A TWO‐STAGE DECISION APPROACH TO THE SELECTION PROBLEM
Donald A. Rock, John L. Barone, Robert F. Boldt · British Journal of Mathematical and Statistical Psychology · 1972
A mathematical solution to the two‐stage selection problem was developed which only requires predictor criterion intercorrelations and selection ratio information. Cutting scores on the first stage test are so determined that some individuals are ( a ) accepted after the first stage, ( b ) rejected after the first stage, ( c ) decision withheld, i.e. the decision to accept or reject is postponed until the second stage. The upper and lower cutting scores from stage one, z 1 ″ and z 1 ′ respectively, and the cutting score at the second stage z 2.1 , where z 2.1 = F ( z 1 ), and z 1 ’ ≤ z 1 ≤ z 1 ” are located such that the expected value on the criterion for accepted applicants is maximized subject to two constraints. The two constraints are the selection ratio and a function of the independent contribution of the second‐stage test. Theoretical solutions developed on the computer suggest that a considerable amount of testing time may be saved with little or no decrease in the validity of the selection procedure for all values of the selection ratios.