An Evaluation of Some Tests of Trend in Contingency Tables
评估了多种用于有序分类列联表中检验独立性与局部对数优势比非负的检验方法，发现多数检验可被改进，并提出了一个具有更优理论性质和更高检验功效的新检验。
Abstract Consider an r × c contingency 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 the p values of the test procedures, which do not use auxiliary randomization.