Which statistical method is used to determine if variances of differences are not equal?

The choice of Mauchly's test is particularly relevant when examining the assumption of sphericity in repeated measures ANOVA, which involves determining whether the variances of the differences between conditions are equal. Sphericity is a specific case of the equality of variances across different groups or conditions when the structure of these groups is dependent on one another, such as in repeated measures designs.

Mauchly's test provides a statistical means to evaluate this assumption; if the test indicates that the assumption is violated, it suggests that the variances of the differences among the groups being compared are not equal. In such cases, adjustments or alternative statistical methods may be necessary to ensure valid results from the ANOVA.

The other methods mentioned—like the T-test, ANOVA, and Friedman’s test—serve different purposes or assumptions. A T-test focuses primarily on comparing means between two groups, ANOVA compares means across three or more groups but assumes homogeneity of variance without a specific test for equality of variances, and Friedman’s test is a non-parametric alternative to repeated measures ANOVA which does not directly assess equal variances. Therefore, Mauchly's test is specifically designed for assessing the equality of variances in contexts like repeated measures ANOVA