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 adjustment estimator. The difficulty of the estimation problem arises from the fact that it involves missing posttest data. The gain score and the covariance adjustment estimator both use the pretest to predict these missing data, but in different ways: The gain score estimator treats the pretest as a baseline and the covariance adjustment estimator treats it as a covariate. Using a result by D. B. Rubin (1977), it is shown that, if the assignment is not on the basis of the pretest, there is no basis for preferring the covariance adjustment estimator over the gain score estimator. Contrary to what is sometimes suggested, regression toward the mean is not a reason for not using the gain score estimator; neither is measurement error in the pretest, unless the assignment is affected by the pretest.