I'm interested in the findings of this paper from 2009:
Why are (the best) women so good at chess? Participation rates and gender differences in intellectual domains
This paper attempts to explain why the very best male chess players appear to be so much better than the very best female players (females make up only 2% of the world's best 1000 players). Specifically, they claim that the large discrepancy between the best male and the best female chess players is entirely explained by 2 facts:
- There are 15 times more male than female chess players
- We expect this ratio to be exacerbated at the extreme ends of the distribution, entirely for statistical reasons. To quote the paper:
Even if two groups have the same average (mean) and variability (s.d.), the highest performing individuals are more likely to come from the larger group. The greater the difference in size between the two groups, the greater is the difference to be expected between the top performers in the two groups
This study demonstrates that the great discrepancy in the top performance of male and female chess players can be largely attributed to a simple statistical fact—more extreme values are found in larger populations.
And so, according to the authors, if only 6% of chess players are female, then we'd only expect 2% of them in the top 1000, so no other explanations regarding biological differences or social biases are required.
I can't get my head around the idea that small differences in population size are exacerbated at the extreme ends of the distribution. In particular, what's wrong with this counter-example:
About 1 in 12 chess players are born in the month of January. So they make up a small fraction of all chess players. By these statistical methods, we'd expect them to be particularly under-represented at the highest level - maybe only 1 in 30 of the top players would be born in January. But of course you could apply this same logic to every month, and you ultimately reach an absurd conclusion.
It seems to me that if you divide a population into 2 groups, you'd expect the same ratio of performers at all ends of the scale.
As I'm contradicting the results of a published paper, I guess I must ask - what am I doing wrong?