Some Properties of Two Measures of Multivariate Association

Two kinds of measures of multivariate association, based on Wilks' Λ and the Bartlett-Nanda-Pillai trace criterion V , respectively, are compared in terms of properties of the univariate R 2 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 a symmetric index based on Λ allows generalization of the multiplicative decomposition of R 2 in terms of squared partial correlations, but not the additive decomposition in terms of squared semipartial correlations, while the reverse is true for an asymmetric index based on V .