Women Who Think, cont'd
Maybe English majors really are better at this stuff than MIT biologists. Here's Megan McArdle on the Summers flap. Here's a small sample:
4) People who are arguing that it's stupid to generalise from means or distributions to individuals...are right, but only in a trivial, irrelevant way. The particular discussion at hand revolves around the fact that there are fewer women than men in many scientific disciplines, particularly, it seems to me from the outside, the ones that involve a great deal of rather abstruse math. We are looking at a population, not an individual, and it is entirely proper--nay, necessary--to discuss group averages. That we cannot divine any individual's ability from those averages is true, but irrelevant; we're looking at the group.
Look at it this way: I am 6'2 (1.88 metres), which puts me four standard deviations from the mean height of American women--approximately one tenth of one percent of American women will be as tall as, or taller than, I am.
Could we use the average of the female population to predict that I am not 6'2? No! I am 6'2. We would get the answer wrong if we tried to use the average predictively.
Could we use the average to bet, sight unseen, on whether or not I am taller than 6'1? Yes! Only 0.3% of the female population is taller than 6'1. If you had to bet, you'd bet against it. Of course, in my case you'd be wrong--but it would still be the right way to bet.
But do we need to bet? No! We can measure me. Similarly, physicists considering female candidates have lots of other means to assess their physics ability. They don't need to look at whether or not she's female.
But if we were looking at an organisation that only hired people who were taller than 6 feet because they needed them to reach very tall shelves, most of the employees would be men. We might infer discrimination, but we'd be wrong. It's just that innate differences would produce differing results for men and women. And if I showed up and they refused to hire me because I'm a women, and women have a very low probability of being that tall, that would be discrimination, because they can look right at me and see that despite being a member of a group with a lower mean height, I myself am in fact configured like a beanstalk.