Nonindependence of Parameters of the Validity and Reliability of Gain Scores

Gain scores can be valid and reliable under certain scenarios stipulating the ratios of pretest and posttest reliability coefficients, the ratios of pretest and posttest variances, and the correlations of pretest and posttest scores with a criterion. Although no assumptions about the size of these ratios can be ruled out in the absence of empirical evidence, one can nevertheless infer from inspection of mathematical formulas and from characteristics of pretest-posttest experimental designs that some scenarios are more likely in practice than others.