Randomization-based causal inference from split-plot designs

Abstract

Under the potential outcomes framework, we propose a randomization based estimation procedure for causal inference from split-plot designs, with special emphasis on $2^{2}$ designs that naturally arise in many social, behavioral and biomedical experiments. Point estimators of factorial effects are obtained and their sampling variances are derived in closed form as linear combinations of the between- and within-group covariances of the potential outcomes. Results are compared to those under complete randomization as measures of design efficiency. Conservative estimators of these sampling variances are proposed. Connection of the randomization-based approach to inference based on the linear mixed effects model is explored. Results on sampling variances of point estimators and their estimators are extended to general split-plot designs. The superiority over existing model-based alternatives in frequency coverage properties is reported under a variety of simulation settings for both binary and continuous outcomes.