Improved likelihood ratio tests and pearson chi-square tests for independence in two dimensional contingency tables

When an I×J contingency table has many cells having very small frequencies, the usual chi-square approximation to the upper tail of the likelihood ratio goodness-of-fit statistic, G2 and Pearson chi-square statistic, X2, for testing independence, are not satisfactory. In this paper we consider the problem of adjusting G2 and X2. Suitable adjustments are suggested on the basis of analytical investigation of asymptotic bias terms for G2 and X2. A Monte Carlo simulation is performed for several tables to assess the adjustments of G2 and X2 in order to obtain a closer approximation to the nominal level of significance.