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An Improved Approximate Formula for Calculating Sample Sizes for Comparing Two Binomial Distributions
Abstract
If x and y are each binomially distributed with index n and parameters pl and p2 respectively, then the comparison of these two binomial distributions is usually displayed as a 2 X 2 table and Fisher's (one-sided) test may be used to test the null hypothesisp1 = p2, against the alternative hypothesis that pl > p2. The exact test is based on arguing conditionally on the observed number ofsuccesses, i.e., x + y, see Yates (1934) and Fisher (1935). The distribution of x with x + y = m fixed depends on pl and P2 only through the odds ratio 0 = (p1q2)/(q,p2), where qi 1-Pi rhe conditional distribution is Pr (x 1 0) C (n,x) C (n,y) AX/zzC(n,i)C(n,m-i)0i, where i takes the values L = max(O, m-n) to U = min(n, m). Let xc be the critical value of x for the exact test of P1 > P2 (i.e., 0 > 1 ) against the null hypothesis 0 = 1 with type I error oe, so that
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Cites
Statistical Methods for Rates and Proportions
Fleiss, J. L., Levin, B., & Paik, M. C. (2003) · Wiley Series in Probability and Statistics · doi:10.1002/0471445428 · Cited by 18,646
Exact Sample Sizes for Use with the Fisher-Irwin Test for 2 x 2 Tables
Haseman, J. K. (1978) · Biometrics · doi:10.2307/2529595 · Cited by 99
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Metadata
- Authors
- Casagrande, J. T., Pike, M. C., & Smith, P. G.
- Venue
- Biometrics
- Publisher
- JSTOR
- Published
- 1978-09
- Volume
- 34
- Issue
- 3
- Pages
- 483
- ISSN
- 0006-341X (ISSN-L)
- OpenAlex
- W2167990168
- Cited by
- 431
- References
- 2
- FWCI
- 5.76
- Type
- journal article
- Language
- en
- Open access
- closed
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- Casagrande, J. T., Pike, M. C., & Smith, P. G. (1978). An Improved Approximate Formula for Calculating Sample Sizes for Comparing Two Binomial Distributions. Biometrics. https://doi.org/10.2307/2530613
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