Optimum Reliability of Gain Scores

Abstract

AbstractThere are several studies which show that difference scores or gain scores have low reliability. Recent research by Zimmerman and Williams (1982), however, indicated that under certain assumptions about reliability coefficients and standard deviations of pretest and posttest scores the reliability of gain scores can be high. But they did not provide necessary mathematical treatment for optimization of the reliability of gain scores. In addition to giving a mathematical treatment to the findings of Zimmerman and Williams the present paper establishes a minimum reliability for gain scores when the pretest and posttest have equal reliabilities and equal standard deviations. Moreover, it discusses the behavior of the reliability of gain scores in terms of variations in other test parameters.