Exact Inference for a Population Proportion Based on a Ranked Set Sample

ABSTRACT

This article develops and investigates a confidence interval and hypothesis testing procedure for a population proportion based on a ranked set sample (RSS). The inference is exact, in the sense that it is based on the exact distribution of the total number of successes observed in the RSS. Furthermore, this distribution can be readily computed with the well-known and freely available R statistical software package. A data example that illustrates the methodology is presented. In addition, the properties of the inference procedures are compared with their simple random sample (SRS) counterparts. In regards to expected lengths of confidence intervals and the power of tests, the RSS inference procedures are superior to the SRS methods.

Keywords:

• Binary data
• Confidence
• Exact inference
• Proportion
• Power
• Ranked set sample

Mathematics Subject Classification:

• Primary 62F99
• Secondary 62E15

Acknowledgment

The authors would like to thank an anonymous referee for some suggestions that led to an improved article.