What's Wrong With Statistics (at least the ones you read in the news)

On the web or in newspapers, you can read excellent articles such as this. In it, you can read how the male brain is 10% larger on average, but the female brain has more connections. Men think more with the left side of the brain and are therefore more logical. But women have more nerve connections and a bigger corpus callosum (that's the part of the brain that connects the left and right halves), so they use both hemispheres of their brain more in-sync and are therefore better at intuition, communication... basically, women are better at everything that really matters, while men are good for the workforce, as cannon fodder, and for fixing your PC.

Well, the latter isn't even true anymore, now that the majority of 'puters are tablets that cannot be fixed if you don't have a contract with Apple(TM). D'uh.

Sounds about right, doesn't it?

Well... it doesn't. I often had this vague feeling that those claims were somehow wrong. Regardless of whether statistics were used to prove that men were superior (which is rarely the case nowadays) or (much, much more often!) that women are the epitome of goodness; or to show that immigrants are criminals; or that religious people live longer than atheists; or even when the statistics seemed to support my prejudices, showing that the roman catholic clergy are more prone to become child molesters than the rest of us. Something was... off.

Maybe it's just because I was brought up on the firm idea that stereotypes are bad, period. Or it's because I'm a Jewish Studies minor. At any rate, I tend to mistrust generalizations over large groups of people. The pharisees are hypocrites? Really? Every single last one of them did nothing all day except feigning learnedness and empathy, while really clinging to an absurd law and forcing it on others? None of them had families to support? None of them earned their living with hard work? They didn't build schools for the poor and unprivileged? Look up the facts and be surprised.

I'm getting off topic, yeah.

So, basically, I read all those statistical facts, had a hard time believing them, but never could I pinpoint exactly what was wrong.

Then, some fine day, I talked to a friend who knows her way around maths. I mentioned one of those suspicious statistics. One about men and women, probably. And, with a conspiratorial smile, after she had blown out the candle and looked around the room lest anyone should overhear what secrets she had to tell, she whispered the following words into my ear: "Standard deviation, my friend, standard deviation!"

This came as a huge revelation, which I am glad to pass on to you now.

Here's the deal:

Let's say you are trying to score a goal from the penalty spot. Let's also say that you're not exactly the greatest soccer player never to have roamed the field of the Allianz Arena. You shoot 10 times. 5 times, you shoot 10 meters to the left of the goal. The other 5 times, you shoot 10 meters to the right. Not counting those times when you didn't even manage to hit the ball.

So on average, you have hit the goal exactly 10 times. Right in the middle. That's a 100% success rate, right there.

And that's exactly what's wrong with the article quoted above. And that's exactly what's wrong with about 95% of all articles that quote statistics. They all tell you the average, but not the standard deviation. That's about as useful as telling you that the boiling point of water is 75.5°C.

It's not exactly relevant whether women have a, say, 10% larger corpus callosum on average, if the standard deviation is 2 times larger than that. It won't mean that any specific woman you meet will top any specific man in any one area with any reliability. It doesn't help us much to know that the female sexual partners of circumcised men run a slightly lower risk of cervical cancer (they don't, by the way). Not if sexual faithfulness, personal hygiene and the average time between sexual encounters are much more indicative factors.

So... don't believe me, I implore. But the next time you read your newspaper, look out for that standard deviation. I bet you won't find it.

By the way, the boiling point of water is 75.5°C, according to Wikipedia. At 8000 meters above sea level, of course.