The Screening Count

What a test result does to belief is computed by counting the flagged room — never by quoting the test's accuracy back as the answer.

A clinic screens for a condition carried by 4 percent of the people screened. The test is good: it flags 90 percent of carriers, and wrongly flags 10 percent of non-carriers. Your result comes back flagged — how worried should you be? Count 1,000 screened people. Carriers: 40. Non-carriers: 960. Now the flags. Of the 40 carriers, the test catches 90 percent: 36 flagged. Of the 960 healthy, it wrongly flags 10 percent: 96 flagged. The evidence arrives — you were flagged — and the world shrinks to the flagged room: 36 plus 96, 132 people. Your posterior is the carriers' share of that room: 36 of 132 — 3 in 11, about 27 percent. Sit with the shape of the answer: a 90-percent-accurate test, positive, and the odds still run nearly three to one that you are healthy — because the healthy are so numerous that their small error tide, 96 people, swamps the carriers' large detection, 36. The rarer the condition, the harder this logic bites, which is why real screening is followed by confirmatory testing rather than treated as a verdict. And notice what the right answer required: not the test's advertised numbers alone, but the base rate — the 4 percent — which the advertised numbers never mention. Run the same count in a high-risk clinic where 40 percent carry the condition, and the identical test's flagged room tells a different story — near six in seven. The instrument never changed; the room did.