The selective efficiency of a test battery

In industrial acceptance sampling one frequently makes use of operating characteristic curves to describe the discriminating power of a particular sampling plan. Similarly, it is possible to demonstrate the selective efficiency of a test battery in terms of (a) the Applicant's Operating Characteristic (A.O.C.); (b) the Selector's Operating Characteristic (S.O.C.). The A.O.C. determines the chance of selection by means of a test for any given level of true ability. The S.O.C. connects functionally probability of success on the criterion with the predictor scores of a battery. For the case of a normal bivariate distribution the exact mathematical expressions of the OC curves are derived in terms of the correlation coefficient, the cut-off points and, and the predictor and criterion scoresX andY (in standard measures). The Efficiency IndexH is defined as the percentage of successful subjects gained by the use of a test battery, taking chance selection as a yardstick for comparison. Its optimum, for fixed and , is derived. The distribution law of the criterion scores of selectees is deduced and its first four moments are shown to depart little from normality for cases usually encountered in practice. A Quality-Gain diagram graphically illustrates the improvements secured. Another simple device, the Cost-Utility diagram, explains to management the full implications of selecting personnel by means of a test battery. Neither of the diagrams requires an understanding of the correlation coefficient. The confidence belt of the OC curves, the standard error of the mean criterion score of selectees and the standard error of the predicted number of successful applicants are determined. Finally, the full theory is applied in detail to a real test battery.This paper is the result of an investigation undertaken by the South African National Institute for Personnel Research, Johannesburg, and was completed at the Educational Testing Service, Princeton. The author wishes to thank these organizations for permission to publish this paper.