COVARIANCE ADJUSTMENT VERSUS GAIN SCORES - REVISITED

There are 2 main ways of estimating the average treatment effect in a 2-group pretest-posttest study: the gain score and the covariance adju stment estimator. The difficulty of the estimation problem arises from the fact that it involves missing posttest data. The gain score and t he covariance adjustment estimator both use the pretest to predict the se missing data, but in different ways: The gain score estimator treat s the pretest as a baseline and the covariance adjustment estimator tr eats it as a covariate. Using a result by D. B. Rubin (1977), it is sh own that, if the assignment is not on the basis of the pretest, there is no basis for preferring the covariance adjustment estimator over th e gain score estimator. Contrary to what is sometimes suggested, regre ssion toward the mean is not a reason for not using the gain score est imator; neither is measurement error in the pretest, unless the assign ment is affected by the pretest.