Unbalancedness under RSS-structured Cluster Randomized Designs

Abstract

In this thesis, we consider unbalancedness under cluster randomized designs (CRDs) using ranked set sampling (RSS), and extend nonparametric inference procedures, previously developed by Wang et al. (2016) for the use of balanced RSS (BRSS) with CRDs, to account for the unbalanced structures. The unbalanced structures are from (i) the use of unbalanced ranked set sampling (URSS) with CRDs or (ii) the use of BRSS with CRDs having unbalancedly sized groups. First, we consider URSS-structured CRDs. We theoretically study the URSS estimators of the treatment effect and numerically compare the relative effciency of the URSS vs. BRSS estimators. We also study and compare the power of the URSS tests vs. their BRSS counterparts via simulation. Second, we consider BRSS-structured CRDs having unbalancedly sized groups. We modify and improve the BRSS tests in Wang et al. (2016) and compare power of the modified BRSS tests vs. their original BRSS counterparts via simulation. Further, we illustrate each inference procedure with a data example using an educational data. Finally, we offer flexibility of incorporating RSS in CRDs in practice.