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sensitivity and specificity : ウィキペディア英語版
sensitivity and specificity
Sensitivity and specificity are statistical measures of the performance of a binary classification test, also known in statistics as classification function:
*Sensitivity (also called the true positive rate, or the recall in some fields) measures the proportion of positives that are correctly identified as such (e.g., the percentage of sick people who are correctly identified as having the condition).
*Specificity (also called the true negative rate) measures the proportion of negatives that are correctly identified as such (e.g., the percentage of healthy people who are correctly identified as not having the condition).
Thus sensitivity quantifies the avoiding of false negatives, as specificity does for false positives.
For any test, there is usually a trade-off between the measures. For instance, in an airport security setting in which one is testing for potential threats to safety, scanners may be set to trigger on low-risk items like belt buckles and keys (low specificity), in order to reduce the risk of missing objects that do pose a threat to the aircraft and those aboard (high sensitivity). This trade-off can be represented graphically as a receiver operating characteristic curve.
A perfect predictor would be described as 100% sensitive (e.g., all sick are identified as sick) and 100% specific (e.g., no healthy are identified as sick); however, theoretically any predictor will possess a minimum error bound known as the Bayes error rate.
==Definitions==
/ P = \mathit / (\mathit+\mathit)
; specificity (SPC) or true negative rate
:\mathit = \mathit / N = \mathit / (\mathit+\mathit)
; precision or positive predictive value (PPV)
:\mathit = \mathit / (\mathit + \mathit)
; negative predictive value (NPV)
:\mathit = \mathit / (\mathit + \mathit)
; fall-out or false positive rate (FPR)
:\mathit = \mathit / N = \mathit / (\mathit + \mathit) = 1-\mathit
; false negative rate (FNR)
:\mathit = \mathit / (\mathit + \mathit) = 1-\mathit
; false discovery rate (FDR)
:\mathit = \mathit / (\mathit + \mathit) = 1 - \mathit
----
; accuracy (ACC)
:\mathit = (\mathit + \mathit) / (\mathit + \mathit + \mathit + \mathit)
;F1 score
: is the harmonic mean of precision and sensitivity
:\mathit = 2 \mathit / (2 \mathit + \mathit + \mathit)
; Matthews correlation coefficient (MCC)
: \frac - \mathit \times \mathit } ) ( \mathit + \mathit ) ( \mathit + \mathit ) ( \mathit + \mathit ) } }

;Informedness
:\mathit + \mathit - 1
;Markedness
:\mathit + \mathit - 1
;
''Sources: Fawcett (2006) and Powers (2011).''〔
|}
Imagine a study evaluating a new test that screens people for a disease. Each person taking the test either has or does not have the disease. The test outcome can be positive (classifying the person as having the disease) or negative (classifying the person as not having the disease). The test results for each subject may or may not match the subject's actual status. In that setting:
* True positive: Sick people correctly identified as sick
* False positive: Healthy people incorrectly identified as sick
* True negative: Healthy people correctly identified as healthy
* False negative: Sick people incorrectly identified as healthy
In general, Positive = identified and negative = rejected.
Therefore:
* True positive = correctly identified
* False positive = incorrectly identified
* True negative = correctly rejected
* False negative = incorrectly rejected
Let us consider a group with P positive instances and N negative instances of some condition. The four outcomes can be formulated in a 2×2 ''contingency table'' or ''confusion matrix'', as follows:

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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