Sphericity is a concern for which analysis?

• A. Repeated measures ANOVA
• B. Between-subjects ANOVA
• C. Independent samples t-test
• D. Chi-square test

Answer: (A)

Sphericity matters in repeated measures designs where the same participants are tested under several conditions. When the within-subjects factor has more than two levels, the test assumes that the variances of the differences between all pairs of condition levels are equal. If this assumption is violated, the F-tests in a repeated measures analysis can be too liberal, inflating the chance of a false-positive result. In practice, we check sphericity with tests like Mauchly’s and, if needed, apply corrections such as Greenhouse-Geisser or Huynh-Feldt to adjust the degrees of freedom and obtain accurate p-values.

The other tests don’t involve the same repeated-measures structure: between-subjects ANOVA compares independent groups and doesn’t entail within-subject correlations, so sphericity isn’t relevant. The independent samples t-test also compares two independent groups without repeated measures, and the chi-square test handles categorical data, not continuous repeated-measures data. Therefore, the concern about sphericity specifically arises with the repeated measures ANOVA.