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The Size of the Cochran-Armitage Trend Test in 2 X C Contingency Tables: Two Multinomial Distribution Case

  • Published : 2008.05.30

Abstract

In this paper we show that the peak of the type I error rate of the Oochran-Armitage trend test could be greater than the nominal level when $2\;{\times}\;C$ contingency tables obtained from two multinomial distributions are extremely unbalanced. This result justifies the use of the exact Cochran-Armitage trend test in extremely unbalanced $2\;{\times}\;C$ contingency tables.

Keywords

References

  1. Loh, W. Y. (1989). Bounds on the size of the $\chi^2$2 test of independence in a contingency table, The Annals of Statistics, 17, 1709-1722 https://doi.org/10.1214/aos/1176347389
  2. Loh, W. Y. and Yu, X. (1993). Bounds on the size of the likelihood ratio test of independence in a contingency table, Journal of Multivariate Analysis, 45, 291- 304 https://doi.org/10.1006/jmva.1993.1040
  3. Kang, S. H. and Shin, D. W. (2004). The size of the chi-square test for the HardyWeinberg law, Human Heredity, 58, 10-17 https://doi.org/10.1159/000081452
  4. Kang, S. H., Lee, Y. H. and Park, E. S. (2006). The sizes of the three popular asymptotic tests for testing homogeneity of two binomial proportions, Computational Statistics & Data Analysis, 51, 710-722 https://doi.org/10.1016/j.csda.2006.03.006
  5. Kang, S. H. and Lee, J. W. (2007). The size of the Cochran-Armitage trend test in $2{\times}C$ contingency table, Journal of Statistical Planning and Inference, 137, 1851-1861 https://doi.org/10.1016/j.jspi.2006.03.009
  6. Johnson, N. L. and Kotz, S. (1969). Distributions in Statistics: Discrete Distributions, Jhon Wiley & Sons, New York
  7. Cytel (2007). StatXact, Version 6.0. Software for exact nonparametric statistical inference with continuous or categorical data, Cambridge, Massachusetts: Cytel Software