Abstract
Abstract The statistics of several alternative procedures, proposed to test for independence in contingency tables derived from stratifled samples, all have the same asymptotic chi-square distribution, under the null hypothesis. By considering a modified sampling procedure, it is shown here that they also have the same asymptotic distribution under any alternative hypothesis—the non-central chi square, with the noncentrality parameter of Wald's test for the case of independently and identically distributed variables. Simulation, used to compare the flnite-sample powers of the tests, shows small differences between the various methods and close approximation to the asymptotic results.
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