Sadly, many people do not realize that even if the majority of those who engage in behavior X belong to category Y, that does not mean that the majority of people in category Y engage in X.  This point is often made, rightly, with respect to race and violent crime and religion and terror.  But most treatments I’ve seen either imply that anyone who doesn’t understand is a moron, or manage to scare away the target audience by throwing in a pile of math without explaining it.  In this post, I’ll try to actually explain why we can’t conclude that most members of Y are prone to acts of X even if most acts of X are committed by members of Y.  This post won’t insult anyone for being unfamiliar with Bayes’ Theorem, nor will you find much algebra herein.  I’m just going to try to explain, with a relative minimum of technical detail, why we can’t assume that most members of Y engage in behavior X just because most people who engage in X are members of Y.

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