True or False: Sphericity implies that the differences between condition scores have equal variance.

True or False: Sphericity implies that the differences between condition scores have equal variance.

• A. True
• B. False
• C. Not specified
• D. Both true and false

Answer: (A)

Sphericity is about the pattern of how related measurements vary from one condition to another. It specifically requires that the variance of the difference scores between any pair of conditions is the same across all pairs. So if you look at the differences for every participant between condition A and B, between A and C, and between B and C, the spread (variance) of those difference scores should be equal. This equality of variances of the difference scores is what sphericity means, and it underpins the validity of the F tests in repeated measures ANOVA. If this equality holds, the statement is true; if it doesn’t, the results may be distorted and corrections are typically applied.

Sphericity is about the pattern of how related measurements vary from one condition to another. It specifically requires that the variance of the difference scores between any pair of conditions is the same across all pairs. So if you look at the differences for every participant between condition A and B, between A and C, and between B and C, the spread (variance) of those difference scores should be equal. This equality of variances of the difference scores is what sphericity means, and it underpins the validity of the F tests in repeated measures ANOVA. If this equality holds, the statement is true; if it doesn’t, the results may be distorted and corrections are typically applied.