Sensitivity
Sensitivity, also known as Recall or the True Positive Rate (TPR), is a performance metric used in classification problems. It measures how well a model can identify actual positive instances.
Definition
Where:
- TP = True Positives – actual positives correctly predicted
- FN = False Negatives – actual positives incorrectly predicted as negative
Sensitivity answers the question: "Out of all real positive cases, how many did the model correctly identify?"
Alternate Names
- Recall
- True Positive Rate (TPR)
- Hit Rate (in signal detection theory)
Simple Example
A disease test is applied to 100 patients who have the disease. The model predicts:
- 90 correctly diagnosed as sick → TP = 90
- 10 wrongly predicted as healthy → FN = 10
This means the model successfully detected 90% of the sick patients.
Importance of Sensitivity
Sensitivity is **critical** in applications where missing a positive case can have serious consequences.
Real-World Scenarios
- Medical diagnosis: Missing a disease can be fatal.
- Security systems: Failing to detect a threat may be dangerous.
- Fraud detection: Missed fraud cases are costly.
Sensitivity vs Specificity
- Sensitivity measures how well you find actual positives.
- Specificity measures how well you avoid false alarms (negatives correctly identified).
Formula for Specificity (for comparison)
Where:
- TN = True Negatives
- FP = False Positives
Related Metrics
- Recall – Sensitivity is another name for Recall
- Specificity – Measures true negative rate
- Precision – Measures correctness of positive predictions
- F1 Score – Balances Sensitivity and Precision
- Confusion Matrix – Base table for all classification metrics
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