A test can be very sensitive yet produce many false positives if the condition is rare, which is why predictive values matter.
How to use the Sensitivity and Specificity Calculator
- True positives
- False positives
- False negatives
- True negatives
Results update as you type, and every field accepts the units shown in its menu.
How it works
Each metric is a ratio of counts from the confusion matrix.
Inputs explained
| Field | What to enter |
|---|---|
| True positives | A number |
| False positives | A number |
| False negatives | A number |
| True negatives | A number |
What each result means
- Sensitivity (recall) = [True positives]÷([True positives] + [False negatives])×100
- Specificity = [True negatives]÷([True negatives] + [False positives])×100
- Positive predictive value (precision) = [True positives]÷([True positives] + [False positives])×100
- Negative predictive value = [True negatives]÷([True negatives] + [False negatives])×100
- Accuracy = ([True positives] + [True negatives])÷([True positives] + [False positives] + [False negatives] + [True negatives])×100
- F1 score = 2×[True positives]÷(2×[True positives] + [False positives] + [False negatives])
- Positive likelihood ratio = ([Sensitivity (recall)]÷100)÷(1 – [Specificity]÷100)
Example values
How the main result changes when True positives changes and everything else stays at the example values above:
| True positives | Sensitivity (recall) (%) |
|---|---|
| 45 | 81.82 |
| 67.5 | 87.1 |
| 90 | 90 |
| 112.5 | 91.84 |
| 135 | 93.1 |
| 180 | 94.74 |
Formula
Sensitivity = TP ÷ (TP + FN)Specificity = TN ÷ (TN + FP)PPV = TP ÷ (TP + FP)Worked example
Inputs — True positives: 90; False positives: 40; False negatives: 10; True negatives: 860.
Results — Sensitivity (recall) = 90 %; Specificity = 95.56 %; Positive predictive value (precision) = 69.23 %; Negative predictive value = 98.85 %; Accuracy = 95 %; F1 score = 0.7826; Positive likelihood ratio = 20.25.
Frequently asked questions
Why is PPV low for rare diseases?
Even a small false-positive rate produces many false positives when most people are healthy.
What is the F1 score?
The harmonic mean of precision and recall.
What formula does the Sensitivity and Specificity Calculator use?
Sensitivity = TP ÷ (TP + FN).