The Effect of Dependence on Confidence Intervals for a Population Proportion

American Statistician

Volumn 58, Issue 2, 2004, Pages 124-130

  Miao, Weiwen ^a   Gastwirth, Joseph L ^b  

^a MACALESTER COLLEGE   (United States)

^b GEORGE WASHINGTON UNIVERSITY   (United States)

Author keywords

Coverage probability; Dependent observations; Expected length of confidence interval; Jury discrimination

Indexed keywords

EID: 2442457954     PISSN: 00031305     EISSN: 15372731     Source Type: Journal    
DOI: 10.1198/0003130043303     Document Type: Article

References (30)

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. Bedrick, E. J., and Aragon, J. (1989), “Approximate Confidence Intervals for the Parameters of a Stationary Binary Markov Chain,” Technometrics, 31, 437-448.
3. Beran, J. (1994), Statistics for Long-Memory Processes, New York: Chapman and Hall.
4. Blyth, C. R., and Still, H. A. (1983), “Binomial Confidence Intervals,” Journal of American StatisticalAssociation, 78, 108-116.
5. Bohning, D. (1994), “Better Approximate Confidence Intervals for a Binomial Parameter,” The Canadian Journal of Statistics, 22, 207-218.
6. Brainerd, B., and Chang, S. M. (1982), “Number of Occurrences in Two-State Markov Chains, With an Application in Linguistics,” The Canadian Journal of Statistics, 10,225-231.
7. Brown, L. D., Cai, T., and Dasgupta, A. (2001), “Interval Estimation for a Binomial Proportion,” Statistical Science, 16, 101-133.
8. Brown, L. D., Cai, T., and Dasgupta, A. (2002), “Confidence Intervalsfor a Binomial Proportionand Asymptotic Expansions,” The Annals of Statistics, 30, 160-201.
9. Chernick, M., andLiu, C. Y. (2002), “TheSaw-Toothed Behavior of Power Versus Sample Size and Software Solutions: Single Binomial Proportion Using Exact Methods,” The American Statistician, 56, 149-155.
10. Crow, E. L. (1979), “Approximate Confidence Intervals for a Proportion from Markov Dependent Trials,” Communications in Statistics—Simulation and Computation, B8, 1-42.
11. Crow, E. L., and Miles, M. J. (1979), “Validation of Estimators of a Proportion from Markov Dependent Trials,” Communication of Statistics—Simulation and Computation, B8, 25-52.
12. Fleiss, J. L. (1981), Statistical Methods for Rates and Proportions (2nd ed.), New York: Wiley.
13. Gastwirth, J. L. (1997), “Statistical Evidence in Discrimination Cases,” Journal of the Royal Statistical Society, Series A, 160, 289-303.
14. Gastwirth, J. L., and Miao, W. (2002), “The Potential Effect of Statistical Dependence in the Analysis of Data in Jury Discrimination Cases: Moultrie v. Martin Reconsidered,” Jurimetrics, 43, 115-128.
15. Gastwirth, J. L., and Rubin, H. (1971), “Effect of Dependence on the Level of Some One-Sample Tests,” Journal of the American Statistical Association, 66, 816-820.
16. Gastwirth, J. L., and Rubin, H. (1975), “The Asymptotic Distribution Theory of the Empirical CDF for Mixing Stochastic Processes,” The Annals of Statistics, 3, 809-824.
17. Ghosh, B. K. (1979), “A Comparison of Some Approximate Confidence Intervals for the Binomial Parameter,” Journal of American Statistical Association, 74, 894-900.
18. Herrndorf, N. (1984), “A Functional Central Limit Theorem for Weakly Dependent Sequences of Random Variables,” The Annals of Probability, 12, 141-153.
19. Hoeffding, W., and Robbins, H. E. (1948), “The Central Limit Theory for Dependent Random Variables,” Duke Mathematics Journal, 15, 773-780.
20. Johnson, C. A., and Klotz, J. H. (1974), “The Atom Probe and Markov Chain Statistics of Clustering,” Technometrics, 16,483-493.
21. Katz, R. W. (1981), “On Some Criteria for Estimating the Order of a Markov Chain,” Technometrics, 23, 243-249.
22. Klotz, J. H. (1973), “Statistical Inference in Bernoulli Trials with Dependence,” The Annals of Statistics, 373-379.
23. Ladd, D. W. (1975), “An Algorithm for the Binomial Distirbution with Dependent Trials,” Journal of the American Statistical Association, 70, 333-340.
24. Newcombe, R. G. (1998), “Two-Sided Confidence Intervals for the Single Proportion: Comparison of Seven Methods,” Statistics in Medicine, 17,857-872.
25. Rosenblatt, M. (1984), “Asymptotic Normality, Strong Mixing and Spectral Density Estimate,” The Annals of Probability, 12, 1167-1180.
26. Santner, T. J. (1998), “Teaching Large-Sample Binomial Confidence Intervals,” Teaching Statistics, 20, 20-23.
27. Serfling, R. J. (1968), “The Wilcoxon Two-Sample Statistics on Strong-Mixing Processes,” Annals of Mathematical Statistics, 1202-1209.
28. van Belle, G. (2002), Statistical Rules of Thumb, New York: Wiley.
29. Vollset, S. E. (1993), “Confidence Intervalsfor a Binomial Proportion,” Statistics in Medicine, 12, 809-824.
30. Wolff, S. S., Gastwirth, J. L., and Rubin, H. (1967), “TheEffect of Autoregressive Dependence on a Nonparametric Test,” IEEE Transaction on Information Theory, 13,311-313.