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

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Abstract
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)-1QH, 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 χ2 approximations with associated degrees of freedom. In this article we develop computational formulas for recovering measures of strength of association from approximate F and χ2 tests associated with four multivariate test statistics.

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