Browse > Article
http://dx.doi.org/10.5351/KJAS.2010.23.5.883

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)
Publication Information
The Korean Journal of Applied Statistics / v.23, no.5, 2010 , pp. 883-890 More about this Journal
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.
Keywords
Conditional test; sample size determination; homogeneity; binomial;
Citations & Related Records
연도 인용수 순위
  • Reference
1 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.   DOI   ScienceOn
2 Cytel (2006). StatXact, version 6.0, Software for Exact Nonparametric Statistical Inference with Continuous or Categorical Data, Cytel Software: Cambridge, MA.
3 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.   DOI   ScienceOn
4 Haseman, J. K. (1978). Exact sample sizes for the use with the Fisher-Irwin test for $2{\times}2$ tables, Biometrics, 34, 106-109.   DOI   ScienceOn
5 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.   DOI   ScienceOn
6 Lydersen, S., Fagerland, M. W. and Laake, P. (2009). Recommended tests for association in $2{\times}2$ tables, Statistics in Medicine, 28, 1159-1175.   DOI   ScienceOn
7 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.   DOI   ScienceOn
8 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.   DOI   ScienceOn
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.   DOI   ScienceOn
10 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.   DOI   ScienceOn
11 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.   DOI   ScienceOn
12 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.   DOI