JSM 2005 - Toronto

Abstract #303322

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Activity Number: 127
Type: Topic Contributed
Date/Time: Monday, August 8, 2005 : 10:30 AM to 12:20 PM
Sponsor: Section on Nonparametric Statistics
Abstract - #303322
Title: Nonparametric Tests for Perfect Judgment Rankings
Author(s): Omer Ozturk*+ and Jesse Frey and Jayant V. Deshpande
Companies: The Ohio State University and The Ohio State University and University of Pune
Address: Department of Statistics, Columbus, OH, 43210, United States
Keywords: Ranked-set sample ; Imperfect ranking ; Concordonca statistics ; Empirical powers ; Judgment quality ; Ranking mechanism
Abstract:

In this paper, we introduce three tests for assessing the quality of the judgment rankings used in drawing a given ranked set sample. The first is a likelihood ratio test based on considering the probability of the observed sequence of ranks under the null hypothesis and the alternative of random rankings. The exact null distribution of this test is derived for moderate sample sizes. The second test is constructed using an appropriate function of the standardized differences between the expected and observed ranks. This test is similar in spirit to the Kruskal-Wallis test used in one-way ANOVA. It is shown that the asymptotic distribution of this test is a chi-square with k-1 degrees of freedom, where k is the number of judgment classes. The third test is based on a concordance statistic. The sizes and powers of all three tests are studied through an intensive simulation study. The results of this study show the likelihood ratio and Kruskal-Wallis-type tests perform comparably well for moderately large sample sizes. On the other hand, for small sample sizes, the size of the Kruskal-Wallis test differs from its nominal level.

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Revised March 2005