01 · The dial that does the damage
Drag prevalence down and watch the colour drain out
Leave the test untouched — fix it at a flattering 90% sensitivity and 91% specificity — and move only the prevalence dial. At 30% prevalence a positive is trustworthy; the grid is mostly azure. Slide prevalence toward 1% and the azure shrinks to a few squares while the ochre false alarms flood in, even though the test never changed. The instrument is the same; the meaning of its verdict is not.
This is the whole base-rate fallacy in one motion. The test's accuracy is a property of the test. The worth of a positive is a property of the test and the population it's pointed at — and at low prevalence the population wins.
Switch to "just the positives" and the screen shows only the pool a doctor actually faces: a mix of azure and ochre whose ratio is the positive predictive value. That ratio, not the accuracy on the box, is what your result is worth.
02 · Why counting beats percentages
The numbers are easier as people
Ask someone the probability directly — "90% sensitive, 91% specific, 1% prevalence, what's a positive worth?" — and most people, including clinicians, guess far too high. Lay the same facts out as a count of people, the way the matrix does, and the answer becomes almost obvious: of 1,000 people, 10 are sick and 9 of them test positive; of the 990 healthy, about 89 test positive too; so 9 out of roughly 98 positives are real. That's the explorer's headline number, and it's the format the psychologist Gerd Gigerenzer showed can rescue people from the fallacy.
The lesson generalises past medicine. Any time a rare thing is hunted with an imperfect filter — fraud flags, spam catchers, security alerts, DNA database matches — the same arithmetic applies, and the same trick defuses it. Stop multiplying percentages in your head and count a concrete thousand.
03 · Read more
The full story behind the dials
This sandbox is the playable companion to the compendium's entry on the base-rate fallacy, which walks through David Eddy's mammography problem, the natural-frequency cure in detail, and the courtroom version — the prosecutor's fallacy that helped convict Sally Clark. If the grid above has made the mechanism click, the entry is where it gets its history and its sharper edges.