IDEAS home Printed from https://ideas.repec.org/a/bla/stanee/v69y2015i1p67-83.html
   My bibliography  Save this article

Unconditional tests for association in 2 × 2 contingency tables in the total sum fixed design

Author

Listed:
  • Guogen Shan
  • Gregory Wilding

Abstract

type="main" xml:id="stan12047-abs-0001"> The asymptotic approach and Fisher's exact approach have often been used for testing the association between two dichotomous variables. The asymptotic approach may be appropriate to use in large samples but is often criticized for being associated with unacceptable high actual type I error rates for small to medium sample sizes. Fisher's exact approach suffers from conservative type I error rates and low power. For these reasons, a number of exact unconditional approaches have been proposed, which have been seen to be generally more powerful than exact conditional counterparts. We consider the traditional unconditional approach based on maximization and compare it to our presented approach, which is based on estimation and maximization. We extend the unconditional approach based on estimation and maximization to designs with the total sum fixed. The procedures based on the Pearson chi-square, Yates's corrected, and likelihood ratio test statistics are evaluated with regard to actual type I error rates and powers. A real example is used to illustrate the various testing procedures. The unconditional approach based on estimation and maximization performs well, having an actual level much closer to the nominal level. The Pearson chi-square and likelihood ratio test statistics work well with this efficient unconditional approach. This approach is generally more powerful than the other p-value calculation methods in the scenarios considered.

Suggested Citation

  • Guogen Shan & Gregory Wilding, 2015. "Unconditional tests for association in 2 × 2 contingency tables in the total sum fixed design," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 69(1), pages 67-83, February.
    • Handle: RePEc:bla:stanee:v:69:y:2015:i:1:p:67-83
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1111/stan.12047
    Download Restriction: Access to full text is restricted to subscribers.
    ---><---

    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. Chris J. Lloyd, 2008. "A New Exact and More Powerful Unconditional Test of No Treatment Effect from Binary Matched Pairs," Biometrics, The International Biometric Society, vol. 64(3), pages 716-723, September.
    2. Shan, Guogen, 2014. "Exact approaches for testing non-inferiority or superiority of two incidence rates," Statistics & Probability Letters, Elsevier, vol. 85(C), pages 129-134.
    3. Shan, Guogen & Ma, Changxing & Hutson, Alan D. & Wilding, Gregory E., 2013. "Some tests for detecting trends based on the modified Baumgartner–Weiß–Schindler statistics," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 246-261.
    4. 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.
    Full references (including those not matched with items on IDEAS)

    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. Shan, Guogen, 2013. "More efficient unconditional tests for exchangeable binary data with equal cluster sizes," Statistics & Probability Letters, Elsevier, vol. 83(2), pages 644-649.
    2. Chris J. Lloyd, 2010. "Bootstrap and Second-Order Tests of Risk Difference," Biometrics, The International Biometric Society, vol. 66(3), pages 975-982, September.
    3. Shan, Guogen, 2014. "Exact approaches for testing non-inferiority or superiority of two incidence rates," Statistics & Probability Letters, Elsevier, vol. 85(C), pages 129-134.
    4. Guogen Shan & Changxing Ma, 2014. "Efficient tests for one sample correlated binary data with applications," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 23(2), pages 175-188, June.
    5. Chris J. Lloyd, 2008. "A New Exact and More Powerful Unconditional Test of No Treatment Effect from Binary Matched Pairs," Biometrics, The International Biometric Society, vol. 64(3), pages 716-723, September.
    6. Phipps, Mary C. & Byron, Peter M., 2007. "A filter for "confidence interval P-values"," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 6435-6446, August.
    7. Xiaochun Li & Mengling Liu & Judith D. Goldberg, 2011. "A Note on Monotonicity Assumptions for Exact Unconditional Tests in Binary Matched-Pairs Designs," Biometrics, The International Biometric Society, vol. 67(4), pages 1666-1668, December.
    8. Stefan Wellek, 2015. "Nearly exact sample size calculation for powerful non-randomized tests for differences between binomial proportions," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 69(4), pages 358-373, November.
    9. Langaas Mette & Bakke Øyvind, 2014. "Robust methods to detect disease-genotype association in genetic association studies: calculate p-values using exact conditional enumeration instead of simulated permutations or asymptotic approximati," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 13(6), pages 1-18, December.
    10. Joseph Obaje Ataguba & Celestine Udoka Ugonabo, 2023. "Framework for measuring the efficiency and efficacy of sale of distressed mortgaged properties using imports of statistical tests deployed in clinical studies," SN Business & Economics, Springer, vol. 3(8), pages 1-32, August.
    11. Hidetoshi Murakami, 2016. "All-pairs multiple comparisons based on the Cucconi test," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 100(3), pages 355-368, July.

    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:bla:stanee:v:69:y:2015:i:1:p:67-83. 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: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0039-0402 .

    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.