity test

Mauchly's sphericity test is a statistical test used to validate repeated measures factor ANOVA. SPSS includes it automatically as part of its ANOVA with a repeated measures factor (RMF) output tables. The test was introduced by ENIAC co-inventor John Mauchly in 1940.

What is sphericity?
Sphericity is an assumption of an ANOVA with a RMF and violations of this assumption can invalidate the analysis conclusions. Sphericity relates to the equality of the variances of the differences between levels of the repeated measures factor. Sphericity requires that the variances for each set of difference scores are equal.

Interpreting the Mauchly's sphericity test
When the significance level of the Mauchly’s test is ≤ 0.05 then sphericity cannot be assumed.

Violations of sphericity
When conducting an ANOVA with a RMF SPSS will automatically generate three corrections for violations of sphericity. These are the Greenhouse-Geisser, the Huynh-Feldt and the Lower-bound corrections. To correct for sphericity these corrections alter the degrees of freedom, thereby altering the significance value of the F-ratio. There are different opinions about the best correction to apply. A good rule of thumb is to use the Greenhouse-Geisser estimate unless it leads to a different conclusion from the other two. Another option when sphericity is violated is to use the multivariate test (also automatically provided by SPSS). However, multivariate tests can be less powerful than their univariate counterparts.