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Ranked set sampling

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Abstract The most common sampling approach for collecting data from a population with the goal of making inferences about unknown features of the population is a simple random sample (SRS). There is a probabilistic guarantee that each measured observation in an SRS can be considered representative of the population. Despite this assurance, there remains a distinct possibility that a specific SRS might not provide a truly representative picture of the population. With that in mind, statisticians have developed a variety of ways to guard against obtaining such unrepresentative samples. Sampling designs such as stratified sampling, probability sampling, and cluster sampling all provide additional structure on the sampling process to improve the likelihood that the collected sample data do, indeed, provide a good representation of the population. A secondary goal in most data collection settings is to minimize the costs associated with obtaining the data. Ranked set sampling (RSS) is a relatively recent development that addresses both of these issues. It uses additional information from the population to provide more structure to the data collection process and decreases the likelihood of an unrepresentative sample. In addition, it is designed to minimize the number of measured observations required to achieve the desired precision in making inferences. In this article, we provide a general introduction to both balanced and unbalanced RSS, describing the basic approaches for collecting each type of RSS and some of the associated properties. We discuss a number of important factors that affect the performance of RSS procedures. Copyright © 2010 John Wiley & Sons, Inc. This article is categorized under: Statistical and Graphical Methods of Data Analysis > Sampling

Standard normal density (dotted curve) and the individual marginal densities of the five order statistics X(1), X(2), X(3), X(4), and X(5) (solid curves, in order of peaks, from the minimum, X(1), on the left to the maximum, X(5), on the right) for a random sample of size five from the standard normal distribution.

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