Epsilon is a statistic used to adjust for violations of which assumption?

Epsilon is a statistic used to adjust for violations of which assumption?

• A. Sphericity
• B. Normality
• C. Independence
• D. Homogeneity of variance

Answer: (A)

Sphericity is the aspect being addressed. In repeated-measures designs, the differences between every pair of related treatment levels should have the same variance. If this assumption is violated, the standard F tests can become too liberal, inflating the chance of a false positive. Epsilon is the correction factor used to adjust the degrees of freedom of the F statistic to account for that violation. It ranges from 0 to 1: when sphericity holds, epsilon is about 1 and no adjustment is needed; when sphericity is violated, epsilon is less than 1, which lowers the degrees of freedom and yields a more conservative p-value. This correction specifically targets sphericity and not normality, independence, or homogeneity of variance across groups.

Sphericity is the aspect being addressed. In repeated-measures designs, the differences between every pair of related treatment levels should have the same variance. If this assumption is violated, the standard F tests can become too liberal, inflating the chance of a false positive. Epsilon is the correction factor used to adjust the degrees of freedom of the F statistic to account for that violation. It ranges from 0 to 1: when sphericity holds, epsilon is about 1 and no adjustment is needed; when sphericity is violated, epsilon is less than 1, which lowers the degrees of freedom and yields a more conservative p-value. This correction specifically targets sphericity and not normality, independence, or homogeneity of variance across groups.