Improvement of the test of independence among groups of factors in a multi-way contingency table

Abstract

Tests of complete independence and independence among groups of factors in a multi-way contingency table are considered. An expression to approximate the distribution of a test statistic under the complete independence on the basis of an asymptotic expansion is derived. Using this expression, transformed statistics that converge to a Chi-square limiting distribution faster than the original statistic does are obtained. Simulations are used to compare the performance of the transformed statistics with that of the original ones, and transformed statistics based on a Bartlett-type adjustment and based on improved transformation are proposed. Since the model of independence among groups of factors in an M-way contingency table is considered as a model of complete independence in an N-way contingency table, where N is less than M, we also obtain transformed statistics for testing independence among groups of factors in a multi-way contingency table.