The Significance of Statistics

The science columnist Clive Thompson has an interesting article over at Wired on the problematic interplay between the average person’s lack of statistical understanding, and the increasing importance of statistical evidence in public policy debates.  He takes as his starting point events around the major snowstorms we had this past winter here in the Washington DC area.  Many of those skeptical of the idea of global warming immediately cited the snowstorms as proof that global warming couldn’t be true.

Now, if Thompson’s point was just that this argument was idiotic, there really wouldn’t be much else to say.  But he goes on to talk about something that has become a concern of mine in the last few years: the serious ignorance of journalists — even science journalists — and the public at large when it comes to understanding statistical data.

We live in a world where the thorniest policy issues increasingly boil down to arguments over what the data mean. If you don’t understand statistics, you don’t know what’s going on — and you can’t tell when you’re being lied to.

Climate change is just one example of an area where lack of understanding leads to foolish or pernicious claims.  Lack of statistical understanding also bedevils the criminal justice system: for example, with respect to evidence based on fingerprints or DNA.  It also occasions a great deal of confusion in medical testing, particularly with regard to the base rate fallacy. As Thompson points out, there are many other examples of very dubious conclusions arrived at due to lack of statistical understanding.

I’ve sometimes been asked, by parents of high-school students, whether they should take probability and statistics courses, and why they are important.  There are basically two parts of my answer.  The first is that, as Thompson’s article suggests, understanding at least the basics of statistical analysis is important to playing a constructive role as a citizen.  The second is that, although the mechanics and calculations of statistical analysis are usually not especially difficult, the mental discipline required to think about problems carefully is not easy or intuitive.

Granted, thinking statistically is tricky. We like to construct simple cause-and-effect stories to explain the world as we experience it. “You need to train in this way of thinking. It’s not easy,” says John Allen Paulos, a Temple University mathematician.

Doing it right takes instruction and practice.  Even very simple problems can be traps for the unwary or unskilled.  I’ll talk about that a bit more, and give some examples, in a follow-up post.