Causal Inference from Strip-Plot Designs in a Potential Outcomes Framework

TLDR: In this article, a randomization-based theory of causal inference from stripplot designs in a potential outcomes framework was developed, where an unbiased estimator was proposed, an expression for its sampling variance was worked out, and a conservative estimator of the sampling variance is obtained.

Abstract: Strip-plot designs are very useful when the treatments have a factorial structure and the factors levels are hard-to-change. We develop a randomization-based theory of causal inference from such designs in a potential outcomes framework. For any treatment contrast, an unbiased estimator is proposed, an expression for its sampling variance is worked out, and a conservative estimator of the sampling variance is obtained. This conservative estimator has a nonnegative bias, and becomes unbiased under between-block additivity, a condition milder than Neymannian strict additivity. A minimaxity property of this variance estimator is also established. Simulation results on the coverage of resulting confidence intervals lend support to theoretical considerations.