Specificity (tests)

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The specificity is a statistical measure of how well a binary classification test correctly identifies the negative cases, or those cases that do not meet the condition under study. 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 both mentally and physically.

1 Worked example
2 Definition
3 See also
4 External links

[edit] Worked example

Relationships among terms

		Condition (as determined by "Gold standard")
		True	False
Test outcome	Positive	True Positive	False Positive (Type I error, P-value)	→ Positive predictive value
Test outcome	Negative	False Negative (Type II error)	True Negative	→ Negative predictive value
		↓ Sensitivity	↓ Specificity

A worked example: the Fecal occult blood (FOB) screen test is used in 203 people to look for bowel cancer:

		Patients with bowel cancer (as confirmed on endoscopy)
		True	False	?
FOB test	Positive	TP = 2	FP = 18	= TP / (TP + FP) = 2 / (2 + 18) = 2 / 20 = 0.1 = 10%
FOB test	Negative	FN = 1	TN = 182	= TN / (TN + FN) 182 / (1 + 182) = 182 / 183 = 99.5%
		↓ = TP / (TP + FN) = 2 / (2 + 1) = 2 / 3 = 66.67%	↓ = TN / (FP + TN) = 182 / (18 + 182) = 182 / 200 = 91%

Related calculations

False positive rate (α) = FP / (FP + TN) = 18 / (18 + 182) = 9% = 1 - specificity
False negative rate (β) = FN / (TP + FN) = 1 / (2 + 1) = 33% = 1 - sensitivity
Power = 1 − β

[edit] 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.