Summary

Tversky and Kahneman attribute the small sample fallacy to the heuristic that small and large samples should be equally representative. The normative rule is that small samples are not as representative as are large samples. Today not many people with a scientific training probably believe in what can be called the small sample fallacy for size or reliability of a sample, that samples of all sizes should be equally reliable. They are more likely to believe in what can be called the small sample fallacy for distributions, that small and large sample distributions should be equally regular. Small samples that appear too regular are judged to be less probable than are less regular samples. The gambler's fallacy is another small sample fallacy for distributions.

Investigators can reduce the number of students who believe in the small sample fallacy by demonstrating that small heterogeneous samples are often unrepresentative. A practical example of the small sample fallacy for size or reliability is the belief that an unexpected result in the behavioral sciences can be successfully replicated with a reduced size of sample.

Small samples assumed to be representative

People who commit the small sample fallacy can be said to assume that a small random sample should be as reliable as, and as regular as, a large random sample, but not too regular. Tversky and Kahneman (1971, p. 106; Kahneman and Tversky, 1972b, p. 435) attribute the small sample fallacy to the heuristic of representativeness.