Skip to main content

On Ranked Set Sampling Variation and Its Applications to Public Health Research

  • Chapter
Innovative Statistical Methods for Public Health Data

Part of the book series: ICSA Book Series in Statistics ((ICSABSS))

Abstract

The foundation of any statistical inference depends on the collection of required data through some formal mechanism that should be able to capture the distinct characteristics of the population. One of the most common mechanisms to obtain such data is the simple random sample (SRS). In practice, a more structured sampling mechanism, such as stratified sampling, cluster sampling or systematic sampling, may be obtained to achieve a representative sample of the population of interest. A cost effective alternative approach to the aforementioned sampling techniques is the ranked set sampling (RSS). This approach to data collection was first proposed by McIntyre (Aust. J. Agr. Res. 3:385–390, 1952) as a method to improve the precision of estimated pasture yield. In RSS the desired information is obtained from a small fraction of the available units.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 99.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 129.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 119.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • Al-Saleh, M.F., Al-Kadiri, M.A.: Double ranked set sampling. Stat. Probab. Lett. 48(2), 205–212 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  • Al-Saleh, M.F., Zheng, G.: Estimation of bivariate characteristics using ranked set sampling. Aust. N. Z. J. Stat. 44, 221–232 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  • Bahadur, R.R.: A note on quantiles in large samples. Ann. Math. Stat. 37, 577–590 (1966)

    Article  MathSciNet  MATH  Google Scholar 

  • Bickel, P.J., Doksum, K.A.: Mathematical Statistics. Holden-Day, Inc., Oakland (1977)

    MATH  Google Scholar 

  • Chen, Z.: On ranked-set sample quantiles and their application. J. Stat. Plan. Inference 83, 125–135 (2000)

    Article  MATH  Google Scholar 

  • Chen, Z., Zheng, G., Ghosh, K., Li, Z.: Linkage disequilibrium mapping of quantitative trait loci by selective genotyping. Am. J. Hum. Genet. 77, 661–669 (2005)

    Article  Google Scholar 

  • Chen, Z.: Ranked set sampling: Its essence and new applications. Environ. Ecol. Stat. 14, 355–363 (2007)

    Google Scholar 

  • Dell, T.R., Clutter, J.L.: Ranked set sampling theory with order statistics background. Biometrics 28, 545–555 (1972)

    Article  MATH  Google Scholar 

  • Food and Agriculture Organization (FAO): Date Production and Protection. FAO Plant Production and Protection Paper 35. FAO (1982)

    Google Scholar 

  • Hansen, M.H., Hurwitz, W.N., Madow, W.G.: Sampling Survey Methods and Theory, vol. 2. Wiley, New York (1953)

    Google Scholar 

  • Kaur, A., Patil, G.P., Sinha, A.K., Tailie, C.: Ranked set sampling: an annotated bibliography. Environ. Ecol. Stat. 2, 25–54 (1995)

    Article  Google Scholar 

  • McIntyre, G.A.: A method for unbiased selective sampling using ranked set. Aust. J. Agr. Res. 3, 385–390 (1952)

    Article  Google Scholar 

  • Muttlak, H.A.: Median ranked set sampling. J. Appl. Stat. Sci. 6(4), 245–255 (1997)

    MathSciNet  MATH  Google Scholar 

  • Nelson, W.E., Behrman, R.E., Kliegman, R.M., Vaughan, V.C.: Textbook of Pediatrics, 4th edn. W. B. Saunders Company Harcourt Barace Jovanovich, Inc, Philadelphia (1992)

    Google Scholar 

  • Norris, R.C., Patil, G.P., Sinha, A.K.: Estimation of multiple characteristics by ranked set sampling methods. COENOSES 10(2&3), 95–111 (1995)

    Google Scholar 

  • Ozturk, O., MacEachern, S.N.: Order restricted randomized designs for control versus treatment comparison. Ann. Inst. Stat. Math. 56, 701–720 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  • Patil, G.P., Sinha, A.K., Taillie, C.: Relative efficiency of ranked set sampling: comparison with regression estimator. Environmetrics 4, 399–412 (1993)

    Article  Google Scholar 

  • Patil, G.P., Sinha, A.K., Taillie, C.: Ranked set sampling for multiple characteristics. Int. J. Ecol. Environ. Sci. 20, 94–109 (1994)

    Google Scholar 

  • Patil, G.P., Sinha, A.K., Taillie, C.: Ranked set sampling: a bibliography. Environ. Ecol. Stat. 6, 91–98 (1999)

    Article  Google Scholar 

  • Samawi, H.M.: Stratified ranked set sample. Pak. J. Stat. 12(1), 9–16 (1996)

    MathSciNet  MATH  Google Scholar 

  • Samawi, H.M.: On quantiles estimation using ranked samples with some applications. JKSS 30(4), 667–678 (2001)

    MathSciNet  Google Scholar 

  • Samawi, H.M.: Varied set size ranked set sampling with application to mean and ratio estimation. Int. J. Model. Simul. 32(1), 6–13 (2011)

    Google Scholar 

  • Samawi, H.M., Al-Sageer, O.A.: On the estimation of the distribution function using extreme and median ranked set sampling. Biom. J. 43(3), 357–373 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  • Samawi, H.M., Al-Saleh, M.F.: On bivariate ranked set sampling for ratio and regression estimators. Int. J. Model. Simul. 27(4), 1–7 (2007)

    Google Scholar 

  • Samawi, H.M.: On double extreme ranked set sample with application to regression estimator. Metron LX(1–2), 53–66 (2002)

    Google Scholar 

  • Samawi, H.M., Muttlak, H.A.: Estimation of ratio using ranked set sampling. Biom. J. 38(6), 753–764 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  • Samawi, H.M., Muttlak, H.A.: On ratio estimation using median ranked set sampling. J. Appl. Stat. Sci. 10(2), 89–98 (2001)

    MathSciNet  Google Scholar 

  • Samawi, H.M., Siam, M.I.: Ratio estimation using stratified ranked set sample. Metron LXI(1), 75–90 (2003)

    MathSciNet  Google Scholar 

  • Samawi, H.M., Ahmed, M.S., Abu Dayyeh, W.: Estimating the population mean using extreme ranked set sampling. Biom. J. 38(5), 577–586 (1996)

    Article  MATH  Google Scholar 

  • Serfling, R.J.: Approximation Theorems of Mathematical Statistics. Wiley, New York (1980)

    Book  MATH  Google Scholar 

  • Sinsheimer, J.S., Blangero, J., Lange, K.: Gamete competition models. Am. J. Hum. Genet. 66, 1168–1172 (2000)

    Article  Google Scholar 

  • Slatkin, M.: Disequilibrium mapping of a quantitative-trait locus in an expanding population. Am. J. Hum. Genet. 64, 1765–1773 (1999)

    Article  Google Scholar 

  • Spielman, R.S., McGinnis, R.E., Ewens, W.J.: Transmission test for linkage disequilibrium: the insulin gene region and insulin-dependent diabetes mellitus (IDDM). Am. J. Hum. Genet. 52, 506–516 (1993)

    Google Scholar 

  • Stokes, S.L., Sager, T.W.: Characterization of a ranked set sample with application to estimating distribution functions. J. Am. Stat. Assoc. 83, 374–381 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  • Sukhatme, P.V., Sukhatme, B.V.: Sampling Theory of Surveys with Applications. Iowa State University Press, Ames (1970)

    MATH  Google Scholar 

  • Takahasi, K., Wakimoto, K.: On unbiased estimates of the population mean based on the stratified sampling by means of ordering. Ann. Inst. Stat. Math. 20, 1–31 (1968)

    Article  MathSciNet  MATH  Google Scholar 

  • William, E., Ahmed, M., Ahmed, O., Zaki, L., Arash, N., Tamer, B., Subhy, R.: Date Palm in the GCC countries of the Arabian Peninsula. http://www.icarda.org/aprp/datepalm/introduction/intro-body.htm (2004)

  • Xu, X.P., Rogus, J.J., Terwedom, H.A., et al.: An extreme-sib-pair genome scan for genes regulating blood pressure. Am. J. Hum. Genet. 64, 1694–1701 (1999)

    Article  Google Scholar 

  • Yu, L.H., Lam, K.: Regression estimator in ranked set sampling. Biometrics 53, 1070–1080 (1997)

    Article  MATH  Google Scholar 

  • Zheng, G., Ghosh, K., Chen, Z., Li, Z.: Extreme rank selections for linkage analysis of quantitative trait loci using selected sibpairs. Ann. Hum. Genet. 70, 857–866 (2006)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding authors

Correspondence to Hani Samawi or Robert Vogel .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Samawi, H., Vogel, R. (2015). On Ranked Set Sampling Variation and Its Applications to Public Health Research. In: Chen, DG., Wilson, J. (eds) Innovative Statistical Methods for Public Health Data. ICSA Book Series in Statistics. Springer, Cham. https://doi.org/10.1007/978-3-319-18536-1_13

Download citation

Publish with us

Policies and ethics