Grasple Repeated Measures ANOVA - the sphericity assumption

6 important questions on Grasple Repeated Measures ANOVA - the sphericity assumption

Assumptions for repeated measures ANOVA (4)

  • Measurement levels: the independent variables are categorical, the dependent variable is continuous
  • No outliers on the dependent variable
  • Normality: the residuals are normally distributed for every group
  • Sphericity: the variances of all difference scores are equal.

Checking for sphericity can be done in two ways:

  1. You can manually compute the difference scores and their variances. This is nice for eyeballing if they are about the same, but in this case somewhat cumbersome (=extra work).
  2. You can check for sphericity using Mauchly's Test.

Mauchly's Test for Sphericity a significant p-value means?

p < .001 which means you reject the Null-hypothesis that the variances of the difference scores are equal. This means the assumption of sphericity is violated.
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If the assumption of sphericity is not met, there are several options:

  • Greenhouse-Geisser correction
  • Huynh-Feldt correction
  • MANOVA on the difference scores

What does the Greenhouse-Geisser and Huynh-Feldt corrections correct for?

the degrees of freedom in the repeated measures analysis.

Rule of thumb Epsilson

A rule of thumb is that epsilon values <.75 are considered severe violations, and this is where you apply the stricter Greenhouse-Geisser correction.
For values above .75, you can use the Huynh-Feldt correction.
You probably noticed that there are three Epsilons. You can simply look at the largest one.

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