The Most Powerful Member of the Power-Divergence Family for the Independence Model in Contingency Tables

Abstract

The family of power-divergence (PD) test statistic contains many well-known test statistics used in the analysis of the contingency tables under the independence model. In this work, we compare the various test statistics for the independence model. The type-I and type-II errors of the test statistics are obtained and compared via simulation study considering the different degree of freedoms and sample sizes. According to the simulation results, we recommend the PD(0.4) test statistic for the small sample size based on its power and type-I error rates. Two applications are given to demonstrate the usefulness of the PD(0.4) test statistic over the chi-square test statistic {contingency tables}.

Keywords

• Goodness-of-fit test statistics
• Independence model
• Power-divergence family
• Small sample

References

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