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A practical ad hoc adjustment to the Simes P-value

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  • Lloyd, Chris J.

Abstract

For testing a set of null hypotheses, the chance of at least one significant result is much higher than the nominal size of each test. The P-value of Simes (1986) controls type-1 error under weak conditions and is far less conservative that the Bonferroni P-value when the tests are correlated. However, it can still be quite conservative. In this paper, I perform a large numerical experiment to measure this conservatism as a function of the correlation of the component P-values and the skewness of the underlying test statistics. The results are modelled, and they produce an adjustment to the Simes P-value which is close to exact for a wide range of correlations and distributional shapes.

Suggested Citation

  • Lloyd, Chris J., 2012. "A practical ad hoc adjustment to the Simes P-value," Statistics & Probability Letters, Elsevier, vol. 82(7), pages 1297-1302.
    • Handle: RePEc:eee:stapro:v:82:y:2012:i:7:p:1297-1302
    DOI: 10.1016/j.spl.2012.03.009
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    References listed on IDEAS

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    1. Proschan, Michael A. & Shaw, Pamela A., 2011. "Asymptotics of Bonferroni for dependent normal test statistics," Statistics & Probability Letters, Elsevier, vol. 81(7), pages 739-748, July.
    2. Chris J. Lloyd, 2010. "Bootstrap and Second-Order Tests of Risk Difference," Biometrics, The International Biometric Society, vol. 66(3), pages 975-982, September.
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