Which corrections are used to adjust degrees of freedom when sphericity is violated in repeated-measures ANOVA?

Which corrections are used to adjust degrees of freedom when sphericity is violated in repeated-measures ANOVA?

• A. Bonferroni and Holm corrections
• B. Fisher's LSD correction
• C. Greenhouse-Geisser and Huynh-Feldt corrections
• D. Tukey's HSD

Answer: (C)

Sphericity is about the consistency of variances of the differences between related groups in a repeated-measures design. When this assumption is violated, the F-test can become too liberal, so we adjust the degrees of freedom to control the Type I error rate. The standard corrections are Greenhouse-Geisser and Huynh-Feldt. Both estimate an epsilon (ranging from 0 to 1) that reflects how much sphericity is violated. The corrected test then uses distorted degrees of freedom: the effect’s df and the error df are multiplied by epsilon. This makes the test more conservative and provides a more accurate p-value under violation of sphericity. Greenhouse-Geisser tends to be the more conservative option, especially when the violation is strong (small epsilon). Huynh-Feldt is less conservative and can be preferable when epsilon is not too small, often used when epsilon is reasonably large (and some guidelines suggest reporting both or preferring Huynh-Feldt when appropriate). Other listed corrections address multiple comparisons or post hoc tests rather than adjusting degrees of freedom for sphericity in a repeated-measures ANOVA, so they don’t fit the situation described.

Sphericity is about the consistency of variances of the differences between related groups in a repeated-measures design. When this assumption is violated, the F-test can become too liberal, so we adjust the degrees of freedom to control the Type I error rate.

The standard corrections are Greenhouse-Geisser and Huynh-Feldt. Both estimate an epsilon (ranging from 0 to 1) that reflects how much sphericity is violated. The corrected test then uses distorted degrees of freedom: the effect’s df and the error df are multiplied by epsilon. This makes the test more conservative and provides a more accurate p-value under violation of sphericity.

Greenhouse-Geisser tends to be the more conservative option, especially when the violation is strong (small epsilon). Huynh-Feldt is less conservative and can be preferable when epsilon is not too small, often used when epsilon is reasonably large (and some guidelines suggest reporting both or preferring Huynh-Feldt when appropriate).

Other listed corrections address multiple comparisons or post hoc tests rather than adjusting degrees of freedom for sphericity in a repeated-measures ANOVA, so they don’t fit the situation described.