Student or educator? Sign up with your school email and get 6 months of Pro free.
CoChat
Sign Up
Cited by 3,538

The DOI matches its Crossref record; 2 of the 2 references it cites were found in a registry or an index.

Interval Estimation for a Binomial Proportion

Brown, Lawrence D., Cai, T. Tony, DasGupta, Anirban·2001·Statistical Science
DOI 10.1214/ss/1009213286
Open this paper in CoChat — free account

Abstract

We revisit the problem of interval estimation of a binomial proportion. The erratic behavior of the coverage probability of the standard Wald confidence interval has previously been remarked on in the literature (Blyth and Still, Agresti and Coull, Santner and others). We begin by showing that the chaotic coverage properties of the Wald interval are far more persistent than is appreciated. Furthermore, common textbook prescriptions regarding its safety are misleading and defective in several respects and cannot be trusted. This leads us to consideration of alternative intervals. A number of natural alternatives are presented, each with its motivation and context. Each interval is examined for its coverage probability and its length. Based on this analysis, we recommend the Wilson interval or the equal-tailed Jeffreys prior interval for small n and the interval suggested in Agresti and Coull for larger n. We also provide an additional frequentist justification for use of the Jeffreys interval.

Overview

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Integrity signals

Registry

Crossref · 10.1214/ss/1009213286

Cites

2 of 2 references verified0 citation errors · 0 not checkable

Statistics

Verification

Claims the paper makes

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

The self-check needs the paper’s full text.

Citations

Cites

Show all 2 references

Research works printed but not linked: 40

  1. Rao, C. R. (1973). Linear statistical inference and its applications. Wiley, New York. · DOI · Paper page
  2. Datta, G. S. and Ghosh, M. (1996). On the invariance of noninformative priors. Ann. Statist. 24 141-159. · doi:10.1214/aos/1033066203
  3. AGRESTI, A. and COULL, B. A. (1998). Approximate is better than "exact" for interval estimation of binomial proportions. Amer. Statist. 52 119-126. · DOI · Paper page
  4. BLYTH, C. R. and STILL, H. A. (1983). Binomial confidence intervals. J. Amer. Statist. Assoc. 78 108-116. · doi:10.2307/2287116
  5. GHOSH, J. K. (1994). Higher Order Asymptotics. IMS, Hayward, CA. · doi:10.1214/cbms/1462297300
  6. STERNE, T. E. (1954). Some remarks on confidence or fiducial limits. Biometrika 41 275-278. · DOI
  7. Tibshirani, R. (1989). Noninformative priors for one parameter of many. Biometrika 76 604-608. · DOI · Paper page
  8. Wilson, E. B. (1927). Probable inference, the law of succession, andstatistical inference. J. Amer. Statist. Assoc. 22 209-212. · DOI · Paper page
  9. Larson, H. J. (1974). Introduction to Probability Theory and Statistical Inference, 2nded. Wiley, New York.
  10. Yamagami, S. and Santner, T. J. (1993). Invariant small sample confidence intervals for the difference of two success probabilities. Comm. Statist. Simul. Comput. 22 33-59. · DOI
  11. Anscombe, F. J. (1956). On estimating binomial response relations. Biometrika 43 461-464. · DOI · Paper page
  12. Berger, J. O. (1985). Statistical Decision Theory and Bayesian Analysis, 2nded. Springer, New York. · DOI · Paper page
  13. Casella, G. (1986). Refining binomial confidence intervals Canad. J. Statist. 14 113-129. · DOI
  14. Clopper, C. J. and Pearson, E. S. (1934). The use of confidence or fiducial limits illustrated in the case of the binomial. Biometrika 26 404-413. · DOI · Paper page
  15. Cressie, N. (1980). A finely tunedcontinuity correction. Ann. Inst. Statist. Math. 30 435-442. · doi:10.1007/bf02480234
  16. Ghosh, B. K. (1979). A comparison of some approximate confidence intervals for the binomial parameter J. Amer. Statist. Assoc. 74 894-900. · doi:10.2307/2286420
  17. Hall, P. (1982). Improving the normal approximation when constructing one-sided confidence intervals for binomial or Poisson parameters. Biometrika 69 647-652. · doi:10.1093/biomet/69.3.647
  18. Newcombe, R. G. (1998). Two-sided confidence intervals for the single proportion; comparison of several methods. Statistics in Medicine 17 857-872. · DOI
  19. Samuels, M. L. and Witmer, J. W. (1999). Statistics for the Life Sciences, 2nded. Prentice Hall, Englewood Cliffs, NJ.
  20. Santner, T. J. (1998). A note on teaching binomial confidence intervals. Teaching Statistics 20 20-23. · DOI
  21. Santner, T. J. and Duffy, D. E. (1989). The Statistical Analysis of Discrete Data. Springer, Berlin. · DOI · Paper page
  22. Strawderman, R. L. and Wells, M. T. (1998). Approximately exact inference for the common odds ratio in several 2 × 2 tables (with discussion). J. Amer. Statist. Assoc. 93 1294- 1320. · DOI
  23. Tamhane, A. C. and Dunlop, D. D. (2000). Statistics and Data Analysis from Elementary to Intermediate. Prentice Hall, EnglewoodCliffs, NJ.
  24. Vollset, S. E. (1993). Confidence intervals for a binomial proportion. Statistics in Medicine 12 809-824. · DOI · Paper page
  25. Agresti, A. andCaffo, B. (2000). Simple andeffective confidence intervals for proportions and differences of proportions result from adding two successes and two failures. Amer. Statist. 54. To appear. · DOI
  26. Aitkin, M., Anderson, D., Francis, B. and Hinde, J. (1989). Statistical Modelling in GLIM. OxfordUniv. Press.
  27. Boos, D. D. and Hughes-Oliver, J. M. (2000). How large does n have to be for Z and t intervals? Amer. Statist. 54 121-128. Brown, L. D., Cai, T. and DasGupta, A. (2000a). Confidence intervals for a binomial proportion andasymptotic expansions. Ann. Statist. To appear. Brown, L. D., Cai, T. and DasGupta, A. (2000b). Interval estimation in exponential families. Technical report, Dept. Statistics, Univ. Pennsylvania. · doi:10.2307/2685927
  28. Cai, T. (2001). One-sided confidence intervals and hypothesis testing in discrete distributions. Preprint.
  29. Coe, P. R. and Tamhane, A. C. (1993). Exact repeatedconfidence intervals for Bernoulli parameters in a group sequential clinical trial. Controlled Clinical Trials 14 19-29. · DOI
  30. Cox, D. R. and Reid, N. (1987). Orthogonal parameters and approximate conditional inference (with discussion). J. Roy. Statist. Soc. Ser. B 49 113-147. · DOI · Paper page
  31. DasGupta, A. (2001). Some further results in the binomial interval estimation problem. Preprint.
  32. Duffy, D. and Santner, T. J. (1987). Confidence intervals for a binomial parameter basedon multistage tests. Biometrics 43 81-94. · DOI
  33. Gart, J. J. (1966). Alternative analyses of contingency tables. J. Roy. Statist. Soc. Ser. B 28 164-179. · DOI
  34. Garvan, C. W. and Ghosh, M. (1997). Noninformative priors for dispersion models. Biometrika 84 976-982. · doi:10.1093/biomet/84.4.976
  35. Hall, P. (1983). Chi-squaredapproximations to the distribution of a sum of independent random variables. Ann. Statist. 11 1028-1036. · doi:10.1214/aop/1176993451
  36. Jennison, C. and Turnbull, B. W. (1983). Confidence intervals for a binomial parameter following a multistage test with application to MIL-STD 105D andmedical trials. Technometrics, 25 49-58. · DOI
  37. Pratt, J. W. (1961). Length of confidence intervals. J. Amer. Statist. Assoc. 56 549-567. · doi:10.2307/2282079
  38. Rindskopf, D. (2000). Letter to the editor. Amer. Statist. 54 88. · DOI
  39. Rubin, D. B. and Schenker, N. (1987). Logit-basedinterval estimation for binomial data using the Jeffreys prior. Sociological Methodology 17 131-144. · DOI
  40. Welch, B. L. and Peers, H. W. (1963). On formula for confidence points basedon intergrals of weightedlikelihoods. J. Roy. Statist. Ser. B 25 318-329. · DOI · Paper page

Cited by

Metadata

Authors
Brown, L. D., Cai, T. T., & DasGupta, A.
Venue
Statistical Science
Publisher
Institute of Mathematical Statistics
Published
2001-05-01
Volume
16
Issue
2
Pages
101-133
ISSN
0883-4237 (ISSN-L)
DOI
10.1214/ss/1009213286
OpenAlex
W2106578604
Cited by
3,538
References
2
FWCI
23.75
Type
journal article
Language
ca
Open access
closed

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review

Data sources

Bibliographic data: Semantic Scholar, OpenAlex, Crossref.

Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).

Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.