Which of the following estimates measures departure from sphericity and is used to correct degrees of freedom of F-statistics, with a maximum value of 1 when sphericity is perfect?

• A. Greenhouse-Geisser estimate
• B. Huynh-Feldt estimate
• C. Box's M
• D. Mauchly's test

Answer: (B)

In repeated-measures designs, you adjust the F tests when sphericity (equal variances of the pairwise differences) is violated, because violations inflate Type I error. The Huynh-Feldt estimate is one way to quantify how far from sphericity you are and to scale the degrees of freedom of the F statistics accordingly. When sphericity is perfect, this estimate equals 1, so no correction is needed. It’s often favored because it is less conservative than the Greenhouse-Geisser correction, providing more power while still protecting against inflated error rates. By contrast, Mauchly's test checks whether sphericity holds (a diagnostic, not a correction), and Box's M tests equality of covariance matrices in MANOVA, not sphericity in repeated measures.