Gain Scores, Analysis of

Gain (i.e., change, difference) is defined here as the difference between test scores obtained for an individual or group of individuals from a measurement instrument, intended to measure the same attribute, trait, concept, construct, or skill, between two or more testing occasions. This difference does not necessarily mean that there is an increase in the test score(s). Thus, a negative difference is also described as a “gain score.” There are a multitude of reasons for measuring gain: (a) to evaluate the effects of instruction or other treatments over time, (b) to find variables that correlate with change for developing a criterion variable in an attempt to answer questions such as “What kinds of students grow fastest on the trait of interest?,” and (c) to compare individual differences in gain scores for the purpose of allocating service resources and selecting individuals for further or special study.

The typical and most intuitive approach to the calculation of change is to compute the difference between two measurement occasions. This difference is called a gain score and can be considered a composite in that it is made up of a pretest (e.g., an initial score on some trait) and a posttest (e.g., a score on the same trait after a treatment has been implemented) score where a weight of 1 is assigned to the posttest and a weight of −1 is assigned to the pretest. Therefore, the computation of the gain score is simply the difference between posttest and pretest scores (i.e., gain = posttest – pretest). However, both the pretest and the posttest scores for any individual contain some amount of measurement error such that it is impossible to know a person's true score on any given assessment. Thus, in classical test theory (CTT), a person's observed score (X) is composed of two parts, some true score (T) and some amount of measurement error (E) as defined in Equation 1:

In a gain score analysis, it is the change in the true scores (ΔT) that is of real interest. However, the researcher's best estimate of the true score is the person's observed score, thus making the gain score (i.e., the difference between observed scores) an unbiased estimator of ΔT for any given individual or subject. What follows is a description of methods for analyzing gain scores, a discussion of the reliability of gain scores, alternatives to the analysis of gain scores, and a brief overview of designs that measure change using more than two waves of data collection.