# Specificity (tests)

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Editor-In-Chief: C. Michael Gibson, M.S., M.D. ; Assistant Editor(s)-In-Chief: Kristin Feeney, B.S.

## Overview

The specificity is a statistical measure of how well a binary classification test correctly identifies the negative cases. It is the probability that a test correctly classifies individuals without preclinical disease as negative. It is a proportional measurement and is often expressed in terms of percentage.

## Calculation

For example, given a medical test that determines if a person has a certain disease, the specificity of the test to the disease is the probability that the test indicates `negative' if the person does not have the disease.

That is, the specificity is the proportion of true negatives of all negative cases in the population. It is a parameter of the test.

High specificity is important when the treatment or diagnosis is harmful to the patient mentally and/or physically.

## Definition

${\rm specificity}=\frac{\rm number\ of\ True\ Negatives}{{\rm number\ of\ True\ Negatives}+{\rm number\ of\ False\ Positives}}$

A specificity of 100% means that the test recognizes all healthy people as healthy. The maximum is trivially achieved by a test that claims everybody healthy regardless of the true condition. Therefore, the specificity alone does not tell us how well the test recognizes positive cases. We also need to know the sensitivity of the test to the class, or equivalently, the specificities to the other classes.

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

Specificity is sometimes confused with the precision or the positive predictive value, both of which refer to the fraction of returned positives that are true positives. The distinction is critical when the classes are different sizes. A test with very high specificity can have very low precision if there are far more true negatives than true positives, and vice versa.<

## SPPIN and SNNOUT

SPPIN SNNOUT Neither Near-perfect
Proposed definition Sp > 95% SN > 95% Both < 95% Both > 99%
Example Many physical dx findings Ottawa fracture rules Exercise treadmill test HIV-1/HIV-2 4th gen test
Predictive values:
10% pretest prob PPV= 35%

NPV = 99%

PPV = 64%

NPV = 98%

PPV = 31%

NPV = 97%

PPV = 92%

NPV > 99%

50% pretest prob PPV = 94%

NPV = 83%

PPV = 83%

NPV = 94%

PPV = 80%

NPV = 80%

PPV = 99%

NPV = 99%

90% pretest prob PPV = 98%

NPV = 64%

PPV = 99%

NPV = 35%

PPV = 97%

NPV = 31%

PPV > 99%

NPV = 92%

Clinical messages Accept test result when: