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Testing hypotheses in order

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  • Paul R. Rosenbaum

Abstract

In certain circumstances, one wishes to test one hypothesis only if certain other hypotheses have been rejected. This ordering of hypotheses simplifies the task of controlling the probability of rejecting any true hypothesis. In an example from an observational study, a treated group is shown to be further from both of two control groups than the two control groups are from each other. Copyright 2008, Oxford University Press.

Suggested Citation

  • Paul R. Rosenbaum, 2008. "Testing hypotheses in order," Biometrika, Biometrika Trust, vol. 95(1), pages 248-252.
    • Handle: RePEc:oup:biomet:v:95:y:2008:i:1:p:248-252
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    File URL: http://hdl.handle.net/10.1093/biomet/asm085
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    Citations

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    Cited by:

    1. Jay Bartroff & Jinlin Song, 2016. "A Rejection Principle for Sequential Tests of Multiple Hypotheses Controlling Familywise Error Rates," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(1), pages 3-19, March.
    2. Anders Bredahl Kock & David Preinerstorfer, 2021. "Superconsistency of Tests in High Dimensions," Papers 2106.03700, arXiv.org, revised Jan 2022.
    3. L. Finos & A. Farcomeni, 2011. "k-FWER Control without p -value Adjustment, with Application to Detection of Genetic Determinants of Multiple Sclerosis in Italian Twins," Biometrics, The International Biometric Society, vol. 67(1), pages 174-181, March.
    4. Adam C. Sales & Ben B. Hansen, 2020. "Limitless Regression Discontinuity," Journal of Educational and Behavioral Statistics, , vol. 45(2), pages 143-174, April.
    5. Ruoqi Yu, 2021. "Evaluating and improving a matched comparison of antidepressants and bone density," Biometrics, The International Biometric Society, vol. 77(4), pages 1276-1288, December.
    6. A. Farcomeni & L. Finos, 2013. "FDR Control with Pseudo-Gatekeeping Based on a Possibly Data Driven Order of the Hypotheses," Biometrics, The International Biometric Society, vol. 69(3), pages 606-613, September.
    7. Michael Rosenblum & Han Liu & En-Hsu Yen, 2014. "Optimal Tests of Treatment Effects for the Overall Population and Two Subpopulations in Randomized Trials, Using Sparse Linear Programming," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(507), pages 1216-1228, September.
    8. Linbo Wang & Thomas S. Richardson & Xiao-Hua Zhou, 2017. "Causal analysis of ordinal treatments and binary outcomes under truncation by death," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(3), pages 719-735, June.
    9. Paul R. Rosenbaum & Dylan S. Small, 2017. "An adaptive Mantel–Haenszel test for sensitivity analysis in observational studies," Biometrics, The International Biometric Society, vol. 73(2), pages 422-430, June.

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