Needles in Haystacks

I think we might do a lot of good in the world, and even improve people’s personal decision-making, if we made everyone take a basic statistics class in high school. Certainly both the mammogram dispute and the post-Nidal Hasan resurgence of interest in “profiling” of Muslims is a reminder that most people don’t intuitively grasp the Bayes’ Law point about accurate tests for rare conditions. I’m finding it annoying to watch all these people with no relevant medical or scientific expertise sounding off about who should get checked for breast cancer, so let’s talk about terrorists instead.

Suppose I invent a magical device that can be pointed at a Muslim and say with 90% accuracy whether or not he’s an al-Qaeda operative. Well, if I start waving it around and it starts beeping on one guy, what should we conclude about him? A terrifyingly large number of people are going to say “there’s a ninety percent chance he’s with al-Qaeda! Let’s panic!” In fact, that’s not the case. There are a billion Muslims in the world. A test with 90 percent accuracy is going to mistakenly classify about 100 million of them as al-Qaeda operatives. And al-Qaeda actually has fewer than 10,000 people working for it. I’m going to get something like 10,000 false positives for every actual terrorist I find.

Meanwhile, applying the test to people is going to have severe consequences. The public doesn’t understand this correctly and is going to be put into a wholly unwarranted state of panic about the prevalence of terrorists. People will, of course, demand that those flagged by my machine be subjected to extra-heightened scrutiny. It’s easy to imagine lots of innocent people being mistakenly killed or subjected to discrimination or shunning. And that sense of beseigement and unfair treatment would ultimately heighten tensions between the world’s Muslims and the West, while wasting massive quantities of law enforcement resources chasing basically worthless leads.