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When can we Trust the F-Approximation of the Box-Test?

Published online by Cambridge University Press:  01 January 2025

Friedrich Foerster  and
Gerhard Stemmler
Friedrich Foerster*
Affiliation:
University of Freiburg, F.R.G.
Gerhard Stemmler
Affiliation:
University of Freiburg, F.R.G.
*
Requests for reprints should be sent to Friedrich Foerster, Forschungsgruppe Psychophysiologie, Universität Freiburg, Belfortstr. 20, D-7800 Freiburg, F.R.G.
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Abstract

Consider a multivariate context with p variates and k independent samples, each of size n. To test equality of the k population covariance matrices, the likelihood ratio test is commonly employed. Box's F-approximation to the null distribution of the test statistic can be used to compute p-values, if sample sizes are not too small. It is suggested to regard the F-approximation as accurate if the sample sizes n are greater than or equal to 1+0.0613p2 + 2.7265p -1.4182p0.5 + 0.235p1.4* In (k), for 5≤ p ≤30, k ≤20.

Keywords

Box-testF-approximationhomogeneity of covariance matrices

Information

Type
Notes And Comments
Information
Psychometrika , Volume 55 , Issue 4 , December 1990 , pp. 727 - 728
Copyright
Copyright © 1990 The Psychometric Society

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Footnotes

This research was supported by the Deutsche Forschungsgemeinschaft through Ste 405/2-1.

References

Box, G. E. P. (1949). A general distribution theory for a class of likelihood criteria. Biometrika, 36, 317–346.CrossRefGoogle ScholarPubMed
Korin, B. P. (1968). On the distribution of a statistic used for testing a covariance matrix. Biometrika, 55, 171–178.CrossRefGoogle ScholarPubMed
Tiku, M. L., & Balakrishnan, N. (1985). Testing the equality of variance-covariance matrices the robust way. Communications in Statistics—Theory and Methods, 13, 3033–3051.CrossRefGoogle Scholar