sample size fallacy

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A failure to take account of sample size when estimating the probability of obtaining a particular value in a sample drawn from a known population. Research into the fallacy was first reported by the Israeli psychologists Daniel Kahneman (born 1934) and Amos Tversky (1937–96) in an article in the journal Cognitive Psychology in 1972 describing an experiment in which participants were asked to estimate the probability of a group of people having an average height over 6 feet. The participants produced almost identical estimates for group sizes of 10, 100, and 1,000, whereas in reality the probability of an unusually high sample average, relative to the population average, is much greater in a small sample than in a large one. The fallacy is explained by the use of the representativeness heuristic, which is insensitive to sample size. The most common form of the fallacy is the tendency to assume that small samples should be representative of their parent populations, the gambler's fallacy being a special case of this phenomenon. Compare base-rate fallacy.

Subjects: Psychology.

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