In this paper we propose three approximations to the power of the power-divergence statistic
Ra on the test of homogeneity for multinomial populations. These approximations are based on the approximation theories for the multinomial goodness-of-fit test as proposed by Broffitt and Randles (1977) and Drost et al. (1989). One approximation is constructed from a limiting normal distribution of
Ra. The others are constructed from the linear and quadratic terms of a Taylor series expansion of
Ra. These approximations are compared with the power directly calculated from the product multinomial model. As a result of this comparison, the latter approximations are found to perform well when a≥0. On the homogeneity of two populations, we investigate the power of representative power divergence statistics
R0,
R2/8 and
R1 using the latter approximations. Then, corresponding to alternatives, relations to the power of the three statistics are discussed.
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