34 lines
2.8 KiB
Plaintext
34 lines
2.8 KiB
Plaintext
Given a list of [[wp:p-value|p-values]], adjust the p-values for multiple comparisons. This is done in order to control the false positive, or Type 1 error rate.
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This is also known as the "[[wp:False discovery rate|false discovery rate]]" (FDR). After adjustment, the p-values will be higher but still inside [0,1].
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The adjusted p-values are sometimes called "q-values".
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;Task:
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Given one list of [[Welch's_t-test|p-values]], return the p-values correcting for multiple comparisons
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p = {4.533744e-01, 7.296024e-01, 9.936026e-02, 9.079658e-02, 1.801962e-01,
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8.752257e-01, 2.922222e-01, 9.115421e-01, 4.355806e-01, 5.324867e-01,
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4.926798e-01, 5.802978e-01, 3.485442e-01, 7.883130e-01, 2.729308e-01,
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8.502518e-01, 4.268138e-01, 6.442008e-01, 3.030266e-01, 5.001555e-02,
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3.194810e-01, 7.892933e-01, 9.991834e-01, 1.745691e-01, 9.037516e-01,
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1.198578e-01, 3.966083e-01, 1.403837e-02, 7.328671e-01, 6.793476e-02,
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4.040730e-03, 3.033349e-04, 1.125147e-02, 2.375072e-02, 5.818542e-04,
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3.075482e-04, 8.251272e-03, 1.356534e-03, 1.360696e-02, 3.764588e-04,
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1.801145e-05, 2.504456e-07, 3.310253e-02, 9.427839e-03, 8.791153e-04,
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2.177831e-04, 9.693054e-04, 6.610250e-05, 2.900813e-02, 5.735490e-03}
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There are several methods to do this, see:
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* Yoav Benjamini, Yosef Hochberg "[http://www.math.tau.ac.il/~ybenja/MyPapers/benjamini_hochberg1995.pdf Controlling the False Discovery Rate: A Practical and Powerful Approach to Multiple Testing]", ''Journal of the Royal Statistical Society. Series B'', Vol. 57, No. 1 (1995), pp. 289-300, JSTOR:[http://www.jstor.org/stable/2346101 2346101]
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* Yoav Benjamini, Daniel Yekutieli, "[http://www.math.tau.ac.il/~ybenja/MyPapers/benjamini_yekutieli_ANNSTAT2001.pdf The control of the false discovery rate in multiple testing under dependency]", ''Ann. Statist.'', Vol. 29, No. 4 (2001), pp. 1165-1188, DOI:[https://doi.org/10.1214/aos/1013699998 10.1214/aos/1013699998] JSTOR:[http://www.jstor.org/stable/2674075 2674075]
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* Sture Holm, "A Simple Sequentially Rejective Multiple Test Procedure", ''Scandinavian Journal of Statistics'', Vol. 6, No. 2 (1979), pp. 65-70, JSTOR:[https://www.jstor.org/stable/4615733 4615733]
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* Yosef Hochberg, "A sharper Bonferroni procedure for multiple tests of significance", ''Biometrika'', Vol. 75, No. 4 (1988), pp 800–802, DOI:[https://doi.org/10.1093/biomet/75.4.800 10.1093/biomet/75.4.800] JSTOR:[https://www.jstor.org/stable/2336325 2336325]
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* Gerhard Hommel, "A stagewise rejective multiple test procedure based on a modified Bonferroni test", ''Biometrika'', Vol. 75, No. 2 (1988), pp 383–386, DOI:[https://doi.org/10.1093/biomet/75.2.383 10.1093/biomet/75.2.383] JSTOR:[https://www.jstor.org/stable/2336190 2336190]
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Each method has its own advantages and disadvantages.
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<br><br>
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