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