What does sphericity refer to in the context of a one-way within groups ANOVA?

Sphericity specifically refers to the condition in a repeated measures ANOVA where the variances of the differences between all combinations of related groups are equal. This concept is critical because when the assumption of sphericity is violated, it can lead to incorrect conclusions and inflated Type I error rates.

In a one-way within groups ANOVA, if the assumption of sphericity is met, it indicates that the variance within the groups is uniform, which allows for accurate F-tests and significance testing. If sphericity is violated, adjustments (such as using Greenhouse-Geisser or Huynh-Feldt corrections) may be necessary to ensure that the statistical analyses yield valid results. This is why understanding sphericity is crucial for interpreting the outcomes of a within-subjects design properly.