The lower-bound estimate for sphericity uses which description of k?

The lower-bound estimate for sphericity uses which description of k?

• A. The number of predictor variables.
• B. The number of treatment conditions.
• C. The sample size.
• D. The degrees of freedom.

Answer: (B)

In repeated-measures analyses, sphericity concerns the equality of variances of the differences between every pair of treatment levels. The lower-bound estimate of sphericity is determined by k, the number of treatment conditions, because epsilon_lower is defined as 1 divided by (k minus 1). This means the value of the lower bound depends on how many treatment conditions there are. For two conditions, the lower bound is 1, so no correction is needed; as the number of conditions increases, the lower bound becomes smaller. Therefore, the description of k is specifically the number of treatment conditions.

In repeated-measures analyses, sphericity concerns the equality of variances of the differences between every pair of treatment levels. The lower-bound estimate of sphericity is determined by k, the number of treatment conditions, because epsilon_lower is defined as 1 divided by (k minus 1). This means the value of the lower bound depends on how many treatment conditions there are. For two conditions, the lower bound is 1, so no correction is needed; as the number of conditions increases, the lower bound becomes smaller. Therefore, the description of k is specifically the number of treatment conditions.