What is the False Discovery Rate?

When correcting for the multiple testing problem, you’ve probably been familiar with the stringent Bonferroni correction.  You’ve also probably heard of the False Discovery Rate (FDR), but what is the main difference between the two corrections?

I was browsing around for a simple explanation and came across the totallab website (see below).

I quote:

[FDR] controls the number of false discoveries in those tests that result in a discovery (i.e. a significant result). Because of this, it is less conservative than the Bonferroni approach and has greater ability (i.e. power) to find truly significant results.

Another way to look at the difference is that a p-value of 0.05 implies that 5% of all tests will result in false positives. An FDR adjusted p-value (or q-value) of 0.05 implies that 5% of significant tests will result in false positives. The latter is clearly a far smaller quantity.

http://www.totallab.com/products/samespots/support/faq/pq-values.aspx

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