Design choices in randomization tests that affect power

We consider the problem of evaluating designs for a small-sample two-arm randomized experiment using power one-sided randomization test as criterion. Our evaluation assumes linear response in one observed covariate, an unobserved component and additive treatment effect where model's randomness is due to different allocations. It well-known that depends on allocations’ imbalance covariate. show additionally affected by two other design choices: number allocations degree dependence. prove more allocations, higher lower variability power. theoretical findings simulation studies with highest provide thousands highly independent each providing nominal covariates. These high-powered exhibit less than complete recently proposed employ numerical optimization. This advantage high easily accessible practicing experimenters via popular rerandomization greedy pair switching design, both outperform The tradeoff we find also provides means specify rerandomization’s threshold parameter.