Improved transformed statistics for the test of independence in contingency tables

Abstract: We consider a class of statistics based on -divergence for the test of independence in contingency tables. The class of statistics includes the statistics based on the power divergence as a special case. Statistic is the log likelihood ratio statistic and is Pearson''s statistic. Statistic corresponds to the statistic recommended by Cressie and Read [Multinomial goodness-of-fit tests, J. Roy. Statist. Soc. B 46 (1984) 440–464] for the goodness-of-fit test. All members of statistics have the same chi-square limiting distribution under the hypothesis of independence. In this paper, we show the derivation of an expression of approximation for the distribution of under the hypothesis of independence. The expression consists of continuous and discontinuous terms. Using the continuous term of the expression, we propose a new approximation of the distribution of . Furthermore, on the basis of the approximation, we obtain transformations that improve the speed of convergence to the chi-square limiting distribution of . As a competitor of the transformed statistic, we derive a moment-corrected-type statistic. By numerical comparison in the case of , we show that the transformed statistic performs very well. [Copyright &y& Elsevier]