Mauchly's test assesses which assumption and what happens if significant?

• A. A test of normality of the data distribution.
• B. It tests the assumption of sphericity; if significant, correction to the degrees of freedom is applied.
• C. A test comparing variances across groups.
• D. A test comparing means across time.

Answer: (B)

Mauchly's test checks sphericity, the assumption that the variances of the differences between all pairs of related conditions are equal. In a repeated-measures design with more than two levels, this assumption helps ensure the usual F-tests for within-subject effects have accurate Type I error rates.

If the test is significant, sphericity is violated, so the standard F-tests in the repeated-measures ANOVA become too liberal. To address this, you apply a correction to the degrees of freedom—most commonly Greenhouse-Geisser or Huynh-Feldt corrections. These adjustments reduce the degrees of freedom (via an epsilon estimate), making the test more conservative and maintaining a valid Type I error rate. In some cases, especially with severe violations, a multivariate approach that does not assume sphericity can be used instead.

Remember, this is about the pattern of differences between conditions in a within-subjects design, not about normality or about comparing variances or means in other contexts.