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An exact test for trend among binomial proportions based on a modified Baumgartner-Weiss-Schindler statistic

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  • Markus Neuhauser

Abstract

The Cochran-Armitage test is the most frequently used test for trend among binomial proportions. This test can be performed based on the asymptotic normality of its test statistic or based on an exact null distribution. As an alternative, a recently introduced modification of the Baumgartner-Weiss-Schindler statistic, a novel nonparametric statistic, can be used. Simulation results indicate that the exact test based on this modification is preferable to the Cochran-Armitage test. This exact test is less conservative and more powerful than the exact Cochran-Armitage test. The power comparison to the asymptotic Cochran-Armitage test does not show a clear winner, but the difference in power is usually small. The exact test based on the modification is recommended here because, in contrast to the asymptotic Cochran-Armitage test, it guarantees a type I error rate less than or equal to the significance level. Moreover, an exact test is often more appropriate than an asymptotic test because randomization rather than random sampling is the norm, for example in biomedical research. The methods are illustrated with an example data set.

Suggested Citation

  • Markus Neuhauser, 2006. "An exact test for trend among binomial proportions based on a modified Baumgartner-Weiss-Schindler statistic," Journal of Applied Statistics, Taylor & Francis Journals, vol. 33(1), pages 79-88.
    • Handle: RePEc:taf:japsta:v:33:y:2006:i:1:p:79-88
    DOI: 10.1080/02664760500389756
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    References listed on IDEAS

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    1. Neuhauser, Markus & Hothorn, Ludwig A., 1999. "An exact Cochran-Armitage test for trend when dose-response shapes are a priori unknown," Computational Statistics & Data Analysis, Elsevier, vol. 30(4), pages 403-412, June.
    2. D. A. Williams, 1988. "Tests for Differences between Several Small Proportions," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 37(3), pages 421-434, November.
    3. Cohen Arthur & Sackrowitz Harold B., 2000. "Testing Whether Treatment Is “Better“ Than Control With Ordered Categorical Data: Definitions And Complete Class Theorems," Statistics & Risk Modeling, De Gruyter, vol. 18(1), pages 1-26, January.
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