Computational Formulas for Multivariate Strength of Association from Approximate F and χ2Tests

There are numerous occasions, in conducting a priori, prospective power analyses for example, in which a measure of multivariate strength of association is desired but cannot be recovered from published research reports. Measures of multivariate strength of association, defined as a function of the eigenvalues of Q(-1) EQH or (QE + QH)(-1)QH, may be computed in conjunction with any of four multivariate test statistics. A large majority of research publications that perform multivariate analyses do not report a measure of strength of association, nor do they report sufficient information to compute multivariate measures of strength of association. Most manuscripts, however, do typically report F-test or χ(2) approximations with associated degrees of freedom. In this article we develop computational formulas for recovering measures of strength of association from approximate F and χ(2) tests associated with four multivariate test statistics.