False Positive Paradox Calculator

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The percentage of the population that actually has the condition. Also called the base rate or prior probability.
%
The probability that someone who has the condition tests positive. Also called recall or the true positive rate.
%
The probability that someone who does not have the condition tests negative. A specificity of 99% means 1% of healthy people will test positive (a false alarm).
%
The size of the hypothetical population used to compute absolute counts in the breakdown table. Does not affect the probability result.
people
Positive Predictive Value (PPV)More false than true positives
50%

The probability that a person who tests positive actually has the condition (Bayesian posterior).

Negative Predictive Value (NPV)99.99%
False Discovery Rate (FDR)50%
False Positive Rate (FPR)1%
True positives in population99
False positives in population99
True negatives in population9,801
False negatives in population1
50% %
Mostly false alarms<20Low PPV20-50Moderate PPV50-80High PPV80+

A positive result is more likely a false alarm than a real detection (PPV 50.0%).

  • More than half of all positive results are false alarms: only 50.0% of people who test positive actually have the condition.
  • In a population of 10,000, there would be roughly 99 true positives and 99 false positives among the 198 positive results.
  • Raising specificity reduces false alarms more effectively than raising sensitivity when prevalence is low. Increasing prevalence in the tested group (targeted screening) also improves PPV dramatically.

Next stepIf possible, apply the test to a higher-risk subgroup to raise the effective prevalence, which increases PPV without changing the test itself.

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