A field guide to the ways reasoning breaks
Evidence and sampling
Also called Base rate fallacy
Reading a test result or signal without accounting for how rare the underlying condition is.
The test is 99 percent accurate and positive, so I almost certainly have it.
Ask how common the condition is in the population before reading the result.
Named 'base rate neglect' by psychologists Amos Tversky and Daniel Kahneman, who showed in the 1970s that people ignore how common a condition actually is once they are handed an individuating detail. The taxi-cab problem became the canonical demonstration. The math behind the correction is Bayes' theorem.
A start-up rejects a candidate flagged by a fraud detector that is 95% accurate, forgetting that only 1 in 500 applicants is actually fraudulent — so most flags are false alarms.
A clinic panics over a positive screening whose accuracy is 99%, without mentioning the disease appears in about 1 in 10,000 people.
An airline safety analyst declares an incident pattern 'alarming' after two near-misses in a month, ignoring that the airline runs ten thousand flights a week.
A hiring platform claims its personality quiz predicts success with 90% accuracy, but high performers are so rare in the applicant pool that the quiz labels mostly false positives.