If sphericity is violated, which approach is used to adjust the analysis?

If sphericity is violated, which approach is used to adjust the analysis?

• A. Epsilon correction
• B. Bonferroni correction
• C. Welch correction
• D. Greenhouse–Geisser test

Answer: (A)

When sphericity is violated in repeated-measures ANOVA, the usual F-tests become too liberal because the assumption about equal variances of the differences between conditions is not met. The way to fix this is to adjust the analysis with an epsilon correction to the degrees of freedom. The epsilon factor, estimated from the data, scales the numerator and denominator degrees of freedom, making the F-test more conservative and producing a more accurate p-value. Epsilon can range from 0 to 1; 1 indicates perfect sphericity, while lower values indicate greater violation. This approach directly targets the issue by modifying the test to reflect the actual variance structure, and it underpins common implementations like Greenhouse-Geisser (and Huynh-Feldt). The other options don’t address sphericity: Bonferroni is for controlling error rate across multiple comparisons, Welch correction deals with unequal variances in independent designs, and Greenhouse-Geisser is a specific epsilon-based correction rather than the general concept. So, applying an epsilon correction captures the mechanism used to adjust for sphericity violations.

When sphericity is violated in repeated-measures ANOVA, the usual F-tests become too liberal because the assumption about equal variances of the differences between conditions is not met. The way to fix this is to adjust the analysis with an epsilon correction to the degrees of freedom. The epsilon factor, estimated from the data, scales the numerator and denominator degrees of freedom, making the F-test more conservative and producing a more accurate p-value. Epsilon can range from 0 to 1; 1 indicates perfect sphericity, while lower values indicate greater violation. This approach directly targets the issue by modifying the test to reflect the actual variance structure, and it underpins common implementations like Greenhouse-Geisser (and Huynh-Feldt). The other options don’t address sphericity: Bonferroni is for controlling error rate across multiple comparisons, Welch correction deals with unequal variances in independent designs, and Greenhouse-Geisser is a specific epsilon-based correction rather than the general concept. So, applying an epsilon correction captures the mechanism used to adjust for sphericity violations.