Benjamini–Hochberg Method

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...