and A ij is the cofactor of a,j in the determinant A I = j a1 ijj At a later date Wilks (1932) defined a generalized variance and found the appropriate A-criteria for testing certain hypotheses concerning the means, variances, and covariances of k normal multivariate populations from which k independent samples have been drawn. These criteria were developed more fully by Pearson and Wilks in a subsequent paper (1933) for the case of two variates, but though the sampling distributions obtained were in certain cases relatively simple the arithmetical calculations required for practical application were, in general, not of a very simple nature.* In this paper we shall find a quantity which may be regarded as a generalization of Fisher's z and which provides a test suitable for dealing with certain generalized analysis of variance problems, having the advantage of being easy to apply.