Which choice best captures the idea of sphericity?

Which choice best captures the idea of sphericity?

• A. The variances of the differences between condition scores are equal
• B. The means across conditions are equal
• C. The variances of condition scores are equal
• D. The data are normally distributed

Answer: (A)

Sphericity is about the variability of difference scores between condition levels in a repeated-measures design. For several related conditions, you look at how much each participant’s scores differ when you compare every pair of conditions. The key idea is that the variance of these difference scores should be the same across all pairs of conditions. For example, with three conditions, the spread (variance) of the difference between condition 1 and 2 should be about the same as the spread between 1 and 3 and between 2 and 3. When this holds, the repeated-measures F-tests are valid. Other ideas in the options aren’t what sphericity describes. Mean differences across conditions relate to whether there’s an overall effect of condition, not the consistency of difference variances. Equal variances of the condition scores themselves refer to homogeneity of variances, not to the variances of difference scores. Normal distribution concerns the shape of the data, not the relationship between difference scores across conditions. If sphericity is violated, researchers typically use corrections (like Greenhouse-Geisser or Huynh-Feldt) to adjust the degrees of freedom and keep the test valid.

Sphericity is about the variability of difference scores between condition levels in a repeated-measures design. For several related conditions, you look at how much each participant’s scores differ when you compare every pair of conditions. The key idea is that the variance of these difference scores should be the same across all pairs of conditions. For example, with three conditions, the spread (variance) of the difference between condition 1 and 2 should be about the same as the spread between 1 and 3 and between 2 and 3. When this holds, the repeated-measures F-tests are valid.

Other ideas in the options aren’t what sphericity describes. Mean differences across conditions relate to whether there’s an overall effect of condition, not the consistency of difference variances. Equal variances of the condition scores themselves refer to homogeneity of variances, not to the variances of difference scores. Normal distribution concerns the shape of the data, not the relationship between difference scores across conditions.

If sphericity is violated, researchers typically use corrections (like Greenhouse-Geisser or Huynh-Feldt) to adjust the degrees of freedom and keep the test valid.