The Greenhouse-Geisser estimate is used to adjust degrees of freedom in which analysis?

• A. To correct for violated normality.
• B. To adjust for nonlinearity.
• C. To correct for departures from sphericity in repeated-measures ANOVA.
• D. To fix heteroscedasticity.

Answer: (C)

This is about sphericity in repeated-measures ANOVA and how the Greenhouse-Geisser adjustment works. Sphericity means that the variances of the differences between all pairs of levels of the within-subjects factor are equal. When this assumption is violated, the F tests can become too liberal, inflating the chance of finding a significant effect by mistake. The Greenhouse-Geisser method estimates an epsilon value from the data and multiplies the intended degrees of freedom for the effects and their error terms by this epsilon. Since epsilon is between 0 and 1 (and equals 1 when sphericity holds), the test becomes more conservative, reducing the risk of Type I error. So this adjustment is specifically used to correct for departures from sphericity in repeated-measures ANOVA, not for issues of normality, nonlinearity, or heteroscedasticity.