Choosing between the Exact and the Approximate Confidence Intervals: For the Difference of Two Independent Binomial Proportions

Title & Authors
Choosing between the Exact and the Approximate Confidence Intervals: For the Difference of Two Independent Binomial Proportions
Lee, Seung-Chun;

Abstract
The difference of two independent binomial proportions is frequently of interest in biomedical research. The interval estimation may be an important tool for the inferential problem. Many confidence intervals have been proposed. They can be classified into the class of exact confidence intervals or the class of approximate confidence intervals. Ore may prefer exact confidence interval s in that they guarantee the minimum coverage probability greater than the nominal confidence level. However, someone, for example Agresti and Coull (1998) claims that "approximation is better than exact." It seems that when sample size is large, the approximate interval is more preferable to the exact interval. However, the choice is not clear when sample, size is small. In this note, an exact confidence and an approximate confidence interval, which were recommended by Santner et al. (2007) and Lee (2006b), respectively, are compared in terms of the coverage probability and the expected length.
Keywords
Exact confidence interval;approximate confidence interval;coverage probability;expected length;
Language
English
Cited by
1.
Confidence Intervals for a Proportion in Finite Population Sampling,Lee, Seung-Chun;

Communications for Statistical Applications and Methods, 2009. vol.16. 3, pp.501-509
References
1.
Agresti, A. and Coull, B. A. (1998). Approximate is better than "exact" for interval estimation of binomial proportions, The American Statistician, 52, 119-126

2.
Agresti, A. and Caffo, B. (2000). Simple and effective confidence intervals for proportions and differ-ences of proportions result from adding two successes and two failures, The American Statistician, 54, 280-288

3.
Agresti, A. and Min, Y. (2001). On small-sample confidence intervals for parameters in discrete distributions, Biometrics, 57, 963-971

4.
Blyth, C. R. and Still, H. A. (1983). Binomial confidence intervals, Journal of the American Statistical Association, 78, 108-116

5.
Brown, L. D., Cai, T. T. and DasGupta, A. (2001). Interval estimation for a binomial proportion, Statistical Science, 16, 101-133

6.
Casella, G. T., Hwang, T. G. and Robert C. P. (1994). Loss functions for set estimation, Statistical Decision Theory and Related Topics V (Edited by S. S. Gupta and J. O. Berger), Springer-Verlag

7.
Chan, I. S. F. and Zhang, Z. (1999). Test-based exact confidence intervals for the difference of two binomial proportions, Biometrics, 55, 1202-1209

8.
Coe, P. R. and Tamhane, A. C. (1993). Small sample confidence intervals for the difference, ratio and odds ratio of two success probabilities, Communications in Statistics Part B-Simulation and Computation, 22, 925-938

9.
Esty. W. E. and Banfleld, J. D. (2003). The box-percentile plot, Journal of Statistical Software, 8, Issue 17

10.
Lehmann, F. L. (1986) Testing statistical hypotheses, John Wiley & Sons, New York

11.
Lee, S.-C. (2006a). Interval estimation of binomial proportions based on weighted Polya posterior, Computational Statistics & Data Analysis, 51, 1012-1021

12.
Lee, S.-C. (2006b). The weighted Polya posterior confidence interval for the difference between two independent proportions, The Korean Journal of Applied Statistics, 19, 171-181

13.
Lee, S.-C. (2007). Confidence intervals for a linear function of binomial proportions based on a Bayesian approach, The Korean Journal of Applied Statistics, 20, 257-266

14.
Meeden, G. D. (1999). Interval estimators for the population mean for skewed distributions with a small sample size, Journal of Applied Statistics, 26, 81-96

15.
Miettinen, O. S. and Nuriminen, M. (1985). Comparative analysis of two rates, Statistics in Medicine, 4, 213-226

16.
Newcombe, R. G. (1998), Interval estimation for the difference between independent porportions: Comparison of eleven methods, Statistics in Mediciene, 17, 873-890

17.
Price, R. M. and Bonett, D. G. (2004). An improved confidence interval for a linear function of binomial proportions, Computational Statistics & Data Analysis, 45, 449-456

18.
R Development Core Team (2008). R: A language and environment for statistical computing. R Foun-dation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0, URL http://www.R-project.org

19.
Santner, T. J., Pradhan, V., Senchaudhuri, P., Mehta, C. R. and Tamhane, A. C. (2007). Small-sample comparisons of confidence intervals for the difference of two independent binomial proportions, Computational Statistics & Data Analysis, 51, 5791-5799

20.
Santner, T. J. and Snell, M. K. (1980). Small-sample confidence intervals for $p_{1}$ - $p_{2}$ and $p_{1}$/$p_{2}$in $2{\times}2$ contingency tables, Statistics in Medicine, 17, 873-890

21.
Santner, T. J. and Yamagami, S. (1993). Invariant small sample confidence intervals for the difference of two success probabilities, Communications in Statistics, Part B-Simulation and Computation, 22, 33-59

22.
Wilson, E. B. (1927). Probable inference, the law of succession, and statistical inference, Journal of the American Statistical Association, 22, 209-212