Even Bernoulli might have been wrong: a comment on intuitions about sample size

Abstract

The size of a sample is an essential concept of inferential statistics. The exact role of sample size is not entirely part of natural intuitions of either practitioners (Tversky and Kahneman, 1971) or of laypeople (Kahneman and Tversky, 1972). Recently, Sedlmeier and Gigerenzer (1997) proposed a framework that attempts to delineate the conditions under which sample size will (or will not) be appropriately used. We examine their proposed framework and question its validity. We further show that it is inaccurate to assume that a larger sample size will invariably provide a more reliable estimate than the smaller one. Studies in our laboratory and previous empirical data provide overwhelming evidence that, at least under a wide range of conditions, people are insensitive to the role of sample size. It is proposed that Bernoulli's assertion that ‘even the “stupidest man” knows that the larger one's sample of observations, the more confidence one can have in being close to the truth about the phenomenon observed’ (Sedlmeier and Gigerenzer, 1997) may be wrong from both a normative and a descriptive viewpoint. Copyright © 2000 John Wiley & Sons, Ltd.

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