A priori tests in repeated measures designs: Effects of nonsphericity

The validity conditions for univariate repeated measures designs are described. Attention is focused on the sphericity requirement. For av degree of freedom family of comparisons among the repeated measures, sphericity exists when all contrasts contained in thev dimensional space have equal variances. Under nonsphericity, upper and lower bounds on test size and power of a priori, repeated measures,F tests are derived. The effects of nonsphericity are illustrated by means of a set of charts. The charts reveal that small departures from sphericity (.97 <1.00) can seriously affect test size and power. It is recommended that separate rather than pooled error term procedures be routinely used to test a priori hypotheses.Appreciation is extended to Milton Parnes for his insightful assistance.