Sphericity describes which condition?

Sphericity describes which condition?

• A. The variances of the differences between all pairs of treatment conditions are equal
• B. The means of all treatment conditions are equal
• C. The variances across all treatment conditions are equal
• D. Observations are independent across time

Answer: (A)

Sphericity is about the variance of the differences between condition scores. When the same subjects are measured under several conditions, you compare how much a subject’s score changes from one condition to another. Sphericity means the spread (the variance) of these difference scores is the same for every pair of conditions. This uniformity in the variability of differences underpins the validity of the F-tests in repeated measures ANOVA; if it holds, the test's distribution behaves as expected. If sphericity is violated, the risk of false positives increases, and corrections like Greenhouse-Geisser or Huynh-Feldt adjust the degrees of freedom to restore accuracy. The statement about equal means or equal raw variances, or about independence across time, describes different ideas and does not capture what sphericity specifies.

Sphericity is about the variance of the differences between condition scores. When the same subjects are measured under several conditions, you compare how much a subject’s score changes from one condition to another. Sphericity means the spread (the variance) of these difference scores is the same for every pair of conditions. This uniformity in the variability of differences underpins the validity of the F-tests in repeated measures ANOVA; if it holds, the test's distribution behaves as expected. If sphericity is violated, the risk of false positives increases, and corrections like Greenhouse-Geisser or Huynh-Feldt adjust the degrees of freedom to restore accuracy. The statement about equal means or equal raw variances, or about independence across time, describes different ideas and does not capture what sphericity specifies.