Abstract
On the test of independece in s×γ Tables, the power of the family power-divergence statistics R^a can be approximated to the same non-central X^2-destribution for all the statistics of this family. In this paper, we propose two approximations to the power of R^a. These approximations are based on the approximation methods for the multinomial goodness-of-fit test proposed by Broffitt & Randles(1977) and Drost et al. (1989). One approximation is constructed from a limitnomal normal distribution of R^a. The other is constructed from the linear and quadratic terms of a Taylor series expansion of R^a. The proposed approximations vary with the selection of R^a. By numerical comparison, it is found that the latter approximation performs well. In the end of the paper, we discuss about the selection of the statistics.
