A Test of Independence against a Class of Ordered Alternatives in a 2 ×CContingency Table

Publisher Website
Google Scholar
Abstract
A likelihood ratio statistic is derived for testing the hypothesis of independence in a 2 × C table against a class of ordered alternatives defined in terms of cross-product ratios. Asymptotic equivalence on the null hypothesis to a chi-squared—type statistic is established. The large-sample distribution of these statistics depends on the column totals, but numerical evidence for C = 3 and 4 suggests that the exact size of a test derived by ignoring this dependency will remain within reasonable limits for a wide range of tables encountered in practice. Some power comparisons with established test procedures are reported.