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Abstract

Two measures of association between sets of variables X and Y have been proposed for set correlation, R_Y,X² as a proportion of generalized variance and T_Y,X² as a proportion of additive variance. Because these measures are strongly positively biased, approximate expected values and estimators of these measures are derived and checked by means of a Monte Carlo study. It is noted that sample values are subject to more "shrinkage" than is the multiple R², and that, therefore, it is desirable to determine routinely the estimators' values. It is recommended that as a rule of thumb, the ratio of sample size to the product of the numbers of variables in the two sets should be at least 20, and preferably 25 or 30.

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Estimators for Two Measures of Association for Set Correlation

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