False Discovery Rate and the BH method

Dear all,

I am trying to figure out the BH method for controlling the FDR.

The formula for the BH method is to reject all hypotheses up to the Kth hypothesis where k is defined in the attached photo.

Assume that I have 10 hypotheses, and the P-Values are:

0.01, 0.11, 0.21, 0.31, 0.41, 0.51, 0.61, 0.71, 0.81, 0.91

How do I apply the BH method using this formula on this example, and what is the logic behind the formula ?

( I am familiar with the graphical idea of P-Values ~ U(0,1) and choosing only the part of histogram which is the addition to the uniform part, but I don't see it in the mathematical formula).

Thank you !


Yankel, the wikipedia page for "False Discovery Rate" contains a link to the original 1995 Benjamini-Hochberg paper, which explains the procedure. It's very simple to do by hand.