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Sensitivity and specificity are statistical measures of the performance of a binary classification
Binary classification

Binary classification is the task of Statistical classification the members of a given Set of objects into two groups on the basis of whether they have some property or not....
 test. The sensitivity (also called recall rate in some fields) measures the proportion of actual positives which are correctly identified as such (e.g. the percentage of sick people who are identified as having the condition); and the specificity measures the proportion of negatives which are correctly identified (e.g.






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Sensitivity and specificity are statistical measures of the performance of a binary classification
Binary classification

Binary classification is the task of Statistical classification the members of a given Set of objects into two groups on the basis of whether they have some property or not....
 test. The sensitivity (also called recall rate in some fields) measures the proportion of actual positives which are correctly identified as such (e.g. the percentage of sick people who are identified as having the condition); and the specificity measures the proportion of negatives which are correctly identified (e.g. the percentage of well people who are identified as not having the condition). They are closely related to the concepts of type I and type II errors
Type I and type II errors

In statistics, the terms Type I error and type II error are used to describe possible errors made in a statistical decision process. In 1928, Jerzy Neyman and Egon Pearson , both eminent statisticians, discussed the problems associated with "deciding whether or not a particular sample may be judged as likely to have been randomly dr...
.

For any test, there is usually a trade-off between each measure. For example in a manufacturing setting in which one is testing for faults, one may be willing to risk discarding functioning components (low specificity), in order to increase the chance of identifying nearly all faulty components (high sensitivity). This trade-off can be represented graphically using a ROC curve.

Definitions

Imagine a scenario where people are tested for a disease. The test outcome can be positive (sick) or negative (healthy), while the actual health status of the persons may be different. In that setting:
  • True positive: Sick people correctly diagnosed as sick
  • False positive: Healthy people wrongly identified as sick
  • True negative: Healthy people correctly identified as healthy
  • False negative: Sick people wrongly identified as healthy


Sensitivity


A sensitivity of 100% means that the test recognizes all sick people as such. Thus in a high sensitivity test, a negative result is used to rule out the disease.

Sensitivity alone does not tell us how well the test predicts other classes (that is, about the negative cases). In the binary classification, as illustrated above, this is the corresponding specificity test, or equivalently, the sensitivity for the other classes.

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

The positive predictive value, or precision rate, or post-test probability of disease, is the proportion of patients with positive test results who are correctly diagnosed....
 (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.

The calculation of sensitivity does not take into account indeterminate test results. If a test cannot be repeated, the options are to exclude indeterminate samples from analysis (but the number of exclusions should be stated when quoting sensitivity), or, alternatively, indeterminate samples can be treated as false negatives (which gives the worst-case value for sensitivity and may therefore underestimate it).

Specificity


A specificity of 100% means that the test recognizes all healthy people as healthy. Thus a positive result in a high specificity test is used to confirm the disease. 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
Type I and type II errors

In statistics, the terms Type I error and type II error are used to describe possible errors made in a statistical decision process. In 1928, Jerzy Neyman and Egon Pearson , both eminent statisticians, discussed the problems associated with "deciding whether or not a particular sample may be judged as likely to have been randomly dr...
 rate.

Specificity is sometimes confused with the precision
Precision and recall

Precision and Recall are two widely used statistical classifications.Precision can be seen as a measure of exactness or fidelity, whereas Recall is a measure of completeness....
 or the positive predictive value
Positive predictive value

The positive predictive value, or precision rate, or post-test probability of disease, is the proportion of patients with positive test results who are correctly diagnosed....
, 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.

Worked example


Terminology in information retrieval

In information retrieval
Information retrieval

Information retrieval is the science of searching for documents, for information within documents and for Metadata about documents, as well as that of searching relational databases and the World Wide Web....
 positive predictive value is called precision, and sensitivity is called recall.

The F-measure can be used as a single measure of performance of the test. The F-measure is the harmonic mean
Harmonic mean

In mathematics, the harmonic mean is one of several kinds of average. Typically, it is appropriate for situations when the average of Rate s is desired....
 of precision and recall:

In the traditional language of statistical hypothesis testing
Statistical hypothesis testing

A statistical hypothesis test is a method of making statistical decisions using experimental data. It is sometimes called confirmatory data analysis, in contrast to exploratory data analysis....
, the sensitivity of a test is called the statistical power
Statistical power

The power of aStatistical hypothesis testing is the probability that the test will reject a false null hypothesis . As power increases, the chances of a Type II error decrease....
 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 error
Type I and type II errors

In statistics, the terms Type I error and type II error are used to describe possible errors made in a statistical decision process. In 1928, Jerzy Neyman and Egon Pearson , both eminent statisticians, discussed the problems associated with "deciding whether or not a particular sample may be judged as likely to have been randomly dr...
s.

See also

  • binary classification
    Binary classification

    Binary classification is the task of Statistical classification the members of a given Set of objects into two groups on the basis of whether they have some property or not....
  • receiver operating characteristic
    Receiver operating characteristic

    In signal detection theory, a receiver operating characteristic , or simply ROC curve, is a graph of a functionical plot of the Sensitivity vs....
  • statistical significance
    Statistical significance

    In statistics, a result is called statistically significant if it is unlikely to have occurred by chance. "A statistically significant difference" simply means there is statistical evidence that there is a difference; it does not mean the difference is necessarily large, important, or significant in the common meaning of the word....
  • Type I and type II errors
    Type I and type II errors

    In statistics, the terms Type I error and type II error are used to describe possible errors made in a statistical decision process. In 1928, Jerzy Neyman and Egon Pearson , both eminent statisticians, discussed the problems associated with "deciding whether or not a particular sample may be judged as likely to have been randomly dr...
  • Selectivity
    Selectivity

    Selectivity may refer to:* Selectivity , in radio transmission* Functional selectivity, in pharmacology* Socioemotional selectivity theory, in social psychology...
  • Negative predictive value
    Negative predictive value

    The negative predictive value is the proportion of patients with negative test results who are correctly diagnosed....
  • Positive predictive value
    Positive predictive value

    The positive predictive value, or precision rate, or post-test probability of disease, is the proportion of patients with positive test results who are correctly diagnosed....
  • Youden's J statistic
    Youden's J statistic

    Youden's J statistic is a single statistic that captures the performance of a diagnostic test. The use of such a single index is "not generally to be recommended"....


External links

  • Medical University of South Carolina
  • Calculators:
    • OpenEpi
      OpenEpi

      OpenEpi is a free, web-based, open source, operating system-independent series of programs for use in epidemiology, biostatistics, public health, and medicine, providing a number of epidemiologic and statistical tools for summary data....
       software program