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In this chapter, we investigate whether the method of approximation for multinomial goodness-of-fit tests proposed by Yarnold (1972) derived in Sect. 2.4 can be extended to a test of independence in a 2-way contingency table. As a result of our investigation, it was found that it is very difficult to apply to the test of independence in a contingency table. After that, for a test of independence of a 2-way contingency table, we propose an approximation of the test statistic by using a continuous term of the asymptotic expansion. By the continuous term of the expansion, we construct transformed statistics for improving the accuracy of the chi-square approximation of the test statistic.

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A Transformed Statistic for the Test of Independence in a \(J \times K\) Contingency Table

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  • 发表日期：

    2026年

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  • Nobuhiro Taneichi,
  • Yuri Sekiya

摘要

In this chapter, we investigate whether the method of approximation for multinomial goodness-of-fit tests proposed by Yarnold (1972) derived in Sect. 2.4 can be extended to a test of independence in a 2-way contingency table. As a result of our investigation, it was found that it is very difficult to apply to the test of independence in a contingency table. After that, for a test of independence of a 2-way contingency table, we propose an approximation of the test statistic by using a continuous term of the asymptotic expansion. By the continuous term of the expansion, we construct transformed statistics for improving the accuracy of the chi-square approximation of the test statistic.