Base Rate Visualizer
A test that is 99% accurate sounds like a 99% verdict — but if the condition is rare, most positive results are false alarms. This visualizer makes that concrete with a population of 1000 dots. Set the prevalence on a log slider (from 1 in 1000 to 1 in 2), the test’s sensitivity and its specificity, then test everyone: dots recolour into true positives, false positives, true negatives and false negatives, and the headline readout gives P(sick | positive) the way humans actually understand it — “of the N people who test positive, only k are sick.” A natural-frequency tree diagram traces the population through sick/healthy branches and test outcomes, and presets jump to the classic cases: rare-disease screening, a common condition, and airport security screening.
Runs 100% in your browser — simulations are computed locally on your device.
Read the full guide to this tool
Notes
- Bayes’ theorem in count form: P(sick | positive) = true positives ÷ (true positives + false positives). When the condition is rare, the healthy majority generates so many false positives that they swamp the true ones.
- Sensitivity and specificity describe the test; the base rate describes the population. Ignoring the base rate and reading test accuracy as your personal probability is the base rate fallacy — most doctors asked this question get it wrong.
- Natural frequencies (“10 of every 1000 people…”) fix the intuition: studies by Gigerenzer show people who fail the percentage version answer correctly when the same problem is posed in counts.
- The same arithmetic dooms mass screening for rare events: an airport scanner that is 99% accurate on a one-in-a-million threat flags roughly ten thousand innocent travellers per true hit.
- Runs 100% in your browser — simulations are computed locally on your device.
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