It is argued that analyses of subgroup differences utilizing a bivariate correlation strategy do not provide an adequate examination of test fairness. An analysis of differential prediction, which involves slopes and intercepts of regression lines results in more complete coverage of the test fairness issue, since the overall regression line determines the way in which a test is used for prediction. While subgroup correlation coefficients yield information concerning the slopes and intercepts, means and standard deviations must also be examined. A moderated multiple regression strategy is recommended as an alternative to separate analyses by subgroups. An ordered stepup regression procedure is presented which is more encompassing than the bivariate strategies, while avoiding inherent problems associated with subgroup coding in multiple regression.