Sample Size for Confidence Interval of Covariate-Adjusted Mean Difference

This article provides a way to determine adequate sample size for the confidence interval of covariate-adjusted mean difference in randomized experiments. The standard error of adjusted mean difference depends on covariate variance and balance, which are two unknown quantities at the stage of planning sample size. If covariate observations are viewed as randomly varying from one study to another, the covariate variance and balance are related to a t statistic in the standard error of adjusted mean difference. Using this t statistic in the standard error, one can express the expected width of the confidence interval as a function of the sample size. Alternatively, a sample size can be found to achieve a desired probability of having the width of the confidence interval smaller than a predetermined upper bound.