Thursday, September 25, 2014

More remarks on gender and selection

In the spirit of David Sumpter's Open Science 4.0 (what happened to 3.0, did I miss it?), I thought I'd try a simple model to offer as one possible explanation for the low acceptance of female candidates to the Royal Society's University Research Fellowships, which I posted about earlier

But first, a digression to the distant past, when I was a naive young man applying to university. Back in those days a key aspect of your application was your 'personal statement', a short essay in which you tried to convince a 40-50 something year old professor that you, a spotty 17 year old, were a person of great merit and potential, and alluded to all the exciting 'extra-curricula activities' you did -- transforming a few lessons on the clarinet into a deep and abiding passion for music etc.

One teacher of mine (hello Mr Apsy!), while I was writing this absurd statement, gave me some of the best advice I've ever received. 'Say something outrageous' he advised, 'you need to be noticed to get an interview, then they won't care afterwards'. And so, my application to study physics started 'I've never really liked physics...'. A year later a physics professor had, somewhat questionably, agreed to teach me.

E = who the hell cares?

Why this digression? Well, I think it illustrates an important point. We were competing to be admitted to a course where only ~1/5 applicants, all with perfect grades, were accepted. Mathematically, we were in the tail of the distribution. And there were no prizes for being average within this tail. No prizes for playing it safe. My stupid statement would either be interpreted as brilliantly provocative, or simply idiotic. If I was deemed idiotic, nothing lost compared to being average. But if it was deemed provocative, the place could be mine!

How does this have anything to do with the URF scandal. The URF also selects a low percentage (~1/10) of applicants, all of whom are already in the far tail of scientific ability. Several studies (I will use the luxury of blogging not to bother looking them up) have suggested that while men and women perform equally well on most tasks on average, men often have a higher variance. Some people have speculated on evolutionary reasons for this, in the winner-takes-all world of mate selection, but it could equally be due to the way we bring children up, encouraging boys more often in a he-who-dares-wins spirit. The point is, if men have higher variance in their performance, how would this effect their acceptance to prestigious awards like the URF.

I did a little study. Assume that there are 400 applicants to the URF, 20% of whom are women, matching the real figures. Also assume that the men and women are, on average, exactly the same. But the men have a higher variance, some multiple of the women. Everyone's standard is normally distributed. If we then select the best 40, how many will be women? It depends a lot on the ratio of male/female variance.

If the variances are equal, we get exactly 20% of admissions being women. But as the ratio goes up, even though men and women remain the same on average, the number of women selected goes dramatically down. Many men have been deemed idiots, but they suffer no worse fate than the women deemed average. 

Why have this years results been so different to previous years. Well, conditions in academia have been pretty tight for a few years now - perhaps as people get more desperate they increase the variance in their applications as they try more outlandish things. Perhaps men do this more than women, it wouldn't surprise me.

We'd need a ratio of ~1.6 to get this years result. What sort of ratio might be reasonable to assume in real life - I have no idea. What I do know is that I doubt as many girls at school get told to 'say something outrageous' as do boys. Possibly fewer who do are interpreted as 'provocative' rather than 'daft'. The roots of inequality in something like the URF, where selection takes place in the tail, are about far deeper factors than a few selectors favouring men. And if you're a teacher, tell your students to try saying something outrageous on occasion. It can be a brilliant substitute for genuine knowledge or talent! Especially if you're white, male, middle-class...etc etc etc.

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