An Evaluation of Some Tests of Trend in Contingency Tables
作者:
Arthur Cohen,
HaroldB. Sackrowitz,
期刊:
Journal of the American Statistical Association
(Taylor Available online 1992)
卷期:
Volume 87,
issue 418
页码: 470-475
ISSN:0162-1459
年代: 1992
DOI:10.1080/01621459.1992.10475228
出版商: Taylor & Francis Group
关键词: Concordant–discordant pair;Contingency table;Exact test;Goodman-Kruskal gamma test;Inadmissible test;Ordered category;pvalue;Unbiased test
数据来源: Taylor
摘要:
Consider anr×ccontingency table under the full multinomial model in which each classification is ordered. The problem is to test the null hypothesis of independence against the alternative that all local log odds ratios are nonnegative with at least one local log odds ratio positive. A number of tests have been proposed for this problem, including the Goodman–Kruskal gamma test; a family of linear tests studied by Agresti, Mehta, and Patel; and a test based on“C–D,”the difference of concordant and discordant pairs in the table. In this article we show that all of these tests can be improved on in some sense for most cases. In fact the preceding tests sometimes are inadmissible in a strict sense. Furthermore, we show by example that in some cases improved tests can yield substantially improved power functions. We suggest a test based on a linear statistic similar to that presented by Agresti, Mehta, and Patel but that is followed up with a test that orders points by their probabilities on sample points where the linear test would randomize. This latter test compares favorably with competitors and has optimal theoretical properties. Exact tests, which entail auxiliary randomization, are discussed, as are thepvalues of the test procedures, which do not use auxiliary randomization.
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