False Positive Paradox Calculator
Understand how even accurate tests can return mostly false positives when the condition is rare. Adjust prevalence, sensitivity, and false positive rate to see the effect.
Base rate of the condition in the population.
True positive rate (test detects condition).
Probability of a positive test when healthy.
Positive Predictive Value
16.10%
Chance condition is present after a positive test
Negative Predictive Value
99.95%
Chance condition is absent after a negative test
Positive Test Rate
5.90%
Overall probability of testing positive
| Metric | Value | Interpretation |
|---|---|---|
| Specificity | 95.00% | True negative rate |
| False Discovery Rate | 83.90% | Chance a positive test is a false alarm |
| False Omission Rate | 0.05% | Chance a negative test misses the condition |
| Base Rate | 1.00% | Prevalence before testing |
How to Use This Calculator
- Enter the condition's prevalence (base rate) in decimal form.
- Provide the test's sensitivity (true positive rate).
- Enter the false positive rate (1 − specificity).
- Review the positive predictive value to see how likely a positive result represents a true condition.
Formula
PPV = [Se · Prev] / [Se · Prev + FPR · (1 − Prev)]
NPV = [Sp · (1 − Prev)] / [Sp · (1 − Prev) + (1 − Se) · Prev]
Se = sensitivity, Sp = specificity, FPR = 1 − Sp
These formulas arise directly from Bayes' theorem and highlight how low prevalence (Prev) can make PPV surprisingly small even when sensitivity and specificity are high.
Full Description
The false positive paradox describes the unintuitive reality that most positive test results can be wrong when the condition is rare. Even with a high sensitivity and specificity, the sheer number of healthy people means false positives can outnumber true positives. This calculator quantifies that effect to improve medical decision-making, screening program evaluation, and public communication.
Adjust prevalence to explore how targeted testing (higher base rate) boosts the trustworthiness of positive results, or see how broad screening of a low-risk population produces large numbers of false alarms.
Frequently Asked Questions
Why does prevalence matter so much?
When a condition is rare, there are far more healthy people than sick people. Even a tiny false positive rate can overwhelm true positives, lowering the chance that a positive test is meaningful.
How can we improve PPV?
Target testing to higher risk groups (raising prevalence), reduce the false positive rate, or require confirmatory tests before acting on a positive result.
What is the relationship to Bayes' theorem?
PPV is the posterior probability P(Condition | Positive). Bayes' theorem combines the base rate, sensitivity, and false positive rate to compute it exactly.
Can I input percentages?
Convert percentages to decimals first (e.g., 5% = 0.05). Working in decimals keeps the formulas simple and precise.