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

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  • 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
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. 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.
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