Strategies for Designing and Analyzing Multi-factor Randomized Experiments to Achieve Balance with Respect to Several Covariates

In many modern-day social, educational and marketing experiments, multiple covariate measurements are available for each experimental unit. Whereas randomized treatment assignment balances observed and unobserved covariates “in expectation,” a single randomization may result in a highly imbalanced covariate distribution across treatment combinations. When the number of covariates is large, and several of them are continuous, most of the restricted randomization strategies described in literature (e.g., blocking) do not work. In this talk, I will explore, propose and compare strategies to design experiments with a desired level of covariate balance across treatments in different experimental settings ranging from treatment-control studies to factorial experiments. Analysis of such designs using randomization tests and a model-based Bayesian approach will be discussed. The proposed methods will be demonstrated using some real-life experiments.

(Based on joint work with Zach Branson, Rahul Mukherjee and Donald B. Rubin.)