‘Law of small numbers’

A tongue-in-cheek reference to the Law of large numbers by the researchers who coined the 'small numbers' term, Amos Tversky and Daniel Kahneman (http://repositories.cdlib.org/iber/econ/E00-282/), and concerns people’s belief that random samples of a population should closely resemble other samples and the population†, but without making adequate allowance for ordinary variations (combined with the misperception or operation of a ‘corrective bias’ when the sample’s appearance varies too much from what actors’ expect of a “fair” sample – this component of the effect can be recognized as the Gambler's fallacy).

As a result of such insensitivity to sample size, people have a tendency to draw recklessly strong inferences about populations from a knowledge of a very small number of cases. Scientists may also fall victim to this error and sometimes possess an exaggerated confidence in the validity of conclusions based upon small samples and the generalizability of the results obtained to an entire population.

† with such expectations of resemblance being greater than statistical sampling theory would predict.

(see also: clustering illusion, cognitive illusion, Sample size error, sample bias, pattern-seeking, Regression towards the mean, underestimating co-incidence)