The variances of the differences between all pairs of treatment conditions being similar is an aspect of what concept?

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

Answer: (A)

Sphericity is the assumption in repeated-measures designs that the variances of the differences between every pair of treatment levels are equal. In other words, if you have several conditions, the variability of the difference scores for each pair (condition 1 minus condition 2, condition 1 minus condition 3, condition 2 minus condition 3, and so on) should be roughly the same. This equal variability ensures the covariance structure of the repeated measures supports the F-tests used to assess effects.

If sphericity holds, the standard repeated-measures ANOVA tests have valid Type I error rates. When it’s violated, the test statistics can be distorted, which is why corrections like Greenhouse-Geisser or Huynh-Feldt are applied to adjust the degrees of freedom.

This concept is distinct from homogeneity of variance (equal variances across independent groups, not about pairwise differences in repeated measures), normality (the distribution of residuals), and linearity (a straight-line relationship between variables).