# Sensitivity (tests)

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The sensitivity of a binary classification test or algorithm, such as a blood test to determine if a person has a certain disease, or an automated system to detect faulty products in a factory, is a parameter that expresses something about the test's performance. The sensitivity of such a test is the proportion of those cases having a positive test result of all positive cases (e.g., people with the disease, faulty products) tested.

${\rm sensitivity}=\frac{\rm number\ of\ true\ positives}{{\rm number\ of\ true\ positives}+{\rm number\ of\ false\ negatives}}.$

A sensitivity of 100% means that all sick people or faulty products are recognized as such.

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

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

$\frac{\rm number\ of\ true\ positives}{{\rm number\ of\ true\ positives}+{\rm number\ of\ false\ positives}}$

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

In information retrieval, positive predictive value is called precision, and sensitivity is known as recall.

F-measure can be used as a single measure of performance of the test. The F-measure is the harmonic mean of precision and recall:

$F = 2 \times {\rm precision} \times {\rm recall} / ({\rm precision} + {\rm recall}).$

In the traditional language of statistical hypothesis testing, the sensitivity of a test is called the statistical power of the test, although the word power in that context has a more general usage that is not applicable in the present context. A sensitive test will have fewer Type II errors.

In information retrieval, sensitivity is called recall.