Judgement post-stratification for designed experiments

In many scientific studies, information that is not easily translated into covariates is ignored in the analysis. However, this type of information may significantly improve inference. In this research, we apply the idea of judgment post-stratification to utilize such information. Specifically, we consider experiments that are conducted under a completely randomized design. Sets of experimental units are formed, and the units in a set are ranked. Estimation is performed conditional on the sets and ranks. We propose a new estimator for a treatment contrast. We improve the new estimator by Rao-Blackwellization. Asymptotic distribution theory and corresponding inferential procedures for both estimators are developed. Simulation studies quantify the superiority of the new estimators and show their desirable properties for small and moderate sample sizes. The impact of the new techniques is illustrated with data from a clinical trial.