Bayesian Diagnostic
For a test with given sensitivity and specificity, see how PPV / NPV change with disease prevalence. The 2 × 2 table and likelihood-ratio arrows update live so you can see exactly why a "99% accurate" test gives only 10% confidence in a rare disease.
P(disease | test+) = —
P(disease | test−) = —
LR+ = —
LR− = —
2×2 table for N =
Effective confidence after a positive test
Bar fills left→right with PPV. Note how a tiny prevalence collapses it.
How to read this
A test that is "99% accurate" sounds great, but if you test 10,000 random people for a disease that only 1% have, you can expect ~99 true positives, ~10,000 false positives, and you end up with about 1 real case per positive result. The PPV bar makes this gap visible.
Use cases
Medical screening
Evaluate pre-test probability and post-test shifts before ordering confirmatory tests.
Spam / fraud detection
Map "spam recall 99%" to actual precision under realistic prevalences (often <1%).
A/B testing prior
Think of "sensitivity" as α, "prevalence" as base conversion rate. PPV is power-adjusted lift.
When not to trust this
- Real diagnostic accuracy varies by severity, threshold, and population sub-group. Use test-specific values from the literature.
- Sequential testing radically changes PPV; we show only one-shot results.
- Pre-test probability is itself a question — this calculator assumes you have a defensible prior.
FAQ
What is the "base rate fallacy"?
It is the tendency to ignore prevalence when interpreting a test. PPV depends strongly on prevalence; the calculator visualises this so you don't have to memorise the formula.
Are likelihood ratios useful?
Yes — they let you chain tests. LR+ ≈ 10 is a "strong" rule-in test, LR− ≈ 0.1 is a "strong" rule-out. Use them when you have multiple test results.