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Biometrika 1976 63(1):59-67; doi:10.1093/biomet/63.1.59
© 1976 by Biometrika Trust
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On Wilk's multivariate generalization of the correlation ratio

M. L. HART and A. H. MONEY

Department of Mathematical Statistics, University of Cape Town

Wilks's (1932) generalization of the correlation ratio |I–L|, has been proposed as an alternative test statistic to |L|, Wilks's likelihood ratio criterion for multivariate analysis of variance. In this paper the method of convolutions is used to derive exact central percentiles and noncentral linear percentiles and powers of |I–L|. The suitability of this statistic is discussed, and it is shown by exact power comparisons to be inferior to |L|. Selected tables are included.

Key Words: Exact percentile • Generalization of correlation ratio • Method of convolution • Non-central linear distribution • Power comparison • Wilks's statistic


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