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ngton I. The Differential PredictionProblem Methods for developing a test battery to predict success in a single specified type of activity are well known. These methods are concerned primarily with selecting tests to predict a single criterion. But in most practical situations we are not concerned with predicting success in just a single activity or assignment. In the military service it is not a question of predicting the success of a prospective recruit in just a single specialty. Rather, the military services are concerned with predicting success in all or most of their numerous (military occupational) specialties. In an industrial organization, it is not enough to have procedures for predicting success in merely a single type of job. It is desirable to have procedures for predicting success in as many of the different jobs existing in the company as possible.Similarly in our institutions of higher education it is not enough for an entering student to know simply whether he will or 1 This research was carried out under Contract between the University of Washi ngton and the Office of Naval Research. The data used to illustrate the technique were provided by Professor August Dvorak. Most of the computations were carried out by Robert Dear and William Meredith. Charlotte MacEwan al so assi sted with the computations and assumed major editorial responsibility for the preparation of the manuscript. Much credit is due the typist, Eleanor Green. Supervision of both computational and editorial activities was provided by William Cl emans. To each of these able contributors I am deepl y grateful.

In certain situations it is important to obtain as many measures as possible, all presumably measuring the same function, for each of a group of persons. In general the number and source of the measures may vary from one member of the group to another. We take the mean of the measures for each person as the best estimate of the function for that person. The conventional formulas can not be used to determine the reliability of a set of means so obtained. A formula is developed which provides a unique estimate of the reliability of such a set of means. The formula is more general than some of the well-known reliability formulas, so that these formulas are shown to be special cases of the more general formula.