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INTERVALOS DE CONFIANZA Y DE CREDIBILIDAD PARA LA DIFERENCIA DE DOS PROPORCIONES
CONFIDENCE AND CREDIBILITY INTERVALS FOR THE DIFFERENCE OF TWO PROPORTIONS
Keywords:
intervalos de confianza, intervalos de credibilidad, diferencia de dos proporciones (es)Confidence intervals, Credibility intervals, Difference of two proportions (en)
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1Universidad Santo Tomás, Facultad de Estadística, Centro de Investigaciones y Estudios Estadísticos (CIEES), Bogotá, Colombia. Docente investigadora. Email: hanwenzhang@usantotomas.edu.co
2Universidad Santo Tomás, Facultad de Estadística, Centro de Investigaciones y Estudios Estadísticos (CIEES), Bogotá, Colombia. Director. Email: hugogutierrez@usantotomas.edu.co
3Universidad Nacional de Colombia, Facultad de Ciencias, Departamento de Estadística, Bogotá, Colombia. Profesor asociado. Email: ecepedac@unal.edu.co
This paper presents a frequentist comparison of the performance of confidence and credibility intervals for the difference of two proportions from two independent samples. The comparison is carried out considering three frequentist criteria. It was found that the intervals with the best performance, in terms of coverage probability, are Bayesians; in terms of expected length and variance of the length, the Newcombe interval shows the best performance. As a final remark, it was found that traditional intervals such as the Wald and adjusted Wald have a poor performance.
Key words: Confidence intervals, Credibility intervals, Difference of two proportions..
Este artículo presenta una comparación del comportamiento de intervalos de confianza frecuentistas y de credibilidad bayesianos para la diferencia de dos proporciones provenientes de muestras aleatorias independientes. La comparación se lleva cabo considerando tres criterios frecuentistas con los cuales se concluyó que el mejor comportamiento, en términos de la probabilidad de cobertura, lo tienen los intervalos bayesianos, y en términos de la longitud esperada y varianza de la longitud el mejor comportamiento está dado por el intervalo frecuentista de Newcombe. Como resultado de esta investigación se encontró que los intervalos frecuentistas más populares como Wald y Wald ajustado tienen un comportamiento deficiente.
Palabras clave: intervalos de confianza, intervalos de credibilidad, diferencia de dos proporciones.
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References
1. Agresti, A., Bini, M., Bertaccini, B. & Ryu, E. (2008), 'Simultaneous Confidence Intervals for Comparing Binomial Parameters', Biometrics 64, 1270-1275.
2. Agresti, A. & Caffo, B. (2000), 'Simple and Effective Confidence Intervals for Proportions and Differences of Proportions', American Statistician 54(4), 280-288.
3. Agresti, A. & Min, Y. (2005), 'Frequentist Performance of Bayesian Confidence Intervals for Comparing Proportions in 2\times2 Contingency Tables', Biometrics 61, 515-523.
4. Bailey, W. N. (1934), 'On the reducibility of Appell's Function F4', The Quarterly Journal of Mathematics 5, 291-292.
5. Blaker, H. (2000), 'Confidence Curves and Improved Exact Confidence Intervals for Discrete Distributions', The Canadian Journal of Statistics 28(4), 783-798.
6. Brown, L. D., Cai, T. T. & DasGupta, A. (2001), 'Interval estimation of a binomial proportion', Statistical Science16, 101-133.
7. Carlin, B. P. & Louis, T. A. (1998), Bayes and Empirical Bayes Methods for Data Analysis, Chapman & Hall.
8. Cepeda, E., Aguilar, W., Cervantes, V., Corrales, M., Díaz, I. & Rodríguez, D. (2008), 'Intervalos de confianza e intervalos de credibilidad para una proporción', Revista Colombiana de Estadística 31(2), 211-228.
9. Correa, J. C. & Sierra, E. (2003), 'Intervalos de confianza para la comparación de dos proporciones', Revista Colombiana de Estadística 26(1), 61-75.
10. Gelman, A., Carlin, J. B., Stern, H. S. & Rubin, D. B. (2004), Bayesian Data Analysis, Second edn, Chapman & Hall.
11. Ghosh, B. K. (1979), 'A Comparison of Some Approximate Confidence Intervals for the Binomial Parameter',Journal of the American Statistical Association 74, 894-900.
12. Miettinen, O. S. & Nurminen, M. (1985), 'Comparative analysis of two rates', Statistics in Medicine 4, 213-226.
13. Newcombe, R. (1998a), 'Two-Sided Confidence Intervals for the Single Proportion: Comparison of Seven Methods. Statistics in Medicine', Statistics in Medicine 17, 857-872.
14. Newcombe, R. (1998b), 'Interval Estimation for the Difference between Independent Proportions: Comparison of Eleven Methods', Statistics in Medicine 17, 873-890.
15. Pan, W. (2002), 'Approximate Confidence Intervals for One Proportion and Difference of Two Proportions',Computational Statistics and Data Analysis 40, 143-157.
16. Pham-Gia, T. & Turkkan, N. (1993), 'Bayesian Analysis of the Difference of Two Proportions', Communications in Statistics. Theory and Methods 22(6), 1755-1771.
17. Vollset, S. E. (1993), 'Confidence intervals for a binomial proportion', Statistics in Medicine 12, 809-824.
18. Vos, P. W. & Hudson, S. (2008), 'Problems with Binomial Two-Sided Tests and the Associated Confidence Intervals', Australian & New Zealand Journal of Statistics 50(1), 81-89.
19. Wilson, E. B. (1927), 'Probable Inference, the Law of Succession, and Statistical Inference', Journal of the American Statistical Association 22, 209-212.
Este artículo se puede citar en LaTeX utilizando la siguiente referencia bibliográfica de BibTeX:
@ARTICLE{RCEv33n1a05,AUTHOR = {Zhang, Hanwen and Gutiérrez Rojas, Hugo Andrés and Cepeda Cuervo, Edilberto},
TITLE = {{Confidence and Credibility Intervals for the Difference of Two Proportions}},
JOURNAL = {Revista Colombiana de Estadística},
YEAR = {2010},
volume = {33},
number = {1},
pages = {63-88}
}
References
Agresti, A., Bini, M., Bertaccini, B. & Ryu, E. (2008), `Simultaneous Confidence Intervals for Comparing Binomial Parameters', Biometrics 64, 1270-1275.
Agresti, A. & Caffo, B. (2000), 'Simple and Effective Confidence Intervals for Pro-portions and Differences of Proportions', American Statistician 54(4), 280-288.
Agresti, A. & Min, Y. (2005), 'Requentist Performance of Bayesian Confidence Intervals for Comparing Proportions in 2x2 Contingency Tablas', Biometrics 61, 515-523.
Bailey, W. N. (1934), 'On the reducibility of Appell's Punction P4', The Quarterly Journal of Mathematics 5, 291-292.
Blaker, H. (2000), 'Confidence Curves and Improved Exact Confidence Intervals for Discreta Distributions', The Canadian Journal of Statistics 28(4), 783-798.
Brown, L. D., Cai, T. T. & DasGupta, A. (2001), Interval estimation of a binomial proportion', Statistical Science 16, 101-133.
Carlin, B. P. & Louis, T. A. (1998), Bayes and Empirical Bayes Methods for Data Analysis, Chapman & Hall.
Cepeda, E., Aguilar, W., Cervantes, V., Corrales, M., Díaz, I. & Rodríguez, D. (2008), 'Intervalos (le confianza e intervalos de credibilidad para una proporción', Revista Colombiana de Estadística 31(2), 211-228.
Correa, J. C. & Sierra, E. (2003), 'Intervalos (le confianza para la comparación (le dos proporciones', Revista Colombiana de Estadística 26(1), 61-75.
Gelman, A., Carlin, J. B., Stern, H. S. & Rubin, D. B. (2004), Bayesian Data Analysis, second edn, Chapman & Hall.
Ghosh, 13. K. (1979), 'A Comparison of Some Approximate Confidence IntervaLs for the Binomial Parameter', Journal of the American Statistical Association 74, 894-900.
Miettinen, 0. S. & Nurminen, M. (1985), `Comparative analysis of two rates', Statistics in Medicine 4, 213-226.
Newcombe, R. (1998a), Interval Estimation for the Difference between Indepen-dent Proportions: Comparison of Eleven Methods', Statistics in Medicine 17, 873-890.
Newcombe, R. (1998b), `Two-Sided Confidence Intervals for the Single Proportion: Comparison of Seven Methods. Statistics in Medicine', Statistics in Medicine 17, 857-872.
Pan, W. (2002), `Approximate Confidence Intervals for One Proportion and Dif-ference of Two Proportions', Computational Statistics and Data Analysis 40, 143-157.
Pham-Gia, T. & Turkkan, N. (1993), `Bayesian Analysis of the Difference of Two Proportions', Communications in Statistics. Theory and Methods 22(6), 1755-1771.
Vollset, S. E. (1993), `Confidence intervals for a binomial proportion', Statistics in Medicine 12, 809-824.
Vos, P. W. & lludson, S. (2008), Problems with Binomial Two-Sided Tests and the Associated Confidence Intervals', Australian & New Zealand Journal of Statistics 50(1), 81-89.
Wilson, E. B. (1927), 'Probable Inference, the Law of Succession, and Statistical Inference', Journal of the American Statistical Association 22, 209-212.
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