Reliability and Validity of Gain Scores in Three Possible Scenarios

Abstract

In 1996 Williams, et al. presented results on the reliability and validity of difference (gain) scores for the case where the pretest variance is less than the posttest variance. We extend this work to the remaining two possible cases—wherein the two variances are approximately equal and wherein the pretest variance exceeds the posttest variance. Plausible applied scenarios are presented for these two cases. Using these scenarios and varying the pretest-posttest reliabilities, validities, and inter-correlation, the resulting reliabilities and validities for the gain score are delineated. Our results provide the applied researcher with additional insights into the psychometric properties of gain scores in various potential situations.