Rerandomization and Covariate Adjustment in Split-Plot Designs

Split-plot designs are widely used in agricultural, industrial, social, and biomedical experiments to accommodate hard-to-change factors. Given multiple factors of interest and experimental units that are nested within groups, the design assigns a subset of the factors by a cluster randomization at the group level and assigns the remaining factors by a stratified randomization at the unit level. The randomization mechanism ensures covariate balance on average at both the unit and group levels, allowing for consistent inference of average treatment effects. However, chance covariate imbalance is common in specific allocations and subjects subsequent inference to possibly large variability and conditional bias. Building on the literature on using rerandomization to improve covariate balance and inference efficiency in other design types, we propose two strategies for conducting rerandomization in split-plot designs and establish their guaranteed efficiency gains for inferring average treatment effects by the Horvitz–Thompson and Hajek estimators. We then propose two covariate adjustment methods that further improve inference efficiency when combined with rerandomization. All theoretical guarantees are design-based and robust to model misspecification.