Statistics & Probability

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False Positive Paradox Calculator.

Calculate this statistic instantly with validated formulas.

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Set your values

Results update as you type.

Result: True positives: 1000.00 False positives: 4950.00 Positive predictive value: 16.8067%

Result

True positives: 1000.00 False positives: 4950.00 Positive predictive value: 16.8067%

Use Cases

Medical Screening Evaluation

Assess the reliability of a positive test result in a population with low disease prevalence, helping to understand the likelihood of false positives.

Example: Prevalence=0.01, Sensitivity=0.99, Specificity=0.95

Quality Control Testing

Evaluate the effectiveness of a manufacturing test when defects are rare, to determine if a positive result is likely a false alarm.

Example: Prevalence=0.001, Sensitivity=0.98, Specificity=0.99

Frequently Asked Questions

What is the false positive paradox?
The false positive paradox occurs when the number of false positives exceeds true positives, even when a test is highly accurate, because the condition being tested for is rare. This calculator helps you quantify this effect.
How do I use this calculator?
Enter the prevalence, sensitivity, and specificity as comma or space separated values in the 'Values' field. The calculator will compute the probability that a positive result is actually a false positive.
What do the input values represent?
The values are typically the prevalence of the condition, the test's sensitivity (true positive rate), and specificity (true negative rate). Ensure they are in decimal form (e.g., 0.01 for 1%).

Tips & Common Mistakes

Tips

  • Ensure all values are in decimal form (e.g., 0.05 for 5%) to get accurate results.
  • Double-check that sensitivity and specificity are between 0 and 1.
  • Use realistic prevalence values; the paradox is most pronounced when prevalence is low.
  • Interpret the result as the probability that a positive test is wrong, not the overall error rate.

Common Mistakes to Avoid

  • Entering percentages as whole numbers (e.g., 95 instead of 0.95) which leads to incorrect calculations.
  • Confusing sensitivity with specificity or swapping their values.
  • Using prevalence as a percentage without converting to decimal form.

Last updated: August 13, 2026