A one degree of freedom nominal association model for testing independence in two-way contingency tables.

In testing the independence of the row and column variables in a two-way contingency table, the standard Pearson and likelihood ratio chi-square statistics often have low power, especially as the dimensions of the table increase. In this paper, one degree of freedom tests of independence based on likelihood ratio and score statistics from an association model for tables with nominal row and column classifications are described. The score statistic is especially easy to use, since it can be expressed in closed form, is simple to compute, and has size and power properties which are only slightly inferior to those of the more complicated likelihood ratio statistic.