A New Coefficient: Application to Biserial Correlation and to Estimation of Selective Efficiency

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Abstract
A coefficient of selective efficiency is proposed which can be usefully applied to selection problems involving the evaluation of the validity of (1) dichotomous predictors and (2) continuous predictors at a particular or at successive points of cut. Previously the author has shown that the product-moment correlation can be interpreted as a direct index of selective efficiency if the distribution forms of the criterion and the predictor are similar and the regression of the criterion on the predictor is linear. The coefficient proposed in the present article may be employed to evaluate selective efficiency of a continuous predictor at particular points of cut even when these assumptions are not tenable or are not applicable. It also is demonstrated that the proposed coefficient of selective efficiency may—with somewhat simpler and more generally applicable assumptions than those required in deriving the conventional formula—be employed as a substitute for the biserial correlation coefficient.

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