The Effect of a Covariate on Standard Error and Confidence Interval Width

The standard error of covariate-adjusted mean difference is not always smaller than that of the unadjusted mean difference despite the fact that adding a covariate is commonly believed to reduce the unexplained error variance. The covariate mean difference between the contrasted treatment conditions can inflate the standard error of the adjusted mean difference. If the covariate is viewed as randomly varying from one study to another, a minimum sample size can be found to attain a desired probability of reducing the standard error and the confidence interval width for the adjusted mean difference.