IDEAS home Printed from
   My bibliography  Save this article

Augmentation Procedures for Control of the Generalized Family-Wise Error Rate and Tail Probabilities for the Proportion of False Positives


  • van der Laan Mark J.

    (Division of Biostatistics, School of Public Health, University of California, Berkeley)

  • Dudoit Sandrine

    (Division of Biostatistics, School of Public Health, University of California, Berkeley)

  • Pollard Katherine S.

    (University of California, Santa Cruz)


This article shows that any single-step or stepwise multiple testing procedure (asymptotically) controlling the family-wise error rate (FWER) can be augmented into procedures that (asymptotically) control tail probabilities for the number of false positives and the proportion of false positives among the rejected hypotheses. Specifically, given any procedure that (asymptotically) controls the FWER at level alpha, we propose simple augmentation procedures that provide (asymptotic) level-alpha control of: (i) the generalized family-wise error rate, i.e., the tail probability, gFWER(k), that the number of Type I errors exceeds a user-supplied integer k, and (ii) the tail probability, TPPFP(q), that the proportion of Type I errors among the rejected hypotheses exceeds a user-supplied value 0

Suggested Citation

  • van der Laan Mark J. & Dudoit Sandrine & Pollard Katherine S., 2004. "Augmentation Procedures for Control of the Generalized Family-Wise Error Rate and Tail Probabilities for the Proportion of False Positives," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 3(1), pages 1-27, June.
  • Handle: RePEc:bpj:sagmbi:v:3:y:2004:i:1:n:15

    Download full text from publisher

    File URL:
    Download Restriction: For access to full text, subscription to the journal or payment for the individual article is required.

    As the access to this document is restricted, you may want to search for a different version of it.


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    Cited by:

    1. Joseph P. Romano & Michael Wolf, 2008. "Balanced Control of Generalized Error Rates," IEW - Working Papers 379, Institute for Empirical Research in Economics - University of Zurich.
    2. Gordon, Alexander Y., 2009. "Inequalities between generalized familywise error rates of a multiple testing procedure," Statistics & Probability Letters, Elsevier, vol. 79(19), pages 1996-2004, October.
    3. Cerioli, Andrea & Farcomeni, Alessio, 2011. "Error rates for multivariate outlier detection," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 544-553, January.
    4. Joseph Romano & Azeem Shaikh & Michael Wolf, 2008. "Control of the false discovery rate under dependence using the bootstrap and subsampling," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 17(3), pages 417-442, November.
    5. Wang, Li & Xu, Xingzhong, 2012. "Step-up procedure controlling generalized family-wise error rate," Statistics & Probability Letters, Elsevier, vol. 82(4), pages 775-782.
    6. Schumi Jennifer & DiRienzo A. Gregory & DeGruttola Victor, 2008. "Testing for Associations with Missing High-Dimensional Categorical Covariates," The International Journal of Biostatistics, De Gruyter, vol. 4(1), pages 1-17, September.
    7. Montazeri Zahra & Yanofsky Corey M. & Bickel David R., 2010. "Shrinkage Estimation of Effect Sizes as an Alternative to Hypothesis Testing Followed by Estimation in High-Dimensional Biology: Applications to Differential Gene Expression," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 9(1), pages 1-33, June.
    8. Birkner Merrill D. & Hubbard Alan E. & van der Laan Mark J. & Skibola Christine F. & Hegedus Christine M. & Smith Martyn T., 2006. "Issues of Processing and Multiple Testing of SELDI-TOF MS Proteomic Data," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 5(1), pages 1-24, April.
    9. Günther Fink & Margaret McConnell & Sebastian Vollmer, 2014. "Testing for heterogeneous treatment effects in experimental data: false discovery risks and correction procedures," Journal of Development Effectiveness, Taylor & Francis Journals, vol. 6(1), pages 44-57, January.
    10. Alessio Farcomeni, 2009. "Generalized Augmentation to Control the False Discovery Exceedance in Multiple Testing," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(3), pages 501-517.
    11. Irene Castro-Conde & Jacobo Uña-Álvarez, 2015. "Power, FDR and conservativeness of BB-SGoF method," Computational Statistics, Springer, vol. 30(4), pages 1143-1161, December.
    12. Joseph P. Romano & Azeem M. Shaikh & Michael Wolf, 2010. "Hypothesis Testing in Econometrics," Annual Review of Economics, Annual Reviews, vol. 2(1), pages 75-104, September.
    13. Francesca Greselin & Salvatore Ingrassia & Antonio Punzo, 2011. "Assessing the pattern of covariance matrices via an augmentation multiple testing procedure," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 20(2), pages 141-170, June.
    14. Somerville, Paul N. & Hemmelmann, Claudia, 2008. "Step-up and step-down procedures controlling the number and proportion of false positives," Computational Statistics & Data Analysis, Elsevier, vol. 52(3), pages 1323-1334, January.
    15. Merrill Birkner & Sandra Sinisi & Mark van der Laan, 2004. "Multiple Testing and Data Adaptive Regression: An Application to HIV-1 Sequence Data," U.C. Berkeley Division of Biostatistics Working Paper Series 1161, Berkeley Electronic Press.
    16. Christina C. Bartenschlager & Michael Krapp, 2015. "Theorie und Methoden multipler statistischer Vergleiche," AStA Wirtschafts- und Sozialstatistisches Archiv, Springer;Deutsche Statistische Gesellschaft - German Statistical Society, vol. 9(2), pages 107-129, November.
    17. van der Laan Mark J. & Hubbard Alan E., 2006. "Quantile-Function Based Null Distribution in Resampling Based Multiple Testing," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 5(1), pages 1-30, May.

    More about this item


    Access and download statistics


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bpj:sagmbi:v:3:y:2004:i:1:n:15. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Peter Golla). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.