Two-SampLe PartiaLLy SequentiaL Median Test Procedures Using Ranked Set SampLe Data

摘要

One of the primary goals of any statistical procedure is to make quantifiably reliable inferences while minimizing the sample size(s) necessary to reach these conclusions. One class of procedures designed with this goal in mind uses the partially sequential sampling (PS) approach, first introduced by Wolfe (1977a). The use of ranked set sampling (RSS) to obtain more representative samples is a second approach that leads to smaller sample sizes to obtain stipulated statistical properties than can be obtained from the use of simple random samples. RSS is an active area of research in the current literature.(See, for example, Wolfe(2012).)In this paper we meld the two methodologies and study a class of partially sequential ranked set sample (PSRSS) two-sample median test procedures that take advantage of the sample saving properties of both the PS and RSS approaches. The proposed procedures use an initial sample from one population obtained via simple random sampling, while the sequential sample from the second population is obtained via RSS. Properties of our median tests are discussed, including the limiting distributions as the fixed sample size tends to infinity, R software to obtain the necessary exact critical values, and the mechanism for obtaining prescribed power against specified alternatives of interest. Criteria for selecting a particular PSRSS median procedure are discussed.