Saturday, December 08, 2007

A statistical curio

Further to my talk about sexism, here's an example of tricksy statistics where it had a real life implication.

Lets suppose we know that 100 women and 100 men apply for a college each year. Of those, 41 men get in, and only 20 women. That place must be discriminating, right? Not necessarily. Let's suppose that college has two courses, call them super hard course and very easy course. Suppose super hard course only accepted 10% of women and 5% of men, and very easy accepted 60% of women and 50% of men. Now if anything both these courses appear to be discriminating against men. Now let's suppose that 80% of men apply for the super easy course, and 80% of women for the super hard course. Then for the super easy course, 50% of 80 is 40, so 40 men are accepted, and 60% of 20 is 12 women. Then in the super hard course, 5% of 20 is 1, so 1 man is accepted, and 10% of 80 is 8, so only 8 women are accepted.

So, strangely enough, despite the college discriminating in favour of women, so many are applying for the harder to enter course, that their numbers overall are lower! This is an interesting factor, and is why one should always be careful about statistics- they can mislead.

Another example, this time called simpson's paradox. If one looks at the proportion of white men charged with murder put to death compared to that of the proportion of black people, it appears that there is some discrimination against black people. However, if you factor in the colour of the victim, it turns out that juries will very rarely put to death someone who has killed a black person, but more frequently a white person. Indeed, in some statistics I saw, no white person had been put to death for killing a black person. With these statistics, it was clear that there was discrimination against black people- they were getting executed more, but without compensating for extra factors we could not see it. Bear in mind that even this is not a complete picture, as economic status was not considered- this execution bias could be mainly due to economic status rather than race, as more black people are impoverished in the US.

Statistics is a powerful tool, but it can be misused quite easily, either deliberately or not. It's best to look at the data critically, and look at what other statisticians have to say about it, other than just the people doing the study.


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