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Randomized Controlled Trials (RCTs) often adjust for baseline covariates inorder to increase power. This technical note provides a short derivation of asimple rule of thumb for approximating the ratio of the power of an adjustedanalysis to that of an unadjusted analysis. Specifically, if the unadjustedanalysis is powered to approximately 80\%, then the ratio of the power of theadjusted analysis to the power of the unadjusted analysis is approximately $1 +\frac{1}{2} R^2$, where $R$ is the correlation between the baseline covariateand the outcome.

A Rule of Thumb for the Power Gain due to Covariate Adjustment in Randomized Controlled Trials with Continuous Outcomes