Comparing the utility of two procedures for admitting students to liberal arts: An application of decision-theoretic models

The present study applied a threshold utility model to assess the utility of adding a scholastic aptitude test to a selection system, based on achievement tests, designed to screen applicants for university studies in liberal arts. The threshold model was chosen because admitting students to liberal arts is characterized by an undefined quota. The present analysis avoided the exact estimation of the decision-maker's utility function and estimated the range of utility ratios (i.e., the ratio between the costs of false positives and false negatives) for which the additional predictor is useful. A nonselected sample of applicants, including a random group sampled from the applicants who would have been rejected under regular circumstances, was used to obtain the ranges of utility ratios for which the additional test would add to the expected utility under three definitions of success in academic studies. The results revealed that the gains associated with the additional information depend on the definition of success one wishes to adopt. If the goal is to recruit students who can achieve minimal passing grades, no gains are expected. If, however, the goal is to identify potentially excellent students, then the gains associated with the scholastic aptitude test are significant.