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 phenomenon comes up all the time. It’s good to know someone has given it a name.
3 thoughts on “The law of small numbers”
I think The Law of Small Numbers is even stronger than underestimating the variability of small samples: they actually remove whole sections of the outcome space from their visions of distributions. Or, to put it another, people seem to refuse to believe that a random process can produce things that look structured with any probability other than 0.
Not to be confused with the Strong Law of Small Numbers. :) The SLSN provides an explanation for some of those striking coincidences that make mathematics seem so mystical to some.
Hi, don’t want to appear like a spelling nazi, but I always wonder why so many people misspell the word “phenomenon” as “phenomena”. I have even seen this error in scientific papers and theses, so it is widespread even in educated circles. Also, it is obviously not just a typo, but genuinely believed to be correct by the “offenders”. Alas, while “phenomena” is the correct plural form, the singular form is “phenomenon”, and “phenomenon” only!