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Tests of Sphericity of Normal Distributions and the Analysis of Repeated Measures Designs

Published online by Cambridge University Press:  01 January 2025

A. P. Grieve
A. P. Grieve*
Affiliation:
CIBA-GEIGY AG
*
Requests for reprints should be sent to: A. P. Grieve, Mathematical Applications, CIBA-GEIGY AG, CH-4002 Basel, Switzerland.
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Abstract

The locally best invariant test statistic for testing sphericity of normal distributions is shown to be a simple function of the Box/Geisser-Greenhouse degrees of freedom correction factor in a repeated measures design. Because of this relationship it provides a more intuitively appealing test of the necessary and sufficient conditions for valid F-tests in repeated measures analysis of variance than the likelihood ratio test. The properties of the two tests are compared and tables of the critical values of the Box/Geisser-Greenhouse correction factor are given.

Keywords

Sphericity criterialocally best invariant testlikelihood ratio testrepeated measures designcircularity conditionsBox/Geisser-Greenhouse correction factor
Type
Original Paper
Information
Psychometrika , Volume 49 , Issue 2 , June 1984 , pp. 257 - 267
Copyright
Copyright © 1984 The Psychometric Society

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