The clinical use of difference scores: Some psychometric problems
Cattell, Raymond B. (1982). The Clinical Use of Difference Scores: Some Psychometric Problems. Multivariate Experimental Clinical Research, 6(2), 87-98.
Some pure statisticians have raised such difficulties regarding difference scores that clinicians and others who are bound to use them have been doing so only with trepidation. This article examines the dependability of difference scores as a function of (1) the dependability of the single occasion scores, (2) the correlation between pre- and post-interval scores, (3) the pre-post difference of means and (4) the relative pre-post standard deviation--all in regard to the same variable measured twice on the same people. Uncorrelated pre- and post-scores, equal or unequal in variance, yield differences with no larger percent error than the single occasion scores. The difference score has highest dependability with a negative pre-post correlation, and is reduced finally to zero with a positive, except when before and after standard deviations are different. The suitability of procedures depends on the psychological model one is using--merely itemetric or heeding structures recognized in trait and state theory. In the latter one must distinguish between the "instant" pre-post dependability coefficient and the long term stability coefficient, in which the true score itself alters. A trait constancy coefficient of 0.5, not uncommon over, say, six months of therapy, results in a reduction of a difference score dependability coefficient of 0.9 to 0.82, which can readily be compensated by a Spearman-Brown calculated increase of test length. More important than what some statisticians have emphasized is the need for getting equal interval properties in the test, by pan-normalization or relational simplex principles.