Models for cluster randomized designs using ranked set sampling

Cluster randomized designs (CRD) provide a rigorous development for randomization principles for studies where treatments are allocated to cluster units rather than the individual subjects within clusters. It is known that CRDs are less efficient than completely randomized designs since the randomization of treatment allocation is applied to the cluster units. To mitigate this problem, we embed a ranked set sampling design from survey sampling studies into CRD for the selection of both cluster and subsampling units. We show that ranking groups in ranked set sampling act like a covariate, reduce the expected mean squared cluster error, and increase the precision of the sampling design. We provide an optimality result to determine the sample sizes at cluster and sub-sample level. We apply the proposed sampling design to a dental study on human tooth size, and to a longitudinal study from an education intervention program.