What does a significant result in Mauchley's test indicate?

A significant result in Mauchley's test indicates a violation of assumptions regarding sphericity. This statistical test is specifically designed to assess whether the assumption of sphericity has been met when conducting repeated measures analyses of variance (ANOVA).

Sphericity refers to the condition where the variances of the differences between all possible pairs of within-group levels are equal. When sphericity is violated, it can lead to inaccurate statistical inferences, as traditional repeated measures ANOVA relies on this assumption. A significant result in Mauchley's test suggests that the variances are not equal, indicating that the data does not meet the necessary criteria for sphericity, and adjustments or alternative statistical methods may be needed to produce valid results.

This understanding is key for researchers in the field of clinical psychology, especially when interpreting findings from repeated measures designs where the interpretation of the effects can be heavily influenced by the underlying assumptions of the statistical tests being applied.