Transformed statistics for tests of conditional independence in [formula omitted] contingency tables

Abstract

Tests of the hypothesis of conditional independence in J×K×L contingency tables are considered. An expression to approximate the null distribution of the test statistics is derived. Using this expression, transformed statistics are obtained which converge to a chi-square limiting distribution faster than the original statistics do. Simulations are used to compare the transformed statistics with the original ones, and transformed statistics are proposed based on a Bartlett-type adjustment. Through this work and earlier ones, we cover testing hierarchical loglinear models in three-way tables except for a model having three interaction terms.