False Discovery Rate

Definition

$FDR=E(V/R)$ where $V$ is the number of false discoveries and $S$ is the number of discoveries

The false discovery rate (FDR) is the expected proportion of falsely rejected $H_0$ we control FDR at some $q$, $FDR\le q$

Facts

If Family-Wise Error Rate is controlled, then FDR also be controlled.

Let $p_1\le p_2\le \cdots \le p_m$ be the $p$-values of $m$ hypotheses, and $q$ is given. If $j=\underset{1\le 1\le m}{\max }\left\{i|p_i\le \frac{i}{m}q\right\}$, then FDR rejects hypotheses corresponding to $p_1\le p_2\le \cdots \le p_j$