A Causality-based Graphical Test to obtain an Optimal Blocking Set for Randomized Experiments

Randomized experiments are often performed to study the causal effects of interest. Blocking is a technique to precisely estimate the causal effects when the experimental material is not homogeneous. We formalize the problem of obtaining a statistically optimal set of covariates to be used to create blocks while performing a randomized experiment. We provide a graphical test to obtain such a set for a general semi-Markovian causal model. We also propose and provide ideas towards solving a more general problem of obtaining an optimal blocking set that considers both the statistical and economic costs of blocking.