A Step-Down Hierarchical Multiple Regression Analysis for Examining Hypotheses About Test Bias in Prediction

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Abstract
The problem of determining test bias in prediction using regression models is reexamined. Past ap proaches have made use of separate regression anal yses in each subgroup, moderated multiple regression analysis using subgroup coding, and hierarchical mul tiple regression strategies. Although it is agreed that hierarchical multiple regression analysis is preferable to either of the former methods, the approach pre sented here differs with respect to the hypothesis test ing procedure to be employed in such an analysis. This paper describes the difficulties in testing hy potheses about the existence of bias in prediction us ing step-up methods of analysis. Some shortcomings of previously recommended approaches for testing these hypotheses are discussed. Finally, a step-down hierarchical multiple regression procedure is recom mended. Analysis of real data illustrates the potential usefulness of the step-down procedure.