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In this Chapter, with regard to test of complete independence in multi-way contingency tables, we found that only Pearson’s \(X^2\) statistic satisfies the conditions given in this Chapter among the power divergence family of statistics as well as among the family of statistics proposed by Rukhin. This chapter presents a new test statistic that also satisfies the conditions. Furthermore, we numerically investigate whether the distribution of this new test statistic is close to the chi-square limiting distribution, and we show that the new statistic performs well.

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Constructing a New Statistic NT for Testing Complete Independence in Contingency Tables

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  • 发表日期：

    2026年

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  • Nobuhiro Taneichi,
  • Yuri Sekiya

摘要

In this Chapter, with regard to test of complete independence in multi-way contingency tables, we found that only Pearson’s \(X^2\) statistic satisfies the conditions given in this Chapter among the power divergence family of statistics as well as among the family of statistics proposed by Rukhin. This chapter presents a new test statistic that also satisfies the conditions. Furthermore, we numerically investigate whether the distribution of this new test statistic is close to the chi-square limiting distribution, and we show that the new statistic performs well.