Non-asymptotic inferences based on the chi-square statistic for r by c contingency tables

Abstract

A non-asymptotic approach based on the chi-square statistic is described for analyses of r by c contingency tables. This method provides improved analyses for cases where the standard asymptotic approach is questionable, e.g., with small expected cell frequencies due to severely unbalanced and/or very small marginal frequency totals. The non-asymptotic approach is based on an algorithm that obtains the exact mean, variance and skewness under the conditional permutation distribution, which are then utilized for inferences in conjunction with a pearson type III distribution.