SAT predicts GPA better for high ability subjects: Implications for Spearman’s Law of Diminishing Returns

Abstract

This research examined the predictive validity of the SAT (formerly, the Scholastic Aptitude Test) for high and low ability groups. SAT scores and college GPAs were obtained from the 1997 National Longitudinal Survey of Youth. Subjects were classified as high or low ability by g factor scores from the Armed Services Vocational Aptitude Battery. SAT correlations with GPA were higher for high than low ability subjects. SAT g loadings (i.e., SAT correlations with g) were equivalent for both groups. This is the first study to show that the predictive validity of the SAT varies for ability groups that differ in g. The results contradict a presumption, based on Spearman’s Law of Diminishing Returns, that a test’s predictive validity should be lower for high ability subjects. Further research is needed to identify factors that contribute to the predictive validity of the SAT for groups that differ in g.

Introduction

This research examined the predictive validity of the SAT (formerly, the Scholastic Aptitude Test) for high and low ability subjects. The SAT is a standardized test for college admissions in the United States. The SAT correlates moderately with college grade-point average (GPA) (r ≈ .35, Bridgeman, McCamley-Jenkins, & Ervin, 2000, Table 1, p. 4), and strongly with g (r = .82, Frey & Detterman, 2004; see also, Coyle & Pillow, 2008). g measures variance common to cognitive tests. A test’s g loading (i.e., correlation with g) is directly related to its predictive validity at work and school (e.g., Jensen, 1998, pp. 274–294).

The theoretical framework of this research concerns the mental ability hypothesis of Spearman’s Law of Diminishing Returns (SLODR; Jensen, 1998, pp. 585–588). SLODR predicts that the mean correlation among cognitive tests, and the g loading of such tests, declines as ability level increases. SLODR is based on the theory that mental abilities become more independent, and therefore less g loaded (and correlated), as ability increases. SLODR has received substantial, though not unequivocal, support. The g loading of cognitive tests, and the correlation among tests, is generally lower for high ability subjects, though effect sizes (based on average correlations) are small across two standard deviations of ability (effect size ≈ .10; for a review of SLODR research, see te Nijenhuis & Hartmann, 2006, p. 438).

SLODR has implications for the predictive validity of a particular cognitive test. If the mean correlation among cognitive tests is lower for high ability subjects, then the correlation of a particular test with another test should generally be lower for high ability subjects. Given that the predictive validity of a test is a test’s correlation with a criterion (e.g., another test), it follows that a test’s predictive validity should generally be lower for high ability subjects. This prediction is central to the present research on the SAT.

Bridgeman et al. (2000) examined the predictive validity of the SAT for high and low ability groups from 23 colleges. Subjects were divided into ability groups based on the mean SAT score of their college. (SAT scores were the sum of math and verbal scores.) Some subjects (high ability) attended colleges with mean SAT scores greater than 1250; others (low ability) attended colleges with mean SAT scores less than 1050. The results contradicted the prediction, based on SLODR, that predictive validity would be lower for high ability subjects. SAT–GPA correlations (adjusted for range restriction) from three SAT scales were modestly higher for high (M_r = .61) than low ability subjects (M_r = .50) (Bridgeman et al., 2000, Table 3, p. 5). Moreover, SAT–GPA correlations from the 23 colleges increased with the mean SAT scores of the colleges (r = .42, Bridgeman et al., 2000, Table 5, p. 7). Other studies with large samples confirm that the SAT’s predictive validity is higher for high ability subjects (e.g., Kobrin, Patterson, Shaw, Mattern, & Barbuti, 2008).

Bridgeman et al.’s (2000) SAT findings are inconsistent with research on race differences in cognitive ability. Much of this research concerns black-white differences in the population (e.g., Jensen, 1998, pp. 350–417). Given that whites are the higher ability group (as indicated by their test scores), and that predictive validity of cognitive tests is higher for higher ability groups (as in Bridgeman et al.), it follows that predictive validity should be higher for whites. But this is not the case. Black-white differences in predictive validity are typically negligible (Jensen, 1998, pp. 360–362), as are differences in predictive validity for other races that differ in ability (e.g., Rushton et al., 2004, te Nijenhuis and van der Flier, 1999, Zeidner, 1987).

The present study examined the predictive validity of the SAT using SLODR as a predictive framework. Ability groups were formed using g scores from the computer-adapted Armed Services Vocational Aptitude Battery (ASVAB). The ASVAB consists of 12 diverse cognitive tests (e.g., coding speed, word knowledge, assembling objects). It has a large g factor that is comparable (in g variance) for high and low ability groups (Hartmann & Reuter, 2006, Table 2, p. 55). g scores from the ASVAB correlate strongly with cognitive ability tests (e.g., Frey & Detterman, 2004, Table 2, p. 375).

The study had two aims. The first was to examine the g loading of the SAT for high and low ability subjects. g loadings were measured as correlations between SAT scores and g scores. If the mean g loading of cognitive tests is lower for high ability subjects (as SLODR predicts), then the g loading of any particular test (including the SAT) should also generally be lower for high ability subjects. This prediction was not tested by Bridgeman et al. (2000), who did not report g loadings for the SAT.

The second aim was to examine the predictive validity of the SAT (for GPA) for high and low ability subjects. The predictive validity of a cognitive test has been shown to vary directly with a test’s g loading: tests with lower g loadings generally have lower predictive validity (e.g., Jensen, 1998, Table B.1, p. 590). This has implications for the predictive validity of the SAT. If the g loading of the SAT is lower for high ability subjects (as SLODR predicts), then the predictive validity of the SAT should also be lower for high ability subjects. This prediction contradicts Bridgeman et al. (2000), who found that the predictive validity of the SAT was higher for high ability subjects.