In repeated-measures ANOVA, the assumption that the variances of the differences are equal is called?

In repeated-measures ANOVA, the assumption that the variances of the differences are equal is called?

• A. Normality
• B. Homogeneity of variances
• C. Sphericity
• D. Linearity

Answer: (C)

In repeated-measures ANOVA, sphericity is the assumption that the variances of the difference scores between any pair of related conditions are equal. This means the spread of how scores differ from one condition to another is the same no matter which pair you compare. Why this matters is that when sphericity holds, the F-statistic used to test for differences across conditions has the correct distribution under the null hypothesis, giving valid p-values. If sphericity is violated, the test can become too liberal, inflating the risk of a false-positive finding. In practice, you test for this with Mauchly’s test and, if violated, apply corrections such as Greenhouse-Geisser or Huynh-Feldt to adjust the degrees of freedom and obtain accurate inferences. Normality refers to the residuals being normally distributed, not the equality of difference scores. Homogeneity of variances concerns equal variances across groups in designs with independent groups, not the equal variances of differences. Linearity is about the relationship between variables being linear, which is a separate consideration.

In repeated-measures ANOVA, sphericity is the assumption that the variances of the difference scores between any pair of related conditions are equal. This means the spread of how scores differ from one condition to another is the same no matter which pair you compare. Why this matters is that when sphericity holds, the F-statistic used to test for differences across conditions has the correct distribution under the null hypothesis, giving valid p-values. If sphericity is violated, the test can become too liberal, inflating the risk of a false-positive finding. In practice, you test for this with Mauchly’s test and, if violated, apply corrections such as Greenhouse-Geisser or Huynh-Feldt to adjust the degrees of freedom and obtain accurate inferences.

Normality refers to the residuals being normally distributed, not the equality of difference scores. Homogeneity of variances concerns equal variances across groups in designs with independent groups, not the equal variances of differences. Linearity is about the relationship between variables being linear, which is a separate consideration.