Predicting the Relative Magnitudes of Validity Coefficients for Four Types of Gain Scores

Abstract

A set of mathematical relations is introduced which provides a guideline for predicting the rank order of validity coefficients for four types of gain scores. The measures of gain considered are the simple gain score, the residualized change, the base-free measure of change and Lord's estimate of true gain. A large sample data base was used to provide empirical checks of predictions made from the guideline. The sample was comprised of 5987 students from a large public school system in south Florida. These students were administered the Stanford Achievement Test in the fifth grade in 1987 and then again in the sixth grade in 1988. The Mathematics Computation subtest score was used as both the pretest and the posttest. The Mathematics Application subtest score served as the validity criterion. The empirical checks included here were for Normal Curve Equivalent scores derived by using national norms. The rank ordering of the four validity coefficients was perfectly consistent with predictions made from the guideline. Validity coefficients ranged from .22 to .32, with residual scores yielding the highest value.