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

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  • 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
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    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.
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    Cited by:

    1. 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.
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    4. 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.

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