What is the purpose of the Greenhouse-Geisser adjustment?

The Greenhouse-Geisser adjustment is specifically designed to address the violation of the sphericity assumption, which is a key requirement in repeated measures ANOVA. Sphericity refers to the condition where the variances of the differences between all combinations of related groups (levels) are equal. When this assumption is violated, it can lead to inflated Type I error rates, impacting the validity of statistical inferences.

The Greenhouse-Geisser adjustment modifies the degrees of freedom associated with the F-tests in ANOVA, making the analysis more robust and helping to maintain the integrity of the results even when sphericity cannot be assumed. By applying this correction, researchers can confidently interpret the results, knowing that they have accounted for potential biases arising from this assumption violation.

This method focuses on maintaining the statistical rigor of analyses involving repeated measures, which is crucial for clinical psychology research where repeated testing over time or across conditions is common.