Accuracy of Power-Divergence Statistics for Testing Independence and Homogeneity in Two-Way Contingency Tables
Résumé
The small-sample accuracy of seven members of the family of power-divergence statistics for testing independence or homogeneity in contingency tables was studied via simulation at test sizes of .01 and .05 with marginal distributions that could be uniform or skewed and with sample sizes including sparseness conditions. The likelihood ratio statistic rejected the null hypothesis too often even with large table density, and none of the other five statistics outperformed Pearson's X2. A non-asymptotic variant of the latter was even more accurate with table densities of 1 observation/cell. These results advise against the use of the likelihood ratio statistic.
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