24 January 2008 by John.

In case my previous note on the law of small numbers confused anyone, I’ll compare it to the law of large numbers.

The law of large numbers is a mathematical theorem; the law of small numbers is an observation about human psychology.

The name “law of large numbers” is a standard term applied to a theorem about the convergence of random variables. (OK, actually two theorems. Like nuclear forces, the laws of large numbers comes in a strong and a weak form.)

The name “law of small numbers” is a pun, and I don’t believe the term is commonly used. Too bad. It’s a convenient label for a common phenomena.

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24 January 2008 by John.

The book Judgment under uncertainty analyzes common fallacies in how people estimate probabilities. The book asserts that no one has good intuition about probability. Statisticians do better than the general public, not because their intuition is much better, but because they know not to trust their intuition; they know they need to rely on calculations.

One of the common fallacies listed in the book is the “law of small numbers.” In general, people grossly underestimate the variability in small samples. This phenomena comes up all the time. It’s good to know someone has given it a name.

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