Mauchly's sphericity test

Mauchly's sphericity test is used to test the assumption of sphericity in within-subject ANOVAs. This assumption is that: the difference scores between each within-subject variable have similar variances.

If Mauchly's sphericity test is significant (p < .05), then sphericity should not be assumed and adjustments to the degrees of freedom should be made using an adjustment such as:
 * 1) Greenhouse-Geisser
 * 2) Huyn-Feldt
 * 3) Lower-bound

Greenhouse-Geisser is commonly used and recommended.