Sphericity is an assumed characteristic of data analyzed in repeated measures analysis of variance (ANOVA). Sphericity refers to the equality of variances of the differences between treatment conditions. Violations of the sphericity assumption do not invalidate a repeated measures ANOVA but do necessitate using corrected F ratios. To illustrate sphericity, imagine you were conducting a study administering placebo, a low dose of alcohol, and a high dose of alcohol to young adults and measuring subjective ratings of alcohol intoxication. You wish to analyze your results using a repeated measures ANOVA, but to do so you must check whether the sphericity assumption is violated. Sphericity can be measured by the following:

  • Comparing each pair of treatment levels
  • Calculating the differences between each pair of scores
  • Calculating the variances ...
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