Specificity

Specificity

Specificity, also known as the True Negative Rate (TNR), is a performance metric in binary classification tasks. It measures the proportion of actual negative instances that are correctly identified by the model.

Definition

$\text{Specificity}=\frac{TN}{TN+FP}$

Where:

• TN = True Negatives – actual negatives correctly predicted
• FP = False Positives – actual negatives incorrectly predicted as positives

Specificity answers the question: "Out of all real negative cases, how many did the model correctly classify as negative?"

Alternate Names

• True Negative Rate (TNR)
• Selectivity

Simple Example

Suppose a test is used to detect a rare disease. Out of 1,000 healthy people:

• 950 are correctly identified as healthy → TN = 950
• 50 are incorrectly diagnosed with the disease → FP = 50

$\text{Specificity}=\frac{950}{950+50}=\frac{950}{1000}=0.95=95\mathrm{\%}$

This means the test correctly identifies 95% of healthy people.

Importance of Specificity

Specificity is vital when false positives can cause unnecessary stress, cost, or risk.

Real-World Scenarios

• Medical Testing: Avoiding false diagnoses of a disease (e.g., not telling a healthy person they are sick).
• Spam Filters: Ensuring genuine emails are not classified as spam.
• Fraud Detection: Not labeling legitimate transactions as fraudulent.

Specificity vs Sensitivity

These are complementary metrics:

• Sensitivity = Ability to detect positives
• Specificity = Ability to rule out negatives

Together, they form a balanced evaluation of a model, especially in medical or safety-critical applications.

Combined Evaluation: ROC Curve

Receiver Operating Characteristic (ROC) curves plot:

• Sensitivity (True Positive Rate) vs.
• 1 − Specificity (False Positive Rate)

This helps visualize the trade-off between catching positives and avoiding false alarms.

Related Metrics

• Sensitivity – True positive rate
• Precision – Positive prediction correctness
• Recall – Same as Sensitivity
• F1 Score – Harmonic mean of Precision and Recall
• Confusion Matrix – Base for all metrics

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