A robust test for multi-ordered 2 × J ordinal contingency tables

Abstract

Pearson's chi-square test and the Cochran-Armitage trend test are commonly used in the analysis of 2×J contingency tables. When the J columns are nominal, Pearson's test should be considered. On the other hand, when the J columns are ordinal and the ordering is well defined, the trend test should be used. In practice, however, the columns are often ordered but the ordering may not be uniquely defined, especially the J categories may be ordered in multiple ways according to several different factors. We assume that the columns could be either singly or multi-ordered, either being scientifically plausible, and consequently different scores could be assigned to the columns by the different ordering systems. Then the trend test, if applied, may lose substantial power when the orderings are misspecified. To guard against misspecifications of the scores for the columns, we propose a robust test by combining strengths of both Pearson's test and the trend test. In the trend test, we allow several different score specifications according to different ordering criteria and the scores are chosen to be robust enough. Extensive simulation studies demonstrate the efficiency robustness of the proposed approach. The proposed method is applied to two data sets from the Genetic Association Workshop 15 and an experiment on the use of sulfones and streptomycin drugs in the treatment of leprosy.