The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
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The Comparison of the Unconditional and Conditional Exact Power of Fisher's Exact Tes

  • Kang, Seung-Ho (Department of Applied Statistics, Yonsei University) ;
  • Park, Yoon-Soo (Department of Applied Statistics, Yonsei University)
  • Received : 20100600
  • Accepted : 20100800
  • Published : 2010.10.31
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Abstract

Since Fisher's exact test is conducted conditional on the observed value of the margin, there are two kinds of the exact power, the conditional and the unconditional exact power. The conditional exact power is computed at a given value of the margin whereas the unconditional exact power is calculated by incorporating the uncertainty of the margin. Although the sample size is determined based on the unconditional exact power, the actual power which Fisher's exact test has is the conditional power after the experiment is finished. This paper investigates differences between the conditional and unconditional exact power Fisher's exact test. We conclude that such discrepancy is a disadvantage of Fisher's exact test.

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References

  1. Berger, R. L. and Boos, D. D. (1994). P-values maximized over a confidence set for the nuisance parameter, Journal of the American Statistical Association, 89, 1012-1016. https://doi.org/10.2307/2290928
  2. Crans, G. G. and Shuster, J. J. (2008). How conservative is Fisher's exact test? A quantitative evaluation of the two-sample comparative binomial trial, Statistics in Medicine, 27, 3598-3611. https://doi.org/10.1002/sim.3221
  3. Cytel (2006). StatXact, version 6.0, Software for Exact Nonparametric Statistical Inference with Continuous or Categorical Data, Cytel Software: Cambridge, MA.
  4. Gail, M. and Gart, J. J. (1973). The determination of sample sizes for use with the exact conditional test in $22{\times}2$ comparative trials, Biometrics, 29, 441-448. https://doi.org/10.2307/2529167
  5. Haseman, J. K. (1978). Exact sample sizes for the use with the Fisher-Irwin test for $2{\times}2$ tables, Biometrics, 34, 106-109. https://doi.org/10.2307/2529595
  6. Kang, S. H. and Ahn, C. W. (2008). Tests for homogeneity of two binomial proportions in extremely unbalanced $2{\times}2$ contingency tables, Statistics in Medicine, 27, 2524-2535. https://doi.org/10.1002/sim.3055
  7. Lydersen, S., Fagerland, M. W. and Laake, P. (2009). Recommended tests for association in $2{\times}2$ tables, Statistics in Medicine, 28, 1159-1175. https://doi.org/10.1002/sim.3531
  8. Lydersen, S. and Laake, P. (2003). Power comparison of two-sided exact tests for association in $2{\times}2$ contingency tables using standard, mid p, and randomized test versions, Statistics in Medicine, 22, 3859-3871. https://doi.org/10.1002/sim.1671
  9. Martin Andres, A., Quevedo, M. J. S. and Mato, A. S. (1998). Fisher's mid-P-value arrangement in $2{\times}2$ comparative trials, Computational Statistics and Data Analysis, 29, 107-115. https://doi.org/10.1016/S0167-9473(98)90179-7
  10. Martin Andres, A., Silva Mato, A., Tapia Garcia, J. M. and Sanches Quevedo, M. J. (2004). Comparing the asymptotic power of exact tests in $2{\times}2$ tables, Computational Statistics and Data Analysis, 47, 745-756. https://doi.org/10.1016/j.csda.2003.11.012
  11. Sahai, H. and Khurshid, A. (1996). Formulae and tables for the determination of sample sizes and power in clinical trials for testing differences in proportions for the two-sample design: A review, Statistics in Medicine, 15, 1-21. https://doi.org/10.1002/(SICI)1097-0258(19960115)15:1<1::AID-SIM134>3.0.CO;2-E
  12. Suissa, S. and Shuster, J. J. (1985). Exact unconditional sample sizes for the $2{\times}2$ binomial trial, Journal of the Royal Statistical Society, Series A, 148, 317-327. https://doi.org/10.2307/2981892