## Statistical Science

### Ranked Set Sampling: An Approach to More Efficient Data Collection

Douglas A. Wolfe

#### Abstract

This paper is intended to provide the reader with an introduction to ranked set sampling, a statistical technique for data collection that generally leads to more efficient estimators than competitors based on simple random samples. Methods for obtaining ranked set samples are described, and the structural differences between ranked set samples and simple random samples are discussed. Properties of the sample mean associated with a balanced ranked set sample are developed. A nonparametric ranked set sample estimator of the distribution function is discussed and properties of a ranked set sample analog of the Mann–Whitney–Wilcoxon statistic are presented.

#### Article information

Source
Statist. Sci., Volume 19, Number 4 (2004), 636-643.

Dates
First available in Project Euclid: 18 April 2005

https://projecteuclid.org/euclid.ss/1113832728

Digital Object Identifier
doi:10.1214/088342304000000369

Mathematical Reviews number (MathSciNet)
MR2185585

Zentralblatt MATH identifier
1100.62555

#### Citation

Wolfe, Douglas A. Ranked Set Sampling: An Approach to More Efficient Data Collection. Statist. Sci. 19 (2004), no. 4, 636--643. doi:10.1214/088342304000000369. https://projecteuclid.org/euclid.ss/1113832728

#### References

• Barnett, V. and Moore, K. (1997). Best linear unbiased estimates in ranked-set sampling with particular reference to imperfect ordering. J. Appl. Statist. 24 697--710.
• Bohn, L. L. (1996). A review of nonparametric ranked-set sampling methodology. Comm. Statist. Theory Methods 25 2675--2685.
• Bohn, L. L. (1998). A ranked-set sample signed-rank statistic. J. Nonparametr. Statist. 9 295--306.
• Bohn, L. L. and Wolfe, D. A. (1992). Nonparametric two-sample procedures for ranked-set samples data. J. Amer. Statist. Assoc. 87 552--561.
• Bohn, L. L. and Wolfe, D. A. (1994). The effect of imperfect judgment rankings on properties of procedures based on the ranked-set samples analog of the Mann--Whitney--Wilcoxon statistic. J. Amer. Statist. Assoc. 89 168--176.
• Hettmansperger, T. P. (1995). The ranked-set sample sign test. J. Nonparametr. Statist. 4 263--270.
• Koti, K. M. and Babu, G. J. (1996). Sign test for ranked-set sampling. Comm. Statist. Theory Methods 25 1617--1630.
• McIntyre, G. A. (1952). A method for unbiased selective sampling, using ranked sets. Australian J. Agricultural Research 3 385--390.
• Nahhas, R. W., Wolfe, D. A. and Chen, H. (2002). Ranked set sampling: Cost and optimal set size. Biometrics 58 964--971.
• Öztürk, Ö. and Wolfe, D. A. (2000a). Optimal allocation procedure in ranked set sampling for unimodal and multi-modal distributions. Environmental and Ecological Statistics 7 343--356.
• Öztürk, Ö. and Wolfe, D. A. (2000b). An improved ranked set two-sample Mann--Whitney--Wilcoxon test. Canad. J. Statist. 28 123--135.
• Öztürk, Ö. and Wolfe, D. A. (2000c). Alternative ranked set sampling protocols for the sign test. Statist. Probab. Lett. 47 15--23.
• Patil, G. P. (1995). Editorial: Ranked set sampling. Environmental and Ecological Statistics 2 271--285.
• Presnell, B. and Bohn, L. L. (1999). $U$-statistics and imperfect ranking in ranked set sampling. J. Nonparametr. Statist. 10 111--126.
• Randles, R. H. and Wolfe, D. A. (1979). Introduction to the Theory of Nonparametric Statistics. Wiley, New York.
• Stokes, S. L. and Sager, T. W. (1988). Characterization of a ranked-set sample with application to estimating distribution functions. J. Amer. Statist. Assoc. 83 374--381.