Which statement best summarizes the relationship between epsilon and sphericity from the source text?

• A. Epsilon is the statistic used when sphericity is violated to adjust degrees of freedom
• B. Sphericity is the statistic used to adjust epsilon
• C. They are unrelated concepts
• D. Epsilon measures central tendency in spherical data

Answer: (A)

In repeated measures analysis, sphericity is the assumption that the variances of the differences between all pairs of related groups are equal. When this assumption is violated, the F-tests can become too liberal, so a correction is needed. The epsilon correction factor (such as Greenhouse-Geisser or Huynh-Feldt epsilon) is the statistic applied to adjust the degrees of freedom of the F-test, stabilizing the test and controlling Type I error. So the statement that epsilon is the statistic used when sphericity is violated to adjust degrees of freedom best describes their relationship. Sphericity is not itself a statistic but an assumption, and epsilon does not measure central tendency or operate as a separate statistic to adjust epsilon.