# False Discovery Rate = FP / (TP + FP)?

In the context of diagnostic screening (Positive / Negative) for a given outcome, what is the correct term for FP / (TP + FP)?

Wikipedia calls it the False Discovery Rate. However, when I look for more credible references, I'm unable to find any. Further, the peer-reviewed literature I do find on the False Discovery Rate is in the context of multiple hypothesis testing.

So, I would appreciate it if someone could:

• Confirm that FDR is the correct terminology
• Point me towards a credible reference
• They are the same thing. Commented May 18, 2017 at 15:31
• Have you tried the references provided by Wikipedia en.wikipedia.org/wiki/False_discovery_rate#References ?
– Tim
Commented May 18, 2017 at 15:33
• I am more familiar with FDR in multiple testing where it was developed to allow a small number of the tests to be wrong rather than the stricter requirement of making it a high probability that all conclusions are correct. Certainly in diagnostic testing fraction of false possibles out of all positive diagnoses could be called a false discovery rate. I think the context of the problem indicates which is the case. Commented May 18, 2017 at 15:34
• @Tim When I look through the references, they all appear to be related to multiple testing. Commented May 18, 2017 at 15:46

When you do multiple comparisons, a common strategy is to control the expected false discovery rate. Basically, it means to reduce the number of tests to be wrong out of all tests you detect. When you think about it, this is just the definition: $$FP / (TP + FP)$$ you quote.

The denominator is the total number of positive tests you have, while the numerator is the number of false positive tests. Ideally, you'd like it as low as possible.

The Wikipedia you have gives you the definition.

In the original paper for Benjamini-Hochberg, there is a figure:

Ok. Let's compare your Wikipedia definition:

To me, they are the same thing. If you reject a true null hypothesis it counts as an error (false positive).

• "The denominator is the total number of tests you have, while the numerator is the number of false tests". I think this is incorrect. The total number of tests would include the false negatives and true negatives, but they are not part of the FDR definition. And similarly, the false tests would include the false negatives, which are also excluded.
– mkt
Commented May 16, 2018 at 9:43