The Effect of Imperfect Judgment Rankings on Properties of Procedures Based on the Ranked-Set Samples Analog of the Mann-Whitney-Wilcoxon Statistic

Abstract

In this article we address the issue of imperfect judgment rankings in ranked-set sampling and, in particular, their effect on the properties of test procedures based on the ranked-set samples analog of the Mann-Whitney-Wilcoxon statistic, U _rss. We consider the impact of these imperfect rankings on the null distribution of the statistic and the resulting effect on the nominal level of associated hypothesis tests. We propose a model for the probabilities of imperfect judgment rankings based on the concept of expected spacings and use this model to study the properties of tests based on U _rss. This investigation includes both small-sample Monte Carlo power simulations and a detailed analysis of the asymptotic relative efficiency properties of the U _rss procedure. We also examine, as an indication of the merits of using ranked-set sampling, the relative cost of measuring the value of a sample item as compared to obtaining a judgment ordering of a set of sample items.

Key Words:

• Asymptotic relative efficiency
• Imperfect judgment rankings
• Mann-Whitney-Wilcoxon statistic
• Ranked-set data
• Spacings