What is the name of the statistic used when the sphericity assumption is violated?

• A. Epsilon
• B. Greenhouse-Geisser correction
• C. Mauchly's test
• D. Bonferroni correction

Answer: (A)

Sphericity is about the consistency of the variances of the differences between all pairs of related conditions. When this assumption doesn’t hold, the usual F tests in a repeated-measures design become too liberal, so we adjust the test with a correction factor. That correction relies on a value called epsilon, which quantifies how much the sphericity assumption is violated. The smaller the epsilon, the greater the violation and the stronger the adjustment needed. In practice, you’ll often see Greenhouse-Geisser epsilon or Huynh-Feldt epsilon used to modify the degrees of freedom of the F-statistic, making the test more conservative. Mauchly’s test, on the other hand, is used to test whether sphericity holds at all, not the correction itself, and Bonferroni correction is for adjusting for multiple comparisons rather than dealing with sphericity. So the name of the statistic used when sphericity is violated is epsilon.