Confidence intervals for a population proportion based on a ranked set sample

Abstract

This article examines several approximate methods to formulate confidence intervals for a single population proportion based on a ranked set sample (RSS). All of the intervals correspond to certain test statistics. That is, the confidence intervals are obtained by inverting the Wald, Wilson, score, and likelihood ratio tests. The Wald and Wilson intervals are based on the asymptotic distributions of two point estimators; the method of moments (MM) estimator and the maximum likelihood (ML) estimator. Continuity corrected versions of these intervals are also discussed. The R statistical software program is used to both calculate and evaluate the proposed intervals. For instance, an actual data set is analyzed for the sake of illustration. Furthermore, a simulation study which compares the intervals via expected widths and coverage probabilities is presented. The study indicates that the confidence intervals derived from the ML methodology generally outperform those based on MM procedures. Additionally, the Wilson and score intervals do not yield the same results under RSS as they do under simple random sampling. Lastly, the ML-based Wilson interval (without continuity correction) is recommended for use in practice.

Keywords:

• Bernoulli data
• Confidence interval
• Coverage probability
• Expected width
• Proportion
• Ranked set sample

Acknowledgements

We would like to thank the reviewers of this article for making suggestions that led to an improved manuscript.