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A Priori Tests in Repeated Measures Designs: Effects of Nonsphericity

Published online by Cambridge University Press:  01 January 2025

Robert J. Boik
Robert J. Boik*
Affiliation:
Temple University
*
Reprints are available from Robert J, Boik, Department of Statistics, Temple University, Philadelphia, PA 19122.
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Abstract

The validity conditions for univariate repeated measures designs are described. Attention is focused on the sphericity requirement. For a v degree of freedom family of comparisons among the repeated measures, sphericity exists when all contrasts contained in the v 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 ≤ ε < 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.

Keywords

repeated measures designssphericity criterionmultiple contrasts
Type
Original Paper
Information
Psychometrika , Volume 46 , Issue 3 , September 1981 , pp. 241 - 255
Copyright
Copyright © 1981 The Psychometric Society

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Footnotes

Appreciation is extended to Milton Parnes for his insightful assistance.

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