How this calculator works
A rare condition leaves many more people without the condition than with it. Even a small false-positive rate applied to that large group can produce more false positives than true positives. Bayes theorem converts the test properties and prevalence into a positive predictive value. The output counts are expectations and may be fractional. Clinical interpretation requires a relevant patient population, a reliable reference standard and professional assessment; this model does not include confidence intervals or determine care.
Formula
TP = N × prevalence × sensitivity. FP = N × (1 - prevalence) × (1 - specificity). PPV = TP/(TP + FP). False discovery proportion = FP/(TP + FP).
Worked example
Among 10,000 people at 1% prevalence, 90% sensitivity yields 90 true positives. Specificity of 95% gives 495 false positives among the 9,900 people without the condition. The positive predictive value is 90/585 = 15.38%.
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Frequently asked questions
Is sensitivity the chance I have the condition after a positive?
No. Sensitivity conditions on having the condition. Positive predictive value conditions on a positive result and also depends on prevalence.
Why are expected counts fractional?
They are averages implied by probabilities. Actual observed counts must be whole numbers and vary from sample to sample.
Can I interpret a real result with population prevalence alone?
Individual risk and the tested population can differ. A clinician needs the test context and relevant evidence; this demonstration is not a diagnostic recommendation.