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

TL;DR

This paper develops a randomization-based causal inference framework for strip-plot designs, providing unbiased estimators, variance expressions, and confidence interval coverage analysis within a potential outcomes approach.

Contribution

It introduces a novel potential outcomes framework for strip-plot designs, including unbiased estimators and variance estimation methods with theoretical properties.

Findings

Proposed unbiased estimators for treatment contrasts.

Derived conservative variance estimators with nonnegative bias.

Simulation studies support the theoretical coverage properties.

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.