# True Negative Success Rate

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A True Negative Success Rate is a binary classification performance metric based on the Probability that a Predictive Logic Relation will correctly map a False Test Instance to a Negative Prediction.

**AKA:**Specificity, TNR.**Context:****Example(s):**- The probability of a negative test result in a patient who does not have the disease under consideration. E.g. probility that a test for cancer will predict that a patient does not have cancer when in fact they do not have cancer.
- …

**Counter-Example(s):****See:**Type I Error Rate, Type II Error Rate.

## References

### 2015

- (Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/Sensitivity_and_specificity Retrieved:2015-7-19.
**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).

- 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., all healthy are not identified as sick); however, theoretically any predictor will possess a minimum error bound known as the Bayes error rate.

### 2011a

- (Sammut & Webb, 2011) ⇒ Claude Sammut, and Geoffrey I. Webb. (2011). “Specificity.” In: (Sammut & Webb, 2011) p.907

### 2011b

- (Ting, 2011) ⇒ Kai Ming Ting. (2011). “Sensitivity and Specificity.” In: (Sammut & Webb, 2011) p.901

### 2009a

- (Wikipedia, 2009) ⇒ http://en.wikipedia.org/wiki/Sensitivity_(tests)#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 rate.

- 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.

### 2009b

- Eric W. Weisstein. "Statistical Test." From MathWorld -- A Wolfram Web Resource. http://mathworld.wolfram.com/StatisticalTest.html

### 1998

- (Kohavi & Provost, 1998) ⇒ Ron Kohavi, and Foster Provost. (1998). “Glossary of Terms.” In: Machine Leanring 30(2-3).
- True negative rate (Specificity): a/(a+b).
- Specificity: True negative rate (see Confusion matrix).