Small sample size fallacy

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Simple statistics state that we are more likely to observe an unusual event in a small sample compared to a large one. Nevertheless, most people judge probability to b the same in each case, effectively ignoring sample size. When responding to problems dealing with sampling, people often use the representativeness heuristics. Most of the time, individuals ignore the issue of sample size.


Kahneman and Tverksy (1974) showed this presenting research participants with a problem of two hospitals. One is a small one (15 babies are born each day) and the other one is a large one (45 babies are born each day). They asked which hospital could have recorded an unusual event of 60% births of which were boys. Normally, there is a 50% chance that a newborn is either a girl or a boy.

Participants usually think there is an equal chance that this unusual observation occurred in any of the two hospitals. However, a smaller hospital is more likely to record a 60% newborn boys than a large hospital. People ignore the issue of sample size which is crucial to an accurate assessment of the problem.


Sample size errors can also be observed in advertising strategies. Ads state that “Four out of five dentist recommend this toothpaste” without mentioning the exact number of dentists involved. Assume five or ten dentists were surveyed to make this kind of a statement. The size of sample cannot justify the generalisation to the overall population of dentist. The results might be meaningless.

Adapted from

Bazerman, M.H. and Moore, D.A., 1994. Judgment in managerial decision making (p. 226). New York: Wiley.

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