False Discovery Rate

For the multiple hypotheses testing problem consider the proportion of falsely rejected hypotheses (false discoveries) among the total number of rejections. The expected value of this proportion, called the False Discovery Rate (FDR), is a useful criterion to control as an alternative to the traditional familywise error rate (FWE) that suffers from low power properties when the number of tested hypotheses is large. In a way, controlling FDR is adaptively inbetween ignoring multiplicity altogether and a conservative control of FWE. Several FDR controlling procedures are presented and others are reviewed. Various extensions and applications of the FDR are discussed.