False discovery rate (FDR)

The false discovery rate is $\mathbb{E}[V/(R\vee 1)]$, where $V$ is the number of rejected true null hypotheses and $R$ is the total number of rejections.

In multiple hypothesis testing, let $R$ count all rejections and $V$ count rejected true null hypotheses. The false discovery proportion is the random variable $V/(R\vee 1)$, defined to be zero when $R=0$. Its expectation is the false discovery rate. Distinguishing the realized proportion from its expectation matters: controlling the false discovery rate does not by itself give a high-probability bound on the realized proportion.