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A novel characterization of the generalized family wise error rate using empirical null distributions

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  • Miecznikowski Jeffrey C.

    (Department of Biostatistics, SUNY University at Buffalo, 433 Kimball Tower, 3435 Main St., Buffalo, NY 14214, USA)

  • Gaile Daniel P.

    (Department of Biostatistics, SUNY University at Buffalo, 706 Kimball Tower, 3435 Main St., Buffalo, NY 14214, USA)

Abstract

We present a novel characterization of the generalized family wise error rate: kFWER. The interpretation allows researchers to view kFWER as a function of the test statistics rather than current methods based on p-values. Using this interpretation we present several theorems and methods (parametric and non-parametric) for estimating kFWER in various data settings. With this version of kFWER, researchers will have an estimate of kFWER in addition to knowing what tests are significant at the estimated kFWER. Additionally, we present methods that use empirical null distributions in place of parametric distributions in standard p-value kFWER controlling schemes. These advancements represent an improvement over common kFWER methods which are based on parametric assumptions and merely report the tests that are significant under a given value for kFWER.

Suggested Citation

  • Miecznikowski Jeffrey C. & Gaile Daniel P., 2014. "A novel characterization of the generalized family wise error rate using empirical null distributions," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 13(3), pages 299-322, June.
    • Handle: RePEc:bpj:sagmbi:v:13:y:2014:i:3:p:24:n:2
    DOI: 10.1515/sagmb-2013-0032
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    References listed on IDEAS

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    1. 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.
    2. Dudoit Sandrine & van der Laan Mark J. & Pollard Katherine S., 2004. "Multiple Testing. Part I. Single-Step Procedures for Control of General Type I Error Rates," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 3(1), pages 1-71, June.
    3. Guo Wenge & Romano Joseph, 2007. "A Generalized Sidak-Holm Procedure and Control of Generalized Error Rates under Independence," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 6(1), pages 1-35, January.
    4. 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.
    5. Sandrine Dudoit & Mark van der Laan & Katherine Pollard, 2004. "Multiple Testing. Part I. Single-Step Procedures for Control of General Type I Error Rates," U.C. Berkeley Division of Biostatistics Working Paper Series 1137, Berkeley Electronic Press.
    6. Miecznikowski, Jeffrey C. & Gold, David & Shepherd, Lori & Liu, Song, 2011. "Deriving and comparing the distribution for the number of false positives in single step methods to control k-FWER," Statistics & Probability Letters, Elsevier, vol. 81(11), pages 1695-1705, November.
    7. Jin, Jiashun & Cai, T. Tony, 2007. "Estimating the Null and the Proportion of Nonnull Effects in Large-Scale Multiple Comparisons," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 495-506, June.
    8. Efron, Bradley, 2007. "Correlation and Large-Scale Simultaneous Significance Testing," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 93-103, March.
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