A Comparison of Three Models for Determining Test Fairness

There are three prominent models of test fairness in the dichotomous situation: (a) Thorndike's Constant Ratio model (the ratio of the proportion successful to the proportion selected should be equal for the majority and the minority group); (b) Darlington's Conditional Probability model (the probability of selection, given that an individual is successful, should be equal for both groups); and (c) Einhorn and Bass' Equal Probability model (the probability of success, given that an individual is selected, should be equal for both groups). The present study explored, using a Monte Carlo technique, the robustness of these models to divergent sample size. This technique allows the generation of normally distributed variables of known means, standard deviations, and intercorrelations. Results indicated that all three models were equally able to identify test fairness under the conditions specified in the present study. The choice of model to use when evaluating test fairness must remain a subjective one based on the fairness goals of the testing agency and further definition of the test fairness by Federal guidelines.