Investigating Group Differences in Criterion-Related Patterns

• In Event: Profile Analysis via Multivariate Statistics for Continuous and Categorical Data

Abstract

Objective: Davison and Davenport (2002) outlined a two-stage, multiple-regression procedure for identifying a pattern of predictor scores that distinguishes between those with high and low scores on a criterion variable. The present paper will extend earlier work to a test of the null hypothesis that the criterion-related pattern is the same in two or more groups.

Theoretical framework: In Davison and Davenport (2002), the first step in the regression is built around the model Y’p = ΣvbvXpv + a (1), where Y’p is the predicted criterion score for person p, bv is the regression weight for variable v, Xpv is a predictor variable, and a is the intercept. Step 1 involves using least squares regression weights to estimate V contrast coefficients describing the criterion-related pattern. Step 2 involves computing two new predictor variables: level Xbarp = (1/V) ΣvXpv, the mean predictor score for person p, and pattern Covp = (1/V) Σv (bv-bvar), a measure of the match between person p’s score profile of person p and the criterion-related pattern. By regressing the level and the pattern onto the criterion, one can estimate the variance accounted for by the pattern and the variance that pattern contributes over and above the level.

Methods: To test the hypothesis that the criterion-related pattern is the same for two groups, one must replace equation 1 with the usual moderated regression equation: Y’pg = ΣvbvXpv + ΣvWvGXpv +a, where Y’pg is the predicted value for person p in group G =1, 0 and Wv is the regression weight for the moderated variable v. For each person, one must now compute three new variables: level Xbarp , pattern Covp, and a second profile match statistic Covpw = (1/V) ΣvXpv(Wv – Wbar). By fitting various models and submodels of the following equation, one can test various hypothesis, but the key one is the hypothesis that the criterion-related pattern is the same in groups G = 1,0, which can be tested by comparing the variance accounted for by models with and without the last term: Y’p = b1Xbarp + b2GXbarp + b3Covp + b4Covpw + a.

Data Source: The method will be illustrated with data from the Beyond High School Study of the National Center for Educational Statistics. To simplify illustrative computations, we will use a profile composed of only two elements, the SAT verbal and the SAT quantitative tests. The criterion will be college GPA.

Results. We will test the hypothesis that the criterion-related profile differs for STEM majors and non-STEM majors. It is predicted that the criterion-related pattern for STEM majors will be Quantitative > Verbal whereas for non-STEM majors, it will be Verbal > Quantitative.

Scholarly significance. A new method for studying profile patterns will be presented. Results may indicate a method of improving GPA prediction by incorporating information about major. Results may also indicate that SAT patterns provide students with information about majors in which they can expect greater success.

Authors

• Mark L. Davison, University of Minnesota

• Ernest C. Davenport, Jr., University of Minnesota