Presents and evaluates three estimators for "p," the proportion of success in predicting variable "Y," with nominal measurement, using predictor variables that also have nominal measurement. Showed through simulation that one estimator is always biased upward, and then proposed another possible estimator that involves using…

A theorem is presented that describes conditions under which measurement invariance is consistent with predictive invariance for the linear case. These two forms of invariance are shown to be inconsistent under realistic conditions, and the duality is illustrated with simulated data. Implications for group differences research are discussed. (SLD)