EXACT UNCONDITIONAL POWER COMPARISON OF THREE STATISTICS IN TESTING THE EQUALITY OF THREE BINOMIAL PROPORTIONS

We are going to compare the exact unconditional powers resulting from using three well known goodness-of-fit statistics, i.e., Pearson's X~2, deviance and power divergence, in testing conditionally and exactly the equality of three binomial proportions. As far as I know, no paper has paid any attention to the selection of test statistics in the context of an exact conditional test. This is partly because almost all authors, apart from Mehta and Hilton (1993), have treated two binomial proportions, where signed root of each frequently used goodness-of-fit statistic is a monotonous function of an observed value on a conditional reference set. Theoretical investigations are carried out and numerical results are obtained on various settings of binomial parameters.