AbstractA modified chi‐square test statistic is constructed for testing the hypothesis of independence in a two‐way contingency table against a class of ordered alternatives defined in terms of pooled cross‐product ratios. The test procedure can also be used to test for positive quadrant dependence in a two‐way contingency table. The asymptotic distribution of the test statistic under the null hypothesis is obtained. Some power comparisons with known test procedures are given. A numerical example is given to illustrate the use of th