Linear dependence of gain scores on their components imposes constraints on their use and interpretation: Comment on "Are simple gain scores obsolete?"

Abstract

The properties of gain scores are linearly determined by the properties of their components. Thus, the reliability of a gain is uniquely determined by the reliabilities of the components, the correlation between them, and their standard deviations. Reliability is not inherently low, but the components of gains used in many investigations make low reliability likely. Correlations of the difference between two measures and a third variate are also determined uniquely by three correlations and two standard deviations. Raw score standard deviations frequently tell more about the measurement metric and how it is used than about the psychological processes underlying the measurements. Correlations involving gains/ differences cannot be understood adequately unless the essential sample statistics of the components are known and reported. Index terms: change scores, classical test theory, difference scores, gain scores, intraindividual differences, measurement of growth, reliability, test theory, validity.