17/03/2008

What Statistics Should Be Taught in School?

H.G. Wells famously said that in the future, a knowledge of statistics will be as important as the ability to read and write (statisticians' favourite quote). That's taking it a bit far, but statistics certainly is more important than most of the stuff they taught me in school. I've long forgotten how many teeth alsatians have, and I don't feel the poorer for it.

Given that in politics statistics are constantly thrown about, sometimes in misleading ways, one should think that a basic knowledge of statistics comes in quite handy if you want to make a fairly informed decision in the voting booth. It is hence a bit surprising that statistics isn't taught more in schools (at least not here in Germany). What's the elementary stuff every pupil ought to learn? Here's my list.

1. Mean, median, mode.

2. Standard deviation.

3. Percentages. Why they're not the same as percentage points. (Actually, if I remember correctly, I was taught this in school.) Pupils should be able to spot the fallacy in the following sentence: "Mr. A's fortune increased by 10% in 2000 and decreased by 10% in 2001, so in 2002 he had as much money as in 1999."

4. The difference between frequencies and rates. When to use which. Aim: Pupils cringe when they read: "If you look, in fact, at emergency room statistics, you'll see that more people are admitted every year for non-dog bites than dog-bites—which is to say that when you see a Pit Bull, you should worry as much about being bitten by the person holding the leash than the dog on the other end."* Which, sadly, comes from one of America's most popular nonfiction writers.

5. Correlation. Should come with everybody's (well, not everybody's) favourite caveat that it's not causation.

6. The basics of multivariate analysis. No, I don't want them to learn about heteroskedasticity. The lesson should be that, given the complexity of the world, it's sometimes not good enough to just relate two variables.

7. The basics of Bayesian reasoning. Again, I don't want them to learn the actual formula, but they should know why when they get tested positive for some condition with a test that's 99% accurate, it does not follow that their likelihood of having the condition is 99%. This is especially important because many doctors do not know this.

If this were coupled with an introduction to scientific methodology, I wouldn't mind. It should be possible to teach all of the above to a reasonably intelligent sixteen-year-old, and this knowledge is certainly more important than a knowledge of Shakespeare. And I like Shakespeare.

*That actually contains a second fallacy (Pit Bulls = Dogs), but let's leave that aside.

2 comments:

Bill said...

This stuff is not taught in high school in the United States either. While most students are introduced to the concepts of correlations and know how to average numbers (i.e. mean), the rest of your listing is not taught until college and usually in the 3rd and 4th year and again for an advanced degree in any of the sciences.
Bill/Louisiana

LemmusLemmus said...

Yes, kids learn averaging in Germany too, of course, and I would think in most countries where they go to school for more than six years or so.

But according to my recollection, it was that and percentages and nothing else from the list. Of course, my experience may not be representative, especially because these things can differ between states and even individual schools as well as over time.