Extending Classical Test Theory to the Measurement of Change

The concept of a change score has considerable intuitive appeal. A person subtracts last week's weight from today's weight and talks of having gained or lost five pounds. Yet, change scores have more than their share of conceptual problems. Weights are comparable a two-hundred-pounder outweighs a onehundred-pounder regardless of his other traits; but changes are not necessarily comparable a loss of twenty-five pounds may be a godsend for one individual but a disaster for another. Even in cases where changes in one direction are preferred, certain comparisons of changes appear inappropriate. For example, an instructor may grade physical education students on their improvement in running the mile. All of the students running an eight-minute mile at the beginning of the course may cut more than a minute out of their times; none of the four-minute milers are likely to improve by more than a few seconds. Clearly, the eight-minute milers "improved" their time by more seconds than did the four-minute milers. Yet no instructor would give A's to the slowest runners and F's to the fastest, regardless of his commitment to the concept of grading on improvement. Somehow these "improvements" are not comparable for the purposes of evaluation. This inability to directly compare changes at different points of the scale, even with ratio scales, is the fundamental problem of the measurement of change. The comparability problem is related to the fact that change scores are generally correlated with initial status. When change and initial status are negatively correlated, low-scorers have an advantage in the sense they are likely to gain more. Similarly, in rarer instances when change and initial status are positively correlated, the initially highscoring individuals have the advantage.