Using Ranked Set Sampling With Cluster Randomized Designs for Improved Inference on Treatment Effects

This article examines the use of ranked set sampling (RSS) with cluster randomized designs (CRDs), for potential improvement in estimation and detection of treatment or intervention effects. Outcome data in cluster randomized studies typically have nested structures, where hierarchical linear models (HLMs) become a natural choice for data analysis. However, nearly all theoretical developments in RSS to date are within the structure of one-level models. Thus, implementation of RSS at one or more levels of an HLM will require development of new theory and methods. Under RSS-structured CRDs developed to incorporate RSS at different levels, a nonparametric estimator of the treatment effect is proposed; and its theoretical properties are studied under a general HLM that has almost no distributional assumptions. We formally quantify the magnitude of the improvement from using RSS over SRS (simple random sampling), investigate the relationship between design parameters and relative efficiency, and establish connections with one-level RSS under completely balanced CRDs, as well as studying the impact of clustering and imperfect ranking. Further, based on the proposed RSS estimator, a new test is constructed to detect treatment effects, which is distribution-free and easy to use. Simulation studies confirm that in general, the proposed test is more powerful than the conventional F-test for the original CRDs, especially for small or medium effect sizes. Two empirical studies, one using data from educational research (i.e., the motivating application) and the other using human dental data, show that our methods work well in real-world settings and our theory provides useful predictions at the stage of experimental design, and that substantial gains may be obtained from using RSS at either level. Supplementary materials for this article are available online.