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Related Experiment Videos

Unbalanced ranked set sampling for estimating a population proportion.

Haiying Chen1, Elizabeth A Stasny, Douglas A Wolfe

  • 1Department of Public Health Sciences, Wake Forest University, Medical Center Boulevard, Winston Salem, North Carolina 27157, USA. hchen@wfubmc.edu

Biometrics
|March 18, 2006
PubMed
Summary
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Unbalanced ranked set sampling (RSS) with Neyman allocation optimizes population proportion estimation for dichotomous data. This method offers improved precision over simple random sampling (SRS) and balanced RSS, as demonstrated with NHANES III data.

Area of Science:

  • Statistics
  • Biostatistics
  • Survey Methodology

Background:

  • Ranked set sampling (RSS) improves precision over simple random sampling (SRS) for estimating population proportions in dichotomous populations.
  • Balanced RSS offers precision gains but is not always optimal for variance reduction in this context.

Purpose of the Study:

  • To investigate unbalanced RSS for estimating population proportions with perfect ranking.
  • To determine if Neyman allocation is optimal for variance reduction in unbalanced RSS for dichotomous populations.

Main Methods:

  • Utilizing order statistics and their success probabilities, which are functions of the population proportion.
  • Applying Neyman allocation, sampling units proportionally to the standard deviation of each order statistic.

Related Experiment Videos

  • Analyzing the National Health and Nutrition Examination Survey III (NHANES III) data.

    • Main Results:

    • Neyman allocation is shown to be optimal within the class of RSS estimators that are simple averages of order statistic means.
    • Unbalanced RSS with Neyman allocation achieves minimum variance for population proportion estimation.
    • The study demonstrates the practical feasibility and benefits of Neyman allocation in RSS for binary variables using real-world data.

    Conclusions:

    • Neyman allocation provides an optimal strategy for unbalanced ranked set sampling in estimating population proportions for binary data.
    • This approach offers significant advantages in precision and variance reduction compared to traditional methods like SRS and balanced RSS.
    • The findings are validated using a large-scale epidemiological dataset, highlighting its applicability in public health research.