Small-Sample Comparisons for the Power Divergence Goodness-of-Fit Statistics

Abstract

The small-sample properties of the power divergence family of goodness-of-fit statistics (Cressie and Read in press) are examined. The asymptotic χ 2 and three alternative approximations are used to obtain appropriate test levels for comparison with the exact level. It is shown that if the χ 2 approximation is to be used, then there are many preferable statistics to the log-likelihood ratio G 2 (including Pearson's χ 2 ). Furthermore, exact power comparisons under specific alternatives to the symmetric null hypothesis show that the power of the well-known tests based on G 2 and χ 2 can be improved by choosing other statistics from the family. An explanation is proposed in terms of the effect of relative deviations between observed and expected counts.