On a Partially Sequential Ranked Set Sampling Paradigm

Abstract

In a two-sample setting it is important to design statistical procedures that can take advantage of additional information to minimize the sample sizes required to reach reliable inferences about possible differences between the two populations. This is particularly true when it is difficult and/or costly to obtain sample observations from one or both of the populations. One class of procedures designed with this goal in mind uses the partially sequential sampling (PS) approach, first introduced by Wolfe (Journal of the American Statistical Association 72:202–205, 1977a). The use of ranked set sampling (RSS), first introduced by McIntyre (Australian Journal of Agricultural Research 3:385–390, 1952, reprinted in 2005), offers another approach for minimizing required sample sizes through the mechanism of obtaining more representative samples than can be achieved using simple random samples. In this paper we provide a review of these two sampling techniques and discuss options for melding the two methodologies to obtain partially sequential ranked set sample (PSRSS) two-sample test procedures that take advantage of the sample saving properties of both the PS and RSS approaches. To illustrate this combination, we consider PSRSS procedures where the fixed (control) sample is obtained via simple random sampling and the sequential (treatment) sample is obtained via ranked set sampling. Properties of the associated tests are discussed, including the limiting distributions as the fixed sample size tends to infinity.