The Robustness of Homogeneity Tests in 2 x N Tables

Abstract

A Monte Carlo investigation of 2xn tables with fixed marginals has been performed. The results of the Monte Carlo distribution show that the probability of Type I error given by the conventional X2 test is in general conservative for 5 or more degrees of freedom even when expectations of successes are very small in each cell. A very conservative rule of operation would be that if expectations are 1 or greater the test is certainly conservative at the 5%, 2% and 1% level of significance and that for most cases even fractional expectations do not affect the test. For those cases of fractional expectations in which the X2 test is non-conservative, the deviations of the true a values from those given by the X2 distribution are quite small.