# Sensitivity and specificity

sensitivityspecificitysensitivespecificsensitive and specificnonspecificTrue Positive Raterecall rateselectivitysensitivities and specificities
Sensitivity and specificity are statistical measures of the performance of a binary classification test, also known in statistics as a classification function, that are widely used in medicine: * Sensitivity (also called the true positive rate, the recall, or probability of detection in some fields) measures the proportion of actual positives that are correctly identified as such (e.g., the percentage of sick people who are correctly identified as having the condition).wikipedia
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### Binary classification

binary classifierbinarybinary categorization
For example, in medicine sensitivity and specificity are often used, while in information retrieval precision and recall are preferred.

ROC curveAUCROC
This trade-off can be represented graphically using a receiver operating characteristic curve.
The ROC curve is created by plotting the true positive rate (TPR) against the false positive rate (FPR) at various threshold settings.

### Precision and recall

precisionrecallF-measure
The values of sensitivity and specificity are agnostic to the percent of positive cases in the population of interest (as opposed to, for example, precision). Sensitivity is not the same as the precision or positive predictive value (ratio of true positives to combined true and 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 pattern recognition, information retrieval and classification (machine learning), precision (also called positive predictive value) is the fraction of relevant instances among the retrieved instances, while recall (also known as sensitivity) is the fraction of the total amount of relevant instances that were actually retrieved.

### Medical diagnosis

diagnosisdiagnosticdiagnostic criteria
In medical diagnosis, test sensitivity is the ability of a test to correctly identify those with the disease (true positive rate), whereas test specificity is the ability of the test to correctly identify those without the disease (true negative rate).
Diagnosis is often challenging, because many signs and symptoms are nonspecific.

### Medical test

diagnostic testdiagnostic testsdiagnostic testing
In many tests, including diagnostic medical tests, sensitivity is the extent to which actual positives are not overlooked (so false negatives are few), and specificity is the extent to which actual negatives are classified as such (so false positives are few).
The classification of tests into either positive or negative gives a binary classification, with resultant ability to perform bayesian probability and performance metrics of tests, including calculations of sensitivity and specificity.

### Youden's J statistic

InformednessYouden's index
Giving them equal weight optimizes Informedness = Specificity+Sensitivity-1 = TPR-FPR, the magnitude of which gives the probability of an informed decision between the two classes (>0 represents appropriate use of information, 0 represents chance-level performance,
with the two right-hand quantities being sensitivity and specificity.

### Differential diagnosis

differential diagnosesdifferentiateddifferential
But for practical reasons, tests with sensitivity and specificity values above 90% have high credibility, albeit usually no certainty, in differential diagnosis.
One method of estimating likelihoods even after further tests uses likelihood ratios (which is derived from sensitivities and specificities) as a multiplication factor after each test or procedure.

### False positives and false negatives

false positivefalse negativefalse positives
Sensitivity therefore quantifies the avoidance of false negatives and specificity does the same for false positives.
The specificity of the test is equal to 1 minus the false positive rate.

### Classification rule

classifiersclassification testclassifier

### Positive and negative predictive values

positive predictive valuenegative predictive valuepositive
Sensitivity is not the same as the precision or positive predictive value (ratio of true positives to combined true and 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 case-control studies the PPV has to be computed from sensitivity, specificity, but also including the prevalence:

### Confusion matrix

confusion matrices
The four outcomes can be formulated in a 2×2 contingency table or confusion matrix, as follows:
The overall accuracy would be 95%, but in more detail the classifier would have a 100% recognition rate (sensitivity) for the cat class but a 0% recognition rate for the dog class.

### Type I and type II errors

Type I errorfalse-positivefalse positive
A sensitive test will have fewer Type II errors.
Much of statistical theory revolves around the minimization of one or both of these errors, though the complete elimination of either is a statistical impossibility for non-deterministic algorithms.

### Power (statistics)

statistical powerpowerpowerful
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.
In the context of binary classification, the power of a test is called its statistical sensitivity, its true positive rate, or its probability of detection.

### Statistical hypothesis testing

hypothesis testingstatistical teststatistical tests
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.

### Statistical classification

classificationclassifierclassifiers

### Certainty

certainimperfect knowledgeCertainly
Because most medical tests do not have sensitivity and specificity values above 99%, "rarely" does not equate to certainty.

### Airport security

aviation securitysecurityairline security
For any test, there is usually a trade-off between the measures – for instance, in airport security, since testing of passengers is for potential threats to safety, scanners may be set to trigger alarms on low-risk items like belt buckles and keys (low specificity) in order to increase the probability of identifying dangerous objects and minimize the risk of missing objects that do pose a threat (high sensitivity).

### Nondeterministic algorithm

non-deterministicnondeterministicnon-deterministic algorithm
In reality, however, any non-deterministic predictor will possess a minimum error bound known as the Bayes error rate.

### Bayes error rate

correctness proofserror ratestatistical impossibility
In reality, however, any non-deterministic predictor will possess a minimum error bound known as the Bayes error rate.

### Contingency table

cross tabulationcontingency tablescrosstab
The four outcomes can be formulated in a 2×2 contingency table or confusion matrix, as follows:

### Sensitivity index

sensitivity index ''ddd '' (d prime)
The sensitivity index or d' (pronounced 'dee-prime') is a statistic used in signal detection theory.

### Statistic

sample statisticempiricalmeasure
The sensitivity index or d' (pronounced 'dee-prime') is a statistic used in signal detection theory.

### Detection theory

signal detection theorysignal detectionsignal recovery
The sensitivity index or d' (pronounced 'dee-prime') is a statistic used in signal detection theory.

### Normal distribution

normally distributedGaussian distributionnormal
For normally distributed signal and noise with mean and standard deviations \mu_S and \sigma_S, and \mu_N and \sigma_N, respectively, d' is defined as:

### False alarm

false alarmsfalse-alarmfalse
An estimate of d' can be also found from measurements of the hit rate and false-alarm rate.