Nonparametric Tests for Perfect Judgment Rankings

Abstract

The ranked-set sampling literature includes both inference procedures that rely on the assumption of perfect rankings and inference procedures that are robust to violations of this assumption. Procedures that assume perfect rankings tend to be more efficient when rankings are in fact perfect, but they may be invalid when perfect rankings fail. As a result, users of ranked-set sampling must decide between efficiency and robustness, and there is at present little to guide their decision. In this article we introduce three rank-based goodness-of-fit tests that may be consulted in making these decisions. Our strategy in producing these tests is to think of the judgment order statistic classes as separate samples, compute the ranks of the units from each sample within the combined sample, and use these ranks to test whether the judgment rankings are perfect. Consideration of both power and ease of use leads us to recommend use of a test that rejects when the concordance between the vector of mean ranks and its null expectation is small. Tables of critical values and appropriate asymptotic theory for applying this test are provided, and we illustrate the use of the tests by applying them to a biological dataset.