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.