Kahneman and Tversky's ironic label: people act as if the law of large numbers applies to small samples too. Small samples yield extreme results more often; we treat those extremes as meaningful causes instead of sampling noise.
Examples
- Kidney cancer counties: lowest and highest rates both in sparse rural counties — population size, not lifestyle
- Gates Foundation small schools: top performers are often small schools; worst performers are also often small — variance, not quality
- Hospital babies: smaller hospital records more days with >60% boys than larger hospital
- Hot hand: basketball streaks look causal; data show random sequences
Researchers themselves trusted studies with absurd 50% failure risk because they underweighted sample size — the discipline that should know better.
Relation to base rates
base-rate-neglect ignores priors; law of small numbers misreads what a small sample can prove. Both feed overconfident stories from thin evidence (wysiati).