Commentary on the Commentaries of Collins and Humphreys

Abstract

The critiques of Collins (1996) and Humphreys (1996) certainly throw light on properties of gain scores and difference scores that have led to controversies in the past. Collins’ examples reveal that familiar formulas for the reliability of differences do not adequately reflect the precision of measures of change, because they do not allow for intraindividual change. Some additional examples are provided here, and a similar argument is applied to the reliability of a single test. As Collins implies, these arguments indeed disclose flaws, not only in the conventional approach to the reliability of gains and differences, but also in the basic concept of reliability in classical test theory. Index terms: change scores, classical test theory, difference scores, gain scores, intraindividual differences, measurement of growth, reliability, test theory, validity.