Power and Sample Size Calculations for Rerandomized Experiments

Power is an important aspect of experimental design, because it allows researchers to understand the chance of detecting causal effects if they exist. It is common to specify a desired level of power, and then compute the sample size necessary to obtain that level of power; thus, power calculations help determine how experiments are conducted in practice. Power and sample size calculations are readily available for completely randomized experiments; however, there can be many benefits to using other experimental designs. For example, in recent years it has been established that rerandomized designs, where subjects are randomized until a prespecified level of covariate balance is obtained, increase the precision of causal effect estimators. This work establishes the statistical power of rerandomized treatment-control experiments, thereby allowing for sample size calculators. Our theoretical results also clarify how power and sample size are affected by treatment effect heterogeneity, a quantity that is often ignored in power analyses. Via simulation, we confirm our theoretical results and find that rerandomization can lead to substantial sample size reductions; e.g., in many realistic scenarios, rerandomization can lead to a 25% or even 50% reduction in sample size for a fixed level of power, compared to complete randomization. Power and sample size calculators based on our results are in the R package rerandPower on CRAN.