Estimating the Classification Efficiency of a Test Battery

Abstract

Classification decisions relate to situations in which a battery of predictor tests is used to allocate subjects to a number of different assignment positions according to some prespecified quota proportions. In the case that the performance on the assignment criteria is continuously measurable, the efficiency of the predictor-based classification can be equated to the expected criterion score of the optimally assigned individuals: the allocation average. It is shown how a theorem proven by Brogden can be used to estimate the allocation average assuming that the predictor intercorrelations and validities are known and that the predictor variables have a joint multivariate normal distribution. Compared to previous analytical procedures to estimate the efficiency of a classification, the proposed solution is much more generally applicable in that it is no longer assumed that the predictor-based criterion estimates are both equally valid and equi-correlated and that all quota proportions are equal.