Which term is defined as a statistic used when the sphericity assumption is violated?

• A. Epsilon
• B. Sphericity
• C. Mauchly's correction
• D. Eta squared

Answer: (A)

When you have a repeated measures design, sphericity means the variances of the differences between all pairs of conditions are equal. If this assumption is violated, the usual F tests can inflate Type I error, so you apply a correction factor to adjust the test. That correction uses a value called epsilon, which measures how far the data are from satisfying sphericity. Greenhouse-Geisser and Huynh-Feldt corrections are common implementations that rely on this epsilon value to adjust the degrees of freedom and obtain a valid p-value. Mauchly's W is the test statistic that checks whether sphericity holds, not the adjustment itself, and eta squared is an effect size measure. So the statistic used when sphericity is violated is epsilon.