Analysis of covariance (ANCOVA) with difference scores

Abstract

When comparing pretest to posttest changes in non-randomized groups, most researchers are correctly avoiding ANCOVA with posttest as the dependent variable and pretest as the covariate. However, there is a widespread use of ANCOVA in which the difference score (posttest minus pretest) is used as the dependent variable, and pretest as the covariate. A computer simulation study is presented which shows that measurement error causes identical, biased conclusions when comparing changes using either the posttest score or the posttest minus pretest difference score as the dependent variable. The reasons for this bias are explained and illustrated.