The Effectiveness of Multistage Ranked Set Sampling in Stratifying the Population

Abstract

The effectiveness of Ranked Set Sampling (RSS) and Multistage Ranked Set Sampling (MSRSS) in stratifying the population is demonstrated. The overlapping coefficient of Weitzman (1970) is used as a numerical index to measure the degree of stratification at each stage. It turns out that this measure, under the assumption of no error in ranking, doesn't depend on the underlying distribution. Possible uses of this measure at the design stage and at the inference stage are addressed and briefly demonstrated. The overlapping coefficient in the case of judgment order statistics and its possible use in testing for perfect ranking is briefly addressed and put forward for future investigation.

Keywords:

• Judgment order statistic
• Multistage ranked set sampling
• Overlapping coefficient
• Ranked set sampling

Mathematics Subject Classification:

• 62G05
• 62D05
• 62H12

Acknowledgments

Our sincere thanks are due to the referees and Associate Editor who provided many critical comments and helpful suggestions which significantly improved the original version of the article.