August 22, 2010
Easterly on Reversing Conditional Probabilities

Here's a great post from William Easterly in which he points out a fundamental statistical mistake that a lot of opponents of Park51--aka "Ground Zero Mosque"--and similar projects are making.

In short, we're getting our conditional probabilities wrong. A lot of terrorists are Muslims. This does not mean that a lot of Muslims are terrorists. Consider a similar example. Rhodes is now in possession of an interesting collection of papers from a former KKK leader in Tennessee. The papers are mostly from the late 1960s and early 1970s. If I remember correctly, the gentleman in charge was also a prominent member of his church (director of the Sunday School program, I believe). Their local chapter paperwork included a line item for the number of ministers enrolled. If you took a census of KKK members at virtually any time in the organization's history, it's a fair guess that very high percentage would identify themselves as Christians. The probability that one identifies as a Christian given that he or she is a member of the KKK is very high. It would absurd to infer from this that the probability that one is a member of the KKK given that he or she identifies as a Christian is also very high.

I've been following the mosque controversy and participating in the discussion because I view it as a teachable moment (I have a Forbes piece or two or three in the pipeline). Not only does it teach us about institutions, history, theology, and economics, it's a very useful lesson in statistics. I suspect that p(terrorist|Muslim), just like p(Klansman|Christian), is pretty low.

Posted by Art Carden at 01:10 PM in Misc.

The statesman who should attempt to direct private people in what manner they ought to employ their capitals would not only load himself with a most unnecessary attention, but assume an authority which could safely be trusted, not only to no single person, but to no council or senate whatever, and which would nowhere be so dangerous as in the hands of a man who had folly and presumption enough to fancy himself fit to exercise it. -Adam Smith

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