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Definition
The Benjamini–Hochberg method controls the False Discovery Rate (FDR) using sequential modified Bonferroni correction for multiple hypothesis testing. While the Bonferroni correction relies on the Family Wise Error Rate (FWER), Benjamini and Hochberg introduced the idea of a FDR to control for multiple hypotheses testing. In the statistical context, discovery refers to the rejection of a hypothesis. Therefore, a false discovery is an incorrect rejection of a hypothesis and the FDR is the likelihood such a rejection occurs. Controlling the FDR instead of the FWER is less stringent and increases the method’s power. As a result, more hypotheses may be rejected and more discoveries may be made.
In the Benjamini–Hochberg method, hypotheses are first ordered and then rejected or accepted based on their p-values. A p-value is a data point for each hypothesis describing the likelihood of an observation based on a probability distribution. The Benjamini–Hochberg method begins by ordering the m hypothesis by ascending p-values, where P i is the p-value at the ith position with the associated hypothesis H i . Let k be the largest i for which:
Reject hypotheses i = 1, 2, 3,..., k. The Benjamini–Hochberg method has been proven to control the FDR for all tests at a level of q.
References
Benjamini Y, Hochberg Y (1995) Controlling the false discovery rate: a practical and powerful approach to multiple hypothesis testing. J R Stat Soc B 57:289–300
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Haynes, W. (2013). Benjamini–Hochberg Method. In: Dubitzky, W., Wolkenhauer, O., Cho, KH., Yokota, H. (eds) Encyclopedia of Systems Biology. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-9863-7_1215
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DOI: https://doi.org/10.1007/978-1-4419-9863-7_1215
Publisher Name: Springer, New York, NY
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