Some properties of two measures of multivariate association

Two kinds of measures of multivariate association, based on Wilks' and the Bartlett-Nanda-Pillai trace criterionV, respectively, are compared in terms of properties of the univariateR² which they generalize. A unified set of derivations of the properties is provided which are self-contained and not restricted to decompositions in canonical variates. One conclusion is that asymmetric index based on allows generalization of the multiplicative decomposition ofR² in terms of squared partial correlations, but not the additive decomposition in terms of squared semipartial correlations, while the reverse is true for anasymmetric index based onV.We are indebted to Jos M. F. ten Berge for some fruitful discussions.