False discovery rate

Lore & Background

The modern widespread use of the FDR is believed to stem from technological developments in the late 1980s and 1990s, particularly in high-throughput sciences like genomics. Technologies such as microarrays enabled thousands of genes to be tested simultaneously, but with relatively small sample sizes. Standard multiple comparison procedures like the Bonferroni correction were too conservative, leading researchers to seek less stringent error rates to highlight potentially noteworthy findings for follow-up studies.

The FDR concept was formally described by Yoav Benjamini and Yosef Hochberg in 1995. Their procedure, known as the BH procedure, was proven to control the FDR for independent tests. Prior to this, precursor ideas had been considered: in 1979, Holm proposed a stepwise algorithm for controlling FWER; Schweder and Spjotvoll (1982) suggested plotting ranked p-values to estimate the number of true null hypotheses; and Branko Soric (1989) introduced the terminology of 'discovery' and used the expected number of false discoveries divided by the number of discoveries as a warning.

In 2005, the Benjamini and Hochberg paper from 1995 was identified as one of the 25 most-cited statistical papers. The FDR has been particularly influential in the life sciences, from genetics to biochemistry, oncology, and plant sciences, as it was the first alternative to the FWER to gain broad acceptance in many scientific fields.

Reader's Guide

The false discovery rate is significant because it addresses a critical need in modern data analysis: how to handle the massive number of statistical tests generated by high-throughput technologies. By controlling the expected proportion of false discoveries among all rejected null hypotheses, FDR-controlling procedures allow researchers to identify promising leads for follow-up work while accepting a manageable proportion of false positives. This approach provides greater statistical power than traditional FWER methods like the Bonferroni correction, which control the probability of any single Type I error. The FDR is particularly useful when the goal is discovery rather than definitive confirmation, as it balances the trade-off between finding true effects and limiting false leads. Its adoption has been widespread in genomics and other life sciences, where datasets often have many variables but small sample sizes. The formal definition of FDR is the expected value of Q, where Q is the proportion of false discoveries among all discoveries (V/R), with Q defined as 0 when no discoveries are made. The BH procedure, proven to control FDR for independent tests, has become a standard tool in multiple hypothesis testing.

Did You Know?

• The false discovery rate (FDR) is defined as the expected proportion of false discoveries among all rejected null hypotheses, with Q defined as 0 when no discoveries are made.
• The Benjamini and Hochberg paper from 1995 was identified in 2005 as one of the 25 most-cited statistical papers.
• The FDR concept was preceded by ideas from Schweder and Spjotvoll (1982) and Branko Soric (1989), who introduced the terminology of 'discovery' in multiple hypothesis testing.
• FDR-controlling procedures provide less stringent control of Type I errors compared to family-wise error rate (FWER) controlling procedures, resulting in greater power at the cost of increased numbers of Type I errors.