Testing hypothesis for a simple ordering in incomplete contingency tables

Abstract

A test for ordered categorical variables is of considerable importance, because they are frequently encountered in biomedical studies. This paper introduces a simple ordering test approach for the two-way r×c contingency tables with incomplete counts by developing six test statistics, i.e., the likelihood ratio test statistic, score test statistic, global score test statistic, Hausman–Wald test statistic, Wald test statistic and distance-based test statistic. Bootstrap resampling methods are also presented. The performance of the proposed tests is evaluated with respect to their empirical type I error rates and empirical powers. The results show that the likelihood ratio test statistic based on the bootstrap resampling methods perform satisfactorily for small to large sample sizes. A real example from a wheeze study in six cities is used to illustrate the proposed methodologies.