Law of Small Numbers

Jeremy Burrus & Justin Kruger

The law of small numbers refers to the incorrect belief held by experts and laypeople alike that small samples ought to resemble the population from which they are drawn. Although this is true of large samples, it isn't for small ones. So the “law” of small numbers isn't really a law at all, but a fallacy. And as such, it is a law you should feel free to break. To provide an example, suppose you have an urn containing marbles—half of them red and half of them blue (statisticians love urns…especially ones with marbles in them). Suppose further that without looking, you draw 100 of them. What ...

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