Constructing Simultaneous Confidence Intervals for the Difference of Proportions from Multivariate Binomial Distributions

Jeong, Hyeong-Chul;Kim, Dae-Hak

  • Published : 2009.02.28


In this paper, we consider simultaneous confidence intervals for the difference of proportions between two groups taken from multivariate binomial distributions in a nonparametric way. We briefly discuss the construction of simultaneous confidence intervals using the method of adjusting the p-values in multiple tests. The features of bootstrap simultaneous confidence intervals using non-pooled samples are presented. We also compute confidence intervals from the adjusted p-values of multiple tests in the Westfall (1985) style based on a pooled sample. The average coverage probabilities of the bootstrap simultaneous confidence intervals are compared with those of the Bonferroni simultaneous confidence intervals and the Sidak simultaneous confidence intervals. Finally, we give an example that shows how the proposed bootstrap simultaneous confidence intervals can be utilized through data analysis.


Multivariate binomial distribution;simultaneous confidence intervals;bootstrap;multiple test;pooled sample


  1. Beal, S. L. (1987). Asymptotic confidence intervals for the difference between two binomial parameters for use with small samples, Biometrics, 43, 941-950
  2. Brown, C C and Fears, T. R. (1981). Exact significance levels for multiple binomial testing with application to carcinogenicity screens, Biometrics, 37, 763-774
  3. Freedman, D. A. (1984). On bootstrapping two-stage least-squares estimates in stationary linear models, The Annals of Statistics, 12, 827-842
  4. Holland, B. S. and Copenhaver, M. D. (1987). An improved sequentially rejective bonferroni test procedure, Biometrics, 43, 417-424
  5. Jeong, H. C, Jhun, M. and Lee, J. W. (2007). Estimating the simultaneous confidence levels for the difference of proportions from multivariate binomial distributions, Journal of the Korean Statistical Society, 36, 397-410
  6. Jhun, M. and Jeong, H. C (2000). Applications of bootstrap methods for categorical data analysis, Computational Statistics & Data Analysis, 35, 83-91
  7. Jhun, M., Jeong, H. C. and Bahng, J. S. (2007). Simultaneous confidence intervals for the mean of multivariate Poisson distribution: A comparison, Communications in Statistics-Simulation and Computation, 36, 151-164
  8. Park, C. G., Park, T. P. and Shin, D. W. (1996). A simple method for generating correlated Binary varites, American Statistician, 50, 306-310
  9. Singh, K. (1981). On the asymptotic accuracy of Efron's bootstrap, The Annals of Statistics, 9, 1187-1195
  10. Thombs, L. A. and Schucany, W. R. (1990). Bootstrap prediction intervals for autoregression, Journal of the American Statistical Association, 85, 486-492
  11. Westfall, P. H. and Young, S. S. (1989). P-value adjustments for multiple tests in multivariate binomial models, Journal of the American Statistical Association, 84, 780-786
  12. Westfall P. H. (1985). Simultaneous small-sample multivariate bernoulli confidence intervals, Biometrics, 41, 1001-1013
  13. Westfall, P. H. and Young, S. S. (1993). Resampling-Based Multiple Testing: Examples and Methods for p- Value Adjustment, John Wiley & Sons, New York
  14. Wood roofe, M. and Jhun, M. (1988). Singh's theorem in the lattice case, Statistics & Probability Letters, 7, 201-205