The assumption of sphericity in repeated-measures designs: What it means and what to do when it is violated

• Main Author: Lane, David M.
• Format: Article
• Language: English
• Published: Université d'Ottawa 2016-09-01
• Series: Tutorials in Quantitative Methods for Psychology
• Subjects: analysis of variance; sphericity; epsilon correction; repeated measures
• Online Access: http://www.tqmp.org/RegularArticles/vol12-2/p114/p114.pdf

Violating the assumption of sphericity in repeated-measures analysis of variance leads to an inflated Type I error rate. The first portion of this article provides a thorough yet non-technical description of the sphericity assumption and explains why violations of sphericity lead to an inflated Type I error rate. The second portion describes univariate and multivariate approaches for addressing the problem of an inflated Type I error rate. The univariate approach involves estimating the parameter $\varepsilon $ that reflects the degree to which sphericity is violated and then reducimg the degrees of freedom by multiplying them by the estimate of $\varepsilon $. Two estimates of $\varepsilon $, $\mathaccentV{hat}05E\varepsilon $ and $\mathaccentV{tilde}07E\varepsilon $, have been recommended. The former has lower power than the latter whereas the latter fails to fully control the Type I error rate under some circumstances. The multivariate approach does not assume sphericity and therefore does not have an inflated Type I error rate. A decision tree for deciding among $\mathaccentV{hat}05E\varepsilon $, $\mathaccentV{tilde}07E\varepsilon $, and the multivariate approach based on a review of previously published simulations is presented along with a JavaScript program to automate the navigation of the decision tree.