A POWER APPROXIMATION OF THE TEST OF INDEPENDENCE IN s×r CONTINGENCY TABLES BASED ON A NORMALIZING TRANSFORMATION

概要

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Read and Cressie (1988) introduced a class of the power-divergence statistics Ra for the test of independence in s×r contingency tables. This class includes Pearson's χ2 statistic (when a=1) and the loglikelihood ratio statistic (when a=0). All Ra have the same chi-squared limiting null distribution. All Ra have the same noncentral chi-squared limiting distribution under local alternatives, whence the power of the class is the same for all a asymptotically. Applying the power approximation methods for the multinomial goodness-of-fit test developed by Broffitt and Randles(1977) and Drost et al. (1989), Taneichi and Sekiya(1995) proposed three approximations to the power of Ra that vary with the statistic chosen. In this paper we propose a new approximation to the power of Ra. The new approximation is a normal approximation based on normalizing transformations of the statistics. The proposed approximation and the other approximations are compared numerically. As a result of comparison, we find that the proposed approximation is very effective for R-1 and R-2 when all marginal probabilities are equal. We also find that the approximation is effective for the statistics R0, R2/3, and R1.
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