false discovery rate: a standalone construct

Yoav Benjamini and Yosef Hochberg introduced the false discovery rate in 1995 as an alternative to older ways of guarding against false positives when many statistical tests are run at once. When a researcher tests dozens or thousands of hypotheses together, some of the results flagged as significant will be flukes, and the false discovery rate is defined as the expected proportion of such mistaken flags among all the results the researcher chooses to reject. Benjamini and Hochberg also gave a simple step-up procedure that keeps this proportion at or below a chosen level, such as 0.05, so that on average no more than 5 percent of the declared discoveries are false. Benjamini and Yekutieli (2001) extended the guarantee to cases where the tests are statistically dependent rather than independent, and Storey (2002) recast the idea through the q-value, the smallest false discovery rate at which a given result would still be called significant. What makes the false discovery rate a landmark is that it shifted the standard of error control in large-scale testing from avoiding even a single false positive to tolerating a known, small fraction of them, which made fields such as genomics and neuroimaging, where hundreds of thousands of tests are routine, statistically tractable.[1][2][3]

Unit

A proportion (an expected value) between 0 and 1: the fraction of rejected hypotheses that are in fact true null hypotheses

Recovery means

Not applicable

Measured by

Controlled in practice by the Benjamini-Hochberg step-up procedure, which orders the p-values and rejects up to a data-dependent threshold to hold the rate at a chosen level; estimated after the fact through q-values