On the Optimum Predictive Potential of Change Measure

Abstract

Several researchers have criticized use of difference scores as a measure of individual change due to their low reliability and low validity. Recent research by Zimmerman and Williams (1982a), Rogosa and Willett (1983), Sharma and Gupta (1986), however, indicates that under certain assumptions about reliability coefficients and standard deviations of pretest and posttest scores, the reliability of gain scores can be high. Another study by Zimmerman and Williams (1982b) demonstrated that under some realistic testing conditions difference scores can have excellent predictive value. But they did not provide the necessary mathematical treatment for optimization of the validity of gain scores. In addition to giving a mathematical treatment to the findings of Zimmerman and Williams (1982b), the present paper specifies exact conditions under which the validity of gain scores is optimum. Moreover, the paper discusses how the validity of gain scores varies with respect to the correlation between pretest and posttest scores and the relative sizes of the two standard deviations.