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Multiplicity-and dependency-adjusted p-values for control of the family-wise error rate

Author

Listed:
  • Jens Stange

    (Weierstrass Institute for Applied Analysis and Stochastics, Berlin, Germany)

  • Thorsten Dickhaus

    (University of Bremen, Germany)

  • Arcadi Navarro

    (Universitat Pompeu Fabra and Institucio Catalana de Recerca i Estudis Avancats (ICREA) and Center for Genomic Regulation (CRG), Barcelona, Spain)

  • Daniel Schunk

    (Department of Economics, Johannes Gutenberg-Universitaet Mainz, Germany)

Abstract

We are concerned with the problem of testing multiple hypotheses simultaneously based on the same data and controlling the family-wise error rate. The multiplicity- and dependency-adjustment method (MADAM) is proposed which transforms test statistics into multiplicity- and dependency adjusted p-values. The MADAM is closely connected with the concept of the "effective number of tests", but avoids certain inconveniences of the latter. For demonstration, we apply the MADAM to data from a genetic association study by exploiting computational methods for evaluating multivariate chi-square distribution functions.

Suggested Citation

  • Jens Stange & Thorsten Dickhaus & Arcadi Navarro & Daniel Schunk, 2015. "Multiplicity-and dependency-adjusted p-values for control of the family-wise error rate," Working Papers 1505, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz, revised 29 Jun 2015.
    • Handle: RePEc:jgu:wpaper:1505
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    File URL: https://download.uni-mainz.de/RePEc/pdf/Discussion_Paper_1505.pdf
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    References listed on IDEAS

    as
    1. Joseph P. Romano & Michael Wolf, 2005. "Stepwise Multiple Testing as Formalized Data Snooping," Econometrica, Econometric Society, vol. 73(4), pages 1237-1282, July.
    2. Dickhaus Thorsten & Straßburger Klaus & Schunk Daniel & Morcillo-Suarez Carlos & Illig Thomas & Navarro Arcadi, 2012. "How to analyze many contingency tables simultaneously in genetic association studies," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 11(4), pages 1-33, July.
    3. Stange, Jens & Dickhaus, Thorsten & Navarro, Arcadi & Schunk, Daniel, 2016. "Multiplicity- and dependency-adjusted p-values for control of the family-wise error rate," Statistics & Probability Letters, Elsevier, vol. 111(C), pages 32-40.
    4. Jens Stange & Taras Bodnar & Thorsten Dickhaus, 2015. "Uncertainty quantification for the family-wise error rate in multivariate copula models," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 99(3), pages 281-310, July.
    5. Joseph P. Romano & Michael Wolf, 2005. "Exact and Approximate Stepdown Methods for Multiple Hypothesis Testing," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 94-108, March.
    6. Dickhaus, Thorsten & Gierl, Jakob, 2012. "Simultaneous test procedures in terms of p-value copulae," SFB 649 Discussion Papers 2012-049, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    Full references (including those not matched with items on IDEAS)

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    Cited by:

    1. Stange, Jens & Dickhaus, Thorsten & Navarro, Arcadi & Schunk, Daniel, 2016. "Multiplicity- and dependency-adjusted p-values for control of the family-wise error rate," Statistics & Probability Letters, Elsevier, vol. 111(C), pages 32-40.
    2. Anh-Tuan Hoang & Thorsten Dickhaus, 2022. "On the usage of randomized p-values in the Schweder–Spjøtvoll estimator," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(2), pages 289-319, April.

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