Some unexamined aspects of analysis of covariance in pretest-posttest studies.

The use of an analysis of covariance (ANCOVA) model in a pretest-posttest setting deserves to be studied separately from its use in other (non-pretest-posttest) settings. For pretest-posttest studies, the following points are made in this article: (a) If the familiar change from baseline model accurately describes the data-generating mechanism for a randomized study then it is impossible for unequal slopes to exist. Conversely, if unequal slopes exist, then it implies that the change from baseline model as a data-generating mechanism is inappropriate. An alternative data-generating model should be identified and the validity of the ANCOVA model should be demonstrated. (b) Under the usual assumptions of equal pretest and posttest within-subject error variances, the ratio of the standard error of a treatment contrast from a change from baseline analysis to that from ANCOVA is less than 2(1)/(2). (c) For an observational study it is possible for unequal slopes to exist even if the change from baseline model describes the data-generating mechanism. (d) Adjusting for the pretest variable in observational studies may actually introduce bias where none previously existed.