Abstract #302020

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JSM 2003 Abstract #302020
Activity Number: 468
Type: Contributed
Date/Time: Thursday, August 7, 2003 : 10:30 AM to 12:20 PM
Sponsor: Section on Nonparametric Statistics
Abstract - #302020
Title: Nonparametric Two-Sample Methods for Ranked Set Sample Data
Author(s): Steven N. MacEachern*+ and Michael A. Fligner
Companies: Ohio State University and The Ohio State University
Address: 404 Cockins Hall, Columbus, OH, 43210-1247,
Keywords: Mann-Whitney ; Pitman efficacy
Abstract:

A new collection of procedures is developed for the analysis of two-sample, ranked set samples, providing an alternative to the Bohn-Wolfe procedure. The new procedures lead to tests for the centers of distributions, confidence intervals, and point estimators. The advantages of the new procedures are that they require essentially no assumptions about the mechanism by which rankings are imperfect, that tests maintain their level whether rankings are perfect or imperfect, that they lead to generalizations of the Bohn-Wolfe procedure that can be used to increase power in the case of perfect rankings, and that they allow one to analyze both balanced and unbalanced ranked set samples. The new procedure splits the data based on the ranks in the ranked set sample. Performance of the procedure is investigated under a number of assumptions about the value of the rankings. When rankings are random, a theorem is presented which characterizes efficient data splits. Since random rankings are equivalent to not having rankings, this theorem applies to a wide class of statistics and has implications for a variety of computationally intensive methods.

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