A Bluffer’s Guide to ... Sphericity

The use of repeated measures, where the same subjects are tested under a number of conditions, has numerous practical and statistical benefits. For one thing it reduces the error variance caused by between-group individual differences, however, this reduction of error comes at a price because repeated measures designs potentially introduce covariation between experimental conditions (this is because the same people are used in each condition and so there is likely to be some consistency in their behaviour across conditions). In between-group ANOVA we have to assume that the groups we test are independent for the test to be accurate (Scariano & Davenport, 1987, have documented some of the consequences of violating this assumption). As such, the relationship between treatments in a repeated measures design creates problems with the accuracy of the test statistic. The purpose of this article is to explain, as simply as possible, the issues that arise in analysing repeated measures data with ANOVA: specifically, what is sphericity and why is it important? What is Sphericity?