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Some tests for detecting trends based on the modified Baumgartner–Weiß–Schindler statistics


  • Shan, Guogen
  • Ma, Changxing
  • Hutson, Alan D.
  • Wilding, Gregory E.


We propose a modified nonparametric Baumgartner–Weiß–Schindler test and investigate its use in testing for trends among K binomial populations. Exact conditional and unconditional approaches to p-value calculation are explored in conjunction with the statistic in addition to a similar test statistic proposed by Neuhäuser (2006), the unconditional approaches considered including the maximization approach (Basu, 1977), the confidence interval approach (Berger and Boos, 1994), and the E+M approach (Lloyd, 2008). The procedures are compared with regard to actual Type I error and power and examples are provided. The conditional approach and the E+M approach performed well, with the E+M approach having an actual level much closer to the nominal level. The E+M approach and the conditional approach are generally more powerful than the other p-value calculation approaches in the scenarios considered. The power difference between the conditional approach and the E+M approach is often small in the balance case. However, in the unbalanced case, the power comparison between those two approaches based on our proposed test statistic show that the E+M approach has higher power than the conditional approach.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:csdana:v:57:y:2013:i:1:p:246-261
    DOI: 10.1016/j.csda.2012.04.021

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    References listed on IDEAS

    1. Markus Neuhäuser, 2005. "Exact tests based on the Baumgartner-Weiß-Schindler statistic—A survey," Statistical Papers, Springer, vol. 46(1), pages 1-29, January.
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    Cited by:

    1. 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.
    2. 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.
    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. 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.
    5. 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.


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