False Positive Calculator
Calculate false positive rates, diagnostic test accuracy, and predictive values for medical testing
Calculate False Positive Rate
Percentage of population that has the disease
Probability healthy person tests negative
Probability sick person tests positive
Total number of people tested
Diagnostic Test Results
Confusion Matrix
| Test Positive | Test Negative | Total | |
|---|---|---|---|
| Disease Present | 900 | 100 | 1,000 |
| Disease Absent | 450 | 8,550 | 9,000 |
| Total | 1,350 | 8,650 | 10,000 |
Key Formulas
False Positive Rate: (100% - Specificity) = 5.00%
False Positives: (100% - Specificity) × (100% - Prevalence) = 4.50%
True Negatives: Specificity × (100% - Prevalence) = 85.50%
PPV: TP / (TP + FP) = 66.67%
Interpretation Guide
False Positive Rate: Good - Acceptable false alarm rate
Positive Predictive Value: Moderate - Many false positives expected
Overall Accuracy: Good test performance
Key Definitions
False Positive
Healthy person who tests positive (incorrectly diagnosed as sick)
True Negative
Healthy person who tests negative (correctly diagnosed as healthy)
True Positive
Sick person who tests positive (correctly diagnosed as sick)
False Negative
Sick person who tests negative (incorrectly diagnosed as healthy)
Performance Metrics
Common Examples
COVID-19 Test
Mammography
Diabetes Test
Understanding False Positives in Diagnostic Testing
What Are False Positives?
False positives occur when a diagnostic test incorrectly identifies a healthy person as having the disease. These cases can lead to unnecessary anxiety, additional testing, and potentially harmful treatments for people who don't actually have the condition.
Impact of Disease Prevalence
The prevalence of a disease significantly affects the positive predictive value of a test. In low-prevalence populations, even highly specific tests can produce many false positives relative to true positives.
Key Calculations
Clinical Considerations
- •High false positive rates increase healthcare costs
- •Patient anxiety and psychological impact
- •Need for confirmatory testing
- •Risk of overtreatment
Bayes' Theorem and Predictive Values
The positive predictive value (PPV) depends on both the test's specificity and the disease prevalence. Bayes' theorem shows us that even highly accurate tests can have low PPVs when screening low-prevalence populations.
Low Prevalence (1%)
Even with 99% specificity, most positive results will be false positives
Moderate Prevalence (10%)
Better balance between true and false positives with high specificity
High Prevalence (50%)
Most positive results are true positives even with moderate specificity