# Specificity

In binary testing, e.g. a medical diagnostic test for a certain disease, specificity is the proportion of true negatives of all the negative samples tested, that is

[itex]{\rm specificity}=\frac{\rm number\ of\ true\ negatives}{{\rm number\ of\ true\ negatives}+{\rm number\ of\ false\ positives}}[itex]

In information retrieval, specificity is called precision.

For a test to determine who has a certain disease, a specificity of 100% means that all people labeled as sick are actually sick.

Specificity alone does not tell us all about the test, because a 100% specificity can be trivially achieved by labeling all test cases negative. Therefore, we also need to know the sensitivity of the test.

F-measure can be used as a single measure of performance of the test. The F-measure is the geometric mean of sensitivity and specificity:

[itex]F = 2 * precision * recall / (precision + recall)[itex].

A test with a high specificity has a low Type I error.

Sensitivity is not the same as the positive predictive value defined as

[itex]\frac{\rm number\ of\ true\ positives}{{\rm number\ of\ true\ positives}+{\rm number\ of\ false\ positives}}[itex]

which is as much a statement about the proportion of actual positives in the population being tested as it is about the test.

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