5 Ranked set sampling

Abstract McIntyre (1952) proposed a method of sampling to estimate mean pasture yields with greater efficiency than simple random sampling. This method of sampling has come to be known as ranked set sampling (RSS) because it involves a preliminary ranking of randomly selected units from the population, after which only a certain few of these sampled units are actually quantified. The method was used first by Halls and Dell (1966) to estimate the weight of browse and herbage in a pine hardwood forest. Although McIntyre (1952) had mentioned an upper bound on the relative precision (RP) of the RSS estimator of a population mean relative to that of the simple random sample (SRS) estimator with the same sample size, Takahasi and Wakimoto (1968) gave a rigorous mathematical derivation of this bound. Since then, a number of papers discussing the RSS method have appeared. These papers may broadly be classified into three groups: (i) theory, (ii) methods, and (iii) applications. We have, in this chapter, made an attempt to review these various aspects in a single unified notation. This study also illustrates the performance of RSS compared to that of SRS in determining the level of PCB contamination at a hazardous waste site. In this context, we also demonstrate the use of RSS methods for improving the formation of composite samples.

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