(with Nicole Pashley and Dominic Valentino)

Experiments are vital for assessing causal effects, but their high cost often leads to small, sub-optimal sample sizes. We show how a particular experimental design—the Neyman allocation—can lead to more efficient experiments, achieving similar levels of statistical power as traditional designs with significantly fewer units. This design relies on unknown variances, and so previous work has proposed what we call the batch adaptive Neyman allocation (BANA) design that uses an initial pilot study to approximate the optimal Neyman allocation for a second larger batch. We extend BANA to multiarm experiments common in political science, derive an unbiased estimator for the design, and show how to perform inference in this setting. Simulations verify that the design’s advantages are most apparent when the outcome variance differs by treatment conditions. Finally, we review the heteroskedasticity of recent experimental studies and find that political scientists using BANA could achieve sample size savings of 15-30%.