Ranked-Set Sampling (RSS)

Approaches for Ensuring Representative Samples

One way to better ensure representative samples is to put additional structure on the sampling design. Some examples of this approach include stratified element sampling and stratified cluster sampling. Sampling designs can become increasingly complex when the population of interest is large and diverse, such as when the goal is to collect data on a national sample. Although the primary goal is to select sampling units that are representative of the underlying population, a secondary, but often just as important, goal is to minimize the costs associated with collecting the data, that is, both the cost of measurement and that associated with obtaining the sample units.

An alternative cost-effective approach to obtaining more representative sample observations from a population is that of RSS. The RSS technique uses additional information about potential sample units as an aid in choosing which of the units should actually be measured on the variable(s) of interest. In this way information about all of the units selected for potential measurement is used to guide the selection of the specific units to be measured. It is this additional information that enables RSS techniques to generally outperform analogous SRS techniques when both involve the same number of measured observations.

Example of Ranked-Set Sampling

To provide a concrete illustration of how RSS is conducted, we consider the setting where our goal is to estimate the unknown population mean, X, using the information in n measured observations. RSS takes advantage of available information from additional potential sample units to enable us to measure selected units that are, collectively, more representative of the population of interest. The net result of RSS is a set of measurements that are more likely to span the range of values in the population than can be guaranteed from SRS. Following is a more precise description of this process.

Suppose we wish to obtain a ranked-set sample of k measured observations. First, an initial simple random sample of k units from the population is selected and rank-ordered on the attribute of interest. This ranking can result from a variety of mechanisms, including expert opinion (called judgment ranking), visual comparisons, or the use of easy-to-obtain auxiliary variables; it cannot, however, involve actual measurements of the attribute of interest on the sample units. The unit that is judged to be the smallest in this ranking is included as the first item in the ranked-set sample, and the attribute of interest is formally measured on this unit.

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