TESTING FOR FAIRNESS WITH A MODERATED MULTIPLE REGRESSION STRATEGY: AN ALTERNATIVE TO DIFFERENTIAL ANALYSIS¹

Abstract

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.

Prediction of 4-year college student performance using cognitive and noncognitive predictors and the impact on demographic status of admitted students.

“…Step 2), and the set of three product terms (Step 3) following Bartlett et al (1978). This was done separately for each of the three minority groups.…”

“…To answer this question, we used the procedure described originally by Cleary (1968). We regressed the cumulative college GPA on the outcomes of the three components of the admissions decision plus race plus the products of the predictors and race for each minority group separately using an analysis outlined by Bartlett, Bobko, Mosier, and Hannan (1978). Thus, three regression analyses were conducted in each of which the prediction of GPA for one minority group (i.e., African Americans, Hispanics, or Asians) was compared with that for White students.…”

Documentation of Muscularly Demanding Job Tasks and Validation of an Occupational Strength Test Battery (STB)

“…A comparison was made among three kinds of coefficients: simple correlations (one component of the STB and one criterion test), a unit-weighted composite (two or more STB components and a criterion test) and multiple regression application (optimal weighting of two or more STB components and one criterion test). For a determination of selection fairness between the regression lines of the gender subgroups, the multiple regression analysis procedures of Bartlett, Bobko, Mosier, and Hannan (1978) were employed. Extensive work was also undertaken to develop impact analysis and discount procedures.…”

The Process of Physical Fitness Standards Development

“…the validity coefficients or regression lines are similar across subgroups and 2. the test and/or criterion scores differ across subgroups (Bartlett, Bobko, Mosier, & Hannan, 1978;Kerlinger & Pedhazur, 1973).…”

“…The statistical procedure used for this analysis is differential prediction in which a moderated multiple regression analysis is employed to examine whether the validity coefficients (slope) and test a n d o r criterion mean scores (intercept) across subgroups differ from the overall regression equation (Bartlett et al, 1978;Kerlinger & Pedhazur, 1973). In the physical test domain, test fairness analyses are typically used to determine whether a test is biased in relation to gender, ethnic, and age groups.…”