An application of ranked set sampling for mean and median estimation using USDA crop production data

  • Chad E. Husby
  • Elizabeth A. Stasny
  • Douglas A. Wolfe


Ranked set sampling (RSS) is a sampling approach that leads to improved statistical inference in situations where the units to be sampled can be ranked (either through some subjective judgment or via the use of an auxiliary variable) relative to each other prior to formal measurement. It has the most promise for leading to improved methodology in situations where ranking of the items to be sampled can be carried out relatively easily and cheaply compared to the effort and expense required for actual quantification of the characteristic of interest. Although the theoretical benefits of RSS in estimation and statistical inference have been extensively demonstrated in the literature, the methodology has not yet been widely adopted by practitioners. The aim of this study is to use a crop production dataset from the United States Department of Agriculture to demonstrate the practical benefits of RSS relative to the more commonly used simple random sampling in estimation of the mean and median of a population. The results of our study provide clear evidence that the use of RSS can lead to substantial gains in precision of estimation for both of these situations.

Key Words

Auxiliary ranking variable Balanced ranked set sampling Concomitant ranking Set sizes Simple random sampling Simulation study 


  1. Barnett, V., and Moore, K. (1997), “Best Linear Unbiased Estimates in Ranked-Set Sampling with Particular Reference to Imperfect Ordering,” Journal of Applied Statistics, 24, 697–710.CrossRefGoogle Scholar
  2. Bohn, L. L. (1996), “A Review of Nonparametric Ranked-Set Sampling Methodology,” Communications in Statistics—Theory and Methods, 25, 2675–2685.MATHCrossRefGoogle Scholar
  3. Chen, H., Stasny, E. A., and Wolfe, D. A. (2003), “Ranked Set Sampling for Estimating a Population Proportion: How to Improve the Ranking,” Technical Report Number 703, Department of Statistics, Ohio State University.Google Scholar
  4. Cobby, J. M., Ridout, M. S., Bassett, P. J., and Large, R. V. (1985), “An Investigation into the Use of Ranked Set Sampling on Grass and Grass-Clover Swards,” Grass and Forage Science, 40, 257–263.CrossRefGoogle Scholar
  5. Dell, T. R., and Clutter, J. L. (1972), “Ranked Set Sampling Theory with Order Statistics Background,” Biometrics, 28, 545–555.CrossRefGoogle Scholar
  6. Iwig, W. C. (1993), “The National Agricultural Statistics Service County Estimates Program,” in Indirect Estimators in Federal Programs, Statistical Policy Working Paper 21. Report of the Federal Committee on Statistical Methodology, Subcommittee on Small Area Estimation, Washington, DC, 7.1–7.15.Google Scholar
  7. McIntyre, G. A. (1952), “A Method of Unbiased Selective Sampling, Using Ranked Sets,” Australian Journal of Agricultural Research, 3, 385–390.CrossRefGoogle Scholar
  8. Ohio Department of Agriculture (1993), Ohio Department of Agriculture 1992 Annual Report and Statistics, Columbus, OH: Author.Google Scholar
  9. Patil, G. P. (1995), “Editorial: Ranked Set Sampling,” Environmental and Ecological Statistics, 2, 271–285.CrossRefGoogle Scholar
  10. Patil, G. P., Sinha, A. K., and Taillie, C. (1994), “Ranked Set Sampling,” in Handbook of Statistics Volume 12: Environmental Statistics, eds. G. P. Patil and C. R. Rao, New York: Elsevier Science, pp. 167–200.Google Scholar
  11. Stokes, S. L. (1980), “Estimation of Variance Using Judgment Ordered Ranked Set Samples,” Biometrics, 36, 35–42.MATHCrossRefMathSciNetGoogle Scholar
  12. Stokes, S. L., and Sager, T. W. (1988), “Characterization of a Ranked-Set Sample with Application to Estimating Distribution Functions,” Journal of the American Statistical Association, 83, 374–381.MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© International Biometric Society 2005

Authors and Affiliations

  • Chad E. Husby
    • 1
  • Elizabeth A. Stasny
    • 2
  • Douglas A. Wolfe
    • 2
  1. 1.Department of Biological SciencesFlorida International UniversityMiami
  2. 2.Department of StatisticsOhio State UniversityColumbus

Personalised recommendations