IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v52y2008i11p5046-5053.html
   My bibliography  Save this article

An exact confidence set for two binomial proportions and exact unconditional confidence intervals for the difference and ratio of proportions

Author

Listed:
  • Reiczigel, Jeno
  • Abonyi-Tóth, Zsolt
  • Singer, Júlia

Abstract

An exact joint confidence set is proposed for two binomial parameters estimated from independent samples. Its construction relies on inverting the minimum volume test, a two-dimensional analogue of Sterne's test for a single probability. The algorithm involves computer-intensive exact computation based on binomial probabilities. The proposed confidence set has good coverage properties and it performs much better than the likelihood-based confidence set for the same problem. Applying the principle of intersection-union tests, the method can be used to derive exact tests and confidence intervals for functions of the two binomial parameters. Based on this, new exact unconditional two-sided confidence intervals are proposed for the risk difference and risk ratio. The performance of the new intervals is comparable to that of certain well-known confidence intervals in small samples. Extension of the methods described to two hypergeometric or two Poisson variables is straightforward.

Suggested Citation

  • Reiczigel, Jeno & Abonyi-Tóth, Zsolt & Singer, Júlia, 2008. "An exact confidence set for two binomial proportions and exact unconditional confidence intervals for the difference and ratio of proportions," Computational Statistics & Data Analysis, Elsevier, vol. 52(11), pages 5046-5053, July.
    • Handle: RePEc:eee:csdana:v:52:y:2008:i:11:p:5046-5053
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-9473(08)00249-1
    Download Restriction: Full text for ScienceDirect subscribers only.
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Santner, Thomas J. & Pradhan, Vivek & Senchaudhuri, Pralay & Mehta, Cyrus R. & Tamhane, Ajit, 2007. "Small-sample comparisons of confidence intervals for the difference of two independent binomial proportions," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 5791-5799, August.
    2. Agresti, Alan & Gottard, Anna, 2007. "Nonconservative exact small-sample inference for discrete data," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 6447-6458, August.
    3. Gupta, Ramesh C. & Tian, Suzhong, 2007. "Statistical inference for the risk ratio in 2x2 binomial trials with structural zero," Computational Statistics & Data Analysis, Elsevier, vol. 51(6), pages 3070-3084, March.
    4. James F. Troendle & Jennifer Frank, 2001. "Unbiased Confidence Intervals for the Odds Ratio of Two Independent Binomial Samples with Application to Case–Control Data," Biometrics, The International Biometric Society, vol. 57(2), pages 484-489, June.
    5. Munk, A. & Skipka, G. & Stratmann, B., 2005. "Testing general hypotheses under binomial sampling: the two sample case--asymptotic theory and exact procedures," Computational Statistics & Data Analysis, Elsevier, vol. 49(3), pages 723-739, June.
    6. Alan Agresti & Yongyi Min, 2001. "On Small-Sample Confidence Intervals for Parameters in Discrete Distributions," Biometrics, The International Biometric Society, vol. 57(3), pages 963-971, September.
    7. Skipka, G. & Munk, A. & Freitag, G., 2004. "Unconditional exact tests for the difference of binomial probabilities--contrasted and compared," Computational Statistics & Data Analysis, Elsevier, vol. 47(4), pages 757-773, November.
    8. Ivan S. F. Chan & Zhongxin Zhang, 1999. "Test-Based Exact Confidence Intervals for the Difference of Two Binomial Proportions," Biometrics, The International Biometric Society, vol. 55(4), pages 1202-1209, December.
    9. Martin Andres, A. & Herranz Tejedor, I., 2004. "Exact unconditional non-classical tests on the difference of two proportions," Computational Statistics & Data Analysis, Elsevier, vol. 45(2), pages 373-388, March.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Sauer, Stephan & Coppens, François & Mayer, Manuel & Millischer, Laurent & Resch, Florian & Schulze, Klaas, 2016. "Advances in multivariate back-testing for credit risk underestimation," Working Paper Series 1885, European Central Bank.
    2. Schaarschmidt, Frank & Gerhard, Daniel & Vogel, Charlotte, 2017. "Simultaneous confidence intervals for comparisons of several multinomial samples," Computational Statistics & Data Analysis, Elsevier, vol. 106(C), pages 65-76.
    3. Jan Klaschka & Jenő Reiczigel, 2021. "On matching confidence intervals and tests for some discrete distributions: methodological and computational aspects," Computational Statistics, Springer, vol. 36(3), pages 1775-1790, September.
    4. Vytautas Januskevicius & Grazina Januskeviciene & Petras Prakas & Dalius Butkauskas & Saulius Petkevicius, 2019. "Prevalence and intensity of Sarcocystis spp. infection in animals slaughtered for food in Lithuania," Veterinární medicína, Czech Academy of Agricultural Sciences, vol. 64(4), pages 149-157.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Alan Agresti & Sabrina Giordano & Anna Gottard, 2022. "A Review of Score-Test-Based Inference for Categorical Data," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 20(1), pages 31-48, September.
    2. Munk, A. & Skipka, G. & Stratmann, B., 2005. "Testing general hypotheses under binomial sampling: the two sample case--asymptotic theory and exact procedures," Computational Statistics & Data Analysis, Elsevier, vol. 49(3), pages 723-739, June.
    3. Joseph B. Lang, 2017. "Mean-Minimum Exact Confidence Intervals," The American Statistician, Taylor & Francis Journals, vol. 71(4), pages 354-368, October.
    4. Tang, Man-Lai & Qiu, Shi-Fang & Poon, Wai-Yin, 2012. "Confidence interval construction for disease prevalence based on partial validation series," Computational Statistics & Data Analysis, Elsevier, vol. 56(5), pages 1200-1220.
    5. Martin Biehler & Heinz Holling & Philipp Doebler, 2015. "Saddlepoint Approximations of the Distribution of the Person Parameter in the Two Parameter Logistic Model," Psychometrika, Springer;The Psychometric Society, vol. 80(3), pages 665-688, September.
    6. Philippe Flandre, 2011. "Statistical Methods in Recent HIV Noninferiority Trials: Reanalysis of 11 Trials," PLOS ONE, Public Library of Science, vol. 6(9), pages 1-8, September.
    7. Santner, Thomas J. & Pradhan, Vivek & Senchaudhuri, Pralay & Mehta, Cyrus R. & Tamhane, Ajit, 2007. "Small-sample comparisons of confidence intervals for the difference of two independent binomial proportions," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 5791-5799, August.
    8. Kabaila, Paul, 2008. "Statistical properties of exact confidence intervals from discrete data using studentized test statistics," Statistics & Probability Letters, Elsevier, vol. 78(6), pages 720-727, April.
    9. Almendra-Arao, Félix, 2012. "Efficient calculation of test sizes for non-inferiority," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 4138-4145.
    10. Devan V. Mehrotra & Ivan S. F. Chan & Roger L. Berger, 2003. "A Cautionary Note on Exact Unconditional Inference for a Difference between Two Independent Binomial Proportions," Biometrics, The International Biometric Society, vol. 59(2), pages 441-450, June.
    11. Chris J. Lloyd, 2010. "Bootstrap and Second-Order Tests of Risk Difference," Biometrics, The International Biometric Society, vol. 66(3), pages 975-982, September.
    12. Schaarschmidt, Frank & Gerhard, Daniel & Vogel, Charlotte, 2017. "Simultaneous confidence intervals for comparisons of several multinomial samples," Computational Statistics & Data Analysis, Elsevier, vol. 106(C), pages 65-76.
    13. Jan Klaschka & Jenő Reiczigel, 2021. "On matching confidence intervals and tests for some discrete distributions: methodological and computational aspects," Computational Statistics, Springer, vol. 36(3), pages 1775-1790, September.
    14. Agresti, Alan & Gottard, Anna, 2007. "Nonconservative exact small-sample inference for discrete data," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 6447-6458, August.
    15. Nian-Sheng Tang & Man-Lai Tang, 2002. "Exact Unconditional Inference for Risk Ratio in a Correlated 2 × 2 Table with Structural Zero," Biometrics, The International Biometric Society, vol. 58(4), pages 972-980, December.
    16. Peng Bai & Wen Gan & Lei Shi, 2011. "Bayesian confidence interval for the risk ratio in a correlated 2 × 2 table with structural zero," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(12), pages 2805-2817, February.
    17. Nicholas Taylor, 2010. "The Determinants of Future U.S. Monetary Policy: High‐Frequency Evidence," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 42(2‐3), pages 399-420, March.
    18. Habiger, Joshua D. & McCann, Melinda H. & Tebbs, Joshua M., 2013. "On optimal confidence sets for parameters in discrete distributions," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 297-303.
    19. Barry Kronenfeld & Timothy Leslie, 2015. "Restricted random labeling: testing for between-group interaction after controlling for joint population and within-group spatial structure," Journal of Geographical Systems, Springer, vol. 17(1), pages 1-28, January.
    20. Martin Andres, A. & Herranz Tejedor, I., 2004. "Exact unconditional non-classical tests on the difference of two proportions," Computational Statistics & Data Analysis, Elsevier, vol. 45(2), pages 373-388, March.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:52:y:2008:i:11:p:5046-5053. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.