Abstract #300596

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JSM 2003 Abstract #300596
Activity Number: 239
Type: Contributed
Date/Time: Tuesday, August 5, 2003 : 10:30 AM to 12:20 PM
Sponsor: Section on Statistics & the Environment
Abstract - #300596
Title: A Cost Analysis of Ranked Set Sampling to Estimate a Population Mean
Author(s): Rebecca A. Buchanan*+ and Loveday L. Conquest and Jean-Yves P. Courbois
Companies: University of Washington and University of Washington and University of Washington
Address: Box 355020, Seattle, WA, 98195-0001,
Keywords: best linear unbiased estimator ; cost ratio ; environmental sampling ; simple random sampling ; unequal allocation
Abstract:

Ranked set sampling (RSS) can be a useful environmental sampling method when measurement costs are high but ranking costs are low. Estimating a population mean at a given precision may be done with a smaller RSS than a simple random sample (SRS), so RSS may be cheaper than SRS. However, RSS includes ranking costs absent in SRS; these costs must be considered when choosing a sampling method. We use a simple cost model to determine the minimum ratio of measurement to ranking costs (cost ratio) necessary for RSS to be as cost effective as SRS, for data from the normal, exponential, and lognormal distributions. We consider equal and unequal RSS allocations and two types of population mean estimators: the distribution-free estimator (DFE) and the best linear unbiased estimator (BLUE). The minimum cost ratio necessary for RSS to be as cost effective as SRS depends on the underlying distribution of the data and the allocation and type of estimator used. Most minimum cost ratios range from one to six, and are lower for BLUEs than for DFEs. The higher the prior knowledge of the underlying data distribution, the lower the minimum cost ratio and the more attractive RSS is over SRS.

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