Table of Contents
Got n?
There was a 100% increase in 1-hour parking meter costs this year!
(Imagined conversation in a small town.)
It appears to be hardwired into our wetware to forget to look for the underlying integers. You might ask, for example from what to what? and learn that it went up from a nickle to a dime.
This is a manifestation what Daniel Kahneman, author of Thinking Fast, and Slow (2011, Ferrar, Straus and Giroux, New York) calls The Law of Small Numbers. Our favorite ballplayer has a hot hand (random variation), an image of a religious figure appears in the bird tracks on a beach (randomness doesn’t look uniform, there are all sorts of random patterns) and, the big tell, statistical findings based on a small sample size, n are particularly vulnerable to random effects.
In one example the author gives as an example a survey of 1,662 schools in Pennsylvania. Of the top 50, six were small schools, about four times as many as you would expect to be exceptional. So, a well-known philanthropist, joined by some famous foundations, set up a program to split larger schools up into smaller schools. If small schools do better than average, after all, it only makes sense.
Unfortunately, turning the question around, small schools also tend to have worse outcomes than average. The smaller schools, good, bad or indifferent, are simply more variable.
Look for n, your first line of defense against putting your money where the facts aren’t.
