Was bernoulli wrong? On intuitions about sample size

Abstract

Recently we proposed an explanation for the apparently inconsistent result that people sometimes take account of sample size and sometimes do not: Human intuitions conform to the 'empirical law of large numbers,' which helps to solve what we called 'frequency distribution tasks' but not 'sampling distribution tasks' (Sedlmeier and Gigerenzer, 1997). Keren and Lewis (2000) do not provide an alternative explanation but present a three-pronged criticism of ours: (1) the normative argument that a larger sample size will not invariably provide more reliable estimates, (2) the descriptive argument that under certain circumstances, people are insensitive to sample size, and (3) the claim that sampling distributions are essential for solving both frequency and sampling distribution tasks. We argue that (1) the normative argument is irrelevant for our descriptive hypothesis and, as a normative claim, only valid for a specific situation, (2) the descriptive argument is correct but consistent with our review, and (3) is incorrect. Bernoulli's assertion that the intuitions of 'even the stupidest man' follow the empirical law of large numbers may have been rather on the optimistic side, but in general the intuitions of the vast majority of people do. Copyright © 2000 John Wiley & Sons, Ltd.