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Specificity is the fraction of actual negative cases correctly identified as negative.
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Formula
dimensionless, 0 to 1; undefined when TN+FP=0
| Symbol | Meaning | Unit |
|---|---|---|
| True negative predictions | count | |
| False positive predictions | count |
\text{Spezifität}=\frac{TN}{TN+FP}Specificity is the recall of the negative class, or the true negative rate. It measures how many actual negatives avoid a false alert. Together with sensitivity/recall it characterizes both sides of a classifier at a fixed threshold. When TN+FP=0, the test set contains no actual negatives and the ratio is undefined. The value alone does not state prevalence or positive predictive value.
Specificity is the recall of the negative class, or the true negative rate. It measures how many actual negatives avoid a false alert. Together with sensitivity/recall it characterizes both sides of a classifier at a fixed threshold. When TN+FP=0, the test set contains no actual negatives and the ratio is undefined. The value alone does not state prevalence or positive predictive value.
Specificity is the fraction of actual negative cases correctly identified as negative.
False-positive rate from specificity
For a fixed binary class and threshold.
Use the example for Specificity (true negative rate) to explain which inputs determine the requested output.
The example connects concrete inputs to its result.
Specificity is the fraction of actual negative cases correctly identified as negative.
The relation applies only under its stated assumptions.
Applying the relation to a different case without checking its stated assumptions.
Check the validity range before substituting values: Specificity is the recall of the negative class, or the true negative rate. It measures how many actual negatives avoid a false alert. Together with sensitivity/recall it characterizes both sides.
Formula cluster
Specificity is the fraction of actual negative cases correctly identified as negative.
For TN=90 and FP=10, specificity=90/(90+10)=0.90: nine of ten actual negatives are correctly rejected.
Evaluate false-alert behavior in binary classifiers and diagnostic tests.
Here is how to work through a typical Specificity (true negative rate) (TNR = TN/(TN+FP)) task step by step:
Task
Use the example for Specificity (true negative rate) to explain which inputs determine the requested output.
Solution path
The example connects concrete inputs to its result.
Specificity is the fraction of actual negative cases correctly identified as negative.
The relation applies only under its stated assumptions.
Specificity is the fraction of actual negative cases correctly labeled negative. It is TN/(TN+FP), also called the true negative rate. High specificity means few false positives among negatives, but it does not say how many positive cases were found; use recall or sensitivity for that. Specificity concerns actual negative cases and depends on the threshold. Report it with sensitivity, class definition and confusion matrix; a single value does not show prevalence or reliability of positive predictions. Differences in the test population can also shift the observed value.
Read TN as correctly rejected negatives and FP as false positive alerts. With TN=90 and FP=10, specificity is 90/100=0.90. Check that actual classes were read correctly in the confusion matrix. The score is dimensionless; multiply by 100 only when expressing it as a percentage. Specificity concerns actual negative cases and depends on the threshold. Report it with sensitivity, class definition and confusion matrix; a single value does not show prevalence or reliability of positive predictions. Differences in the test population can also shift the observed value.
Both concern actual negatives. Specificity is TN/(TN+FP), while false-positive rate is FP/(TN+FP). They therefore sum to one for the same test and threshold. Do not confuse this with false discovery rate FP/(TP+FP), whose denominator is all positive predictions. Specificity concerns actual negative cases and depends on the threshold. Report it with sensitivity, class definition and confusion matrix; a single value does not show prevalence or reliability of positive predictions. Differences in the test population can also shift the observed value.
The threshold decides when a model score becomes a positive prediction. Raising it often yields fewer positive alerts: FP may fall and TN rise, increasing specificity. More actual positives may then be missed. The score therefore describes one operating point; an ROC curve or multiple thresholds give more context. Specificity concerns actual negative cases and depends on the threshold. Report it with sensitivity, class definition and confusion matrix; a single value does not show prevalence or reliability of positive predictions. Differences in the test population can also shift the observed value.
If TN+FP=0, the evaluation contains no actual negative cases, so the correctly negative fraction cannot be computed. Software may warn or return zero by convention, but that is not observed specificity. Ensure the test set contains relevant classes and report any library convention used for this edge case. Specificity concerns actual negative cases and depends on the threshold. Report it with sensitivity, class definition and confusion matrix; a single value does not show prevalence or reliability of positive predictions. Differences in the test population can also shift the observed value.
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How do you rearrange Specificity (true negative rate) for False-positive rate from specificity?
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