Evaluation of the Power of Rerandomization Tests, with Application to Weather Modification Experiments

Computations of power of rerandomization tests by exact methods are known to be computationally exorbitant. We introduce a much cheaper naive method of evaluating power and show—both by simulation and analytically for a special case—that it very mildly overestimates true power. We further derive a normal approximation to re-randomization distributions of linear statistics and illustrate its closeness to the true distributions. This yields analytical formulas for calculating power approximately at negligible computational cost. The proposed methods therefore eliminate the previously prohibitive cost of calculating power for rerandomization tests and make it practical to evaluate the sample sizes needed for a randomized experiment to be analyzed by rerandomization (see also Gabriel and Hall 1983). Its application to weather modification experiments is illustrated.