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Global and multiple test procedures using ordered p-values—a review

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  • Gudrun Bernhard
  • Markus Klein
  • Gerhard Hommel

Abstract

This paper reviews global and multiple tests for the combination ofn hypotheses using the orderedp-values of then individual tests. In 1987, Röhmel and Streitberg presented a general method to construct global level α tests based on orderedp-values when there exists no prior knowledge regarding the joint distribution of the corresponding test statistics. In the case of independent test statistics, construction of global tests is available by means of recursive formulae presented by Bicher (1989), Kornatz (1994) and Finner and Roters (1994). Multiple test procedures can be developed by applying the closed test principle using these global tests as building blocks. Liu (1996) proposed representing closed tests by means of “critical matrices” which contain the critical values of the global tests. Within the framework of these theoretical concepts, well-known global tests and multiple test procedures are classified and the relationships between the different tests are characterised. Copyright Springer-Verlag 2004

Suggested Citation

  • Gudrun Bernhard & Markus Klein & Gerhard Hommel, 2004. "Global and multiple test procedures using ordered p-values—a review," Statistical Papers, Springer, vol. 45(1), pages 1-14, January.
    • Handle: RePEc:spr:stpapr:v:45:y:2004:i:1:p:1-14
    DOI: 10.1007/BF02778266
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    References listed on IDEAS

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    1. G. Hommel, 1986. "Multiple test procedures for arbitrary dependence structures," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 33(1), pages 321-336, December.
    2. H. Finner & M. Roters, 1994. "On the limit behaviour of the joint distribution function of order statistics," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 46(2), pages 343-349, June.
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    Citations

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    Cited by:

    1. Cai, Gengqian & Sarkar, Sanat K., 2008. "Modified Simes' critical values under independence," Statistics & Probability Letters, Elsevier, vol. 78(12), pages 1362-1368, September.
    2. Marco Marozzi, 2012. "A combined test for differences in scale based on the interquantile range," Statistical Papers, Springer, vol. 53(1), pages 61-72, February.
    3. Djalel-Eddine Meskaldji & Dimitri Van De Ville & Jean-Philippe Thiran & Stephan Morgenthaler, 2020. "A comprehensive error rate for multiple testing," Statistical Papers, Springer, vol. 61(5), pages 1859-1874, October.
    4. Fengqing Zhang & Jiangtao Gou, 2021. "Refined critical boundary with enhanced statistical power for non-directional two-sided tests in group sequential designs with multiple endpoints," Statistical Papers, Springer, vol. 62(3), pages 1265-1290, June.
    5. Wenge Guo & Sanat K. Sarkar & Shyamal D. Peddada, 2010. "Controlling False Discoveries in Multidimensional Directional Decisions, with Applications to Gene Expression Data on Ordered Categories," Biometrics, The International Biometric Society, vol. 66(2), pages 485-492, June.
    6. Li Wang & Xingzhong Xu & Yong A, 2016. "New multiple testing method under no dependency assumption, with application to multiple comparisons problem," Statistical Papers, Springer, vol. 57(1), pages 161-183, March.

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