Randomization-based Joint Central Limit Theorem and Efficient Covariate Adjustment in Randomized Block 2^<i>K</i> Factorial Experiments

Randomized block factorial experiments are widely used in industrial engineering, clinical trials, and social science. Researchers often use a linear model analysis of covariance to analyze experimental results; however, limited studies have addressed the validity robustness resulting inferences because assumptions for might not be justified by randomization randomized experiments. In this article, we establish new finite population joint central limit theorem usual (unadjusted) effect estimators 2K Our is obtained under randomization-based inference framework, making an extension vector form Wald–Wolfowitz–Hoeffding rank statistic. It robust misspecification, numbers blocks, sizes, propensity scores across blocks. To improve estimation efficiency, propose four covariate adjustment methods. We show that mild conditions, covariate-adjusted consistent, jointly asymptotically normal, generally more efficient than unadjusted estimator. addition, Neyman-type conservative asymptotic covariances facilitate valid inferences. Simulation trial data demonstrate benefits Supplementary materials article available online.