On Wilk's multivariate generalization of the correlation ratio

Abstract

SUMMARY 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.