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Tests for Differences between Several Small Proportions

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  • D. A. Williams

Abstract

Motivated by the practical problem of analysing data from in vitro chromosome aberration assays this paper considers tests for differences between several proportions. Various test statistics are described, and the small sample behaviour of tests which refer these statistics to approximating continuous distributions is investigated. The inaccuracies of these approximate tests can be avoided by using the exact conditional distribution of the test statistic. The calculation of the exact significance probability is described and the computation costs are shown to be negligible compared with the costs of data acquisition. Finally the use of the mid‐p value is advocated for discretely distributed test statistics.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:jorssc:v:37:y:1988:i:3:p:421-434
    DOI: 10.2307/2347316
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    Cited by:

    1. Bretz, Frank, 2006. "An extension of the Williams trend test to general unbalanced linear models," Computational Statistics & Data Analysis, Elsevier, vol. 50(7), pages 1735-1748, April.
    2. 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.
    3. 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.

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