Accuracy of Power-Divergence Statistics for Testing Independence and Homogeneity in Two-Way Contingency Tables |
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Authors: | Miguel A García-Pérez Vicente Núñez-Antón |
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Institution: | 1. Departamento de Metodología , Universidad Complutense , Madrid, Spain miguel@psi.ucm.es;3. Departamento de Econometría y Estadística , Universidad del País Vasco , Bilbao, Spain |
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Abstract: | 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. The likelihood ratio statistic G 2 and Pearson's X 2 statistic are among these seven members, whose behavior was studied at nominal test sizes of.01 and.05 with marginal distributions that could be uniform or skewed and with a set of sample sizes that included sparseness conditions as measured through table density (i.e., the ratio of sample size to number of cells). The likelihood ratio statistic G 2 rejected the null hypothesis too often even with large table density, whereas Pearson's X 2 was sufficiently accurate and only presented a minor misbehavior when table density was less than two observations/cell. None of the other five statistics outperformed Pearson's X 2. A nonasymptotic variant of X 2 solved the minor inaccuracies of Pearson's X 2 and turned out to be the most accurate statistic for testing independence or homogeneity, even with table densities of one observation/cell. These results clearly advise against the use of the likelihood ratio statistic G 2. |
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Keywords: | Contingency tables Homogeneity Independence Power-divergence statistics Small-sample accuracy |
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