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Two-stage cluster samples with ranked set sampling designs

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  • Omer Ozturk

    (The Ohio State University)

Abstract

This paper draws statistical inference for population characteristics using two-stage cluster samples. Cluster samples in each stage are constructed using ranked set sample (RSS), probability-proportional-to-size sample, or simple random sample (SRS) designs. Each RSS sampling design is implemented with and without replacement policies. The paper constructs design-unbiased estimators for population mean, total, and their variances. Efficiency improvement of all sampling designs over SRS sampling design is investigated. It is shown that the efficiency of the estimators depends on the intra-cluster correlation coefficient and choice of sampling designs in stage I and II sampling. The paper also constructs an approximate confidence interval for the population mean (total). For a fixed cost, the optimal sample sizes for stage I and stage II samples are constructed by maximizing the information content of the sample. The proposed sampling designs and estimators are applied to California School District Study and Ohio Corn Production Data.

Suggested Citation

  • Omer Ozturk, 2019. "Two-stage cluster samples with ranked set sampling designs," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(1), pages 63-91, February.
    • Handle: RePEc:spr:aistmt:v:71:y:2019:i:1:d:10.1007_s10463-017-0623-z
    DOI: 10.1007/s10463-017-0623-z
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    References listed on IDEAS

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    1. M. Al-Saleh & H. Samawi, 2007. "A note on inclusion probability in ranked set sampling and some of its variations," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 16(1), pages 198-209, May.
    2. Omer Ozturk, 2016. "Estimation of a Finite Population Mean and Total Using Population Ranks of Sample Units," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 21(1), pages 181-202, March.
    3. G. Patil & A. Sinha & C. Taillie, 1995. "Finite population corrections for ranked set sampling," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 47(4), pages 621-636, December.
    4. McIntyre, G.A., 2005. "A Method for Unbiased Selective Sampling, Using Ranked Sets," The American Statistician, American Statistical Association, vol. 59, pages 230-232, August.
    5. Ozturk, Omer & Jafari Jozani, Mohammad, 2014. "Inclusion probabilities in partially rank ordered set sampling," Computational Statistics & Data Analysis, Elsevier, vol. 69(C), pages 122-132.
    6. Xinlei Wang & Johan Lim & Lynne Stokes, 2016. "Using Ranked Set Sampling With Cluster Randomized Designs for Improved Inference on Treatment Effects," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(516), pages 1576-1590, October.
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    Cited by:

    1. Soohyun Ahn & Xinlei Wang & Mumu Wang & Johan Lim, 2022. "On continuity correction for RSS-structured cluster randomized designs with binary outcomes," METRON, Springer;Sapienza Università di Roma, vol. 80(3), pages 383-397, December.
    2. Omer Ozturk & Olena Kravchuk & Raymond Correll, 2022. "Row–Column Sampling Design Using Auxiliary Ranking Variables," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 27(4), pages 652-673, December.

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