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Nonparametric Statistical Methods, 3rd Edition by Eric Chicken, Douglas A. Wolfe, Myles Hollander

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Chapter 15

Ranked Set Sampling

Introduction

This chapter is devoted to the concept of ranked set sampling, a technique for data collection that generally leads to more efficient statistical procedures than competitors based on simple random samples. The rationale behind ranked set sampling and its historical development is provided in Section 15.1. In Section 15.2, we describe how to collect a ranked set sample and discuss (see Comment 1) some of the structural differences between ranked set samples and simple random samples. We illustrate the application of ranked set sampling to the estimation of a population mean in Section 15.3 and present the ranked set sample analog of the two-sample Mann–Whitney–Wilcoxon test procedure (see Section 4.1) in Section 15.4. Other important issues for ranked set sampling are discussed in Section 15.5, and a number of recent developments in statistical inference with similarities to ranked set sampling are discussed briefly in Section 15.6.

15.1 Rationale and Historical Development

When we collect a simple random sample (SRS) from a population, what makes associated statistical inference procedures appropriate is not the fact that each individual measurement in the sample is likely to be representative of the population characteristic of interest. Rather, it is through the concept of the sampling distributions of the relevant statistics that we should, “on the average,” obtain a set of sample observations that are truly representative of the full ...

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