In applied research designed to address conceptual as well as program and policy formulation issues, it is often important to assess the bias present in estimators of association and prediction stemming from the use of multivariate analytical procedures. However, the theoretic sampling distributions of these estimators are often unknown in applied research contexts because of their complexity and the inability to satisfy highly restrictive assumptions. Consequently, in many instances the amounts of bias and subsequent bias corrections have eluded analytic determination. This paper presents and illustrates a method for approximating the amounts of bias in estimators having complex sampling distributions that are influenced by a variety of properties typical of applied research data. The method, which appears to have broad applicability to many multivariate procedures, is illustrated in the context of redundancy analysis.
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