Tuesday, October 16, 2007

Women & math   posted by Razib @ 10/16/2007 02:19:00 PM

Chris has a post, Women in Math, Science, and Engineering: Is It About the Numbers (And Not the Ones You Might Think)?, which addresses issues relating to women in science. Like the debate about IQ I'm not too interested in this...basically one's priors strongly effect their perception of the weight of the evidence and I don't see much value add in getting into arguments. That being said, a few quick points which I discussed with Chris:

1) During the Larry Summers affair I noted that though the proportion of women in mathematical fields differs cross-culturally, the rank order of fields is basically the same in terms of male & female ratio. In other words, the relative underrepresentation of women in mathematical fields seems culturally universal (e.g., in Mongolia where males are discouraged from pursuing higher education only in the mathematical sciences is there a sex ratio parity).

2) In female dominated fields males tend to increase in frequency as one ascends the ladder of achievement and prestige. Some of this might be due to age (e.g., established professors are from a time when women were extremely underrepresented in academia); but Chris points out that even across the undergrad to grad student chasm within his own field, cognitive psychology, it still plays out.

3) Speaking of which, the principle seems to operate on a very fine grained level. Within psychology it is cognitive psychology and psychometrics where women are least dominant. These are also fields where knowing some linear algebra is handy. Within the social sciences women are relatively thin on the ground in economics, which is the most formalized and mathematical discipline.

4) From a biological perspective it seems to me that some of this is likely going to be due to gene/gene expression/environment correlation. That is, small initial differences in biologically rooted propensities can lead to a "virtuous feedback" cycle.

5) Peer groups matter. To be succinct about it, I think female peer groups are nerd-killers.

6) The last two points are important. I think most reasonable people will agree these sorts of outcomes which manifest in young adulthood have many upstream variables (even if some are of relatively larger effect). This is why prior values matter so much in how plausible you find alternative explanations. That being said, I do think that the complexity of the issue here poses a problem for social engineers: a one-size-fits-all solution often presupposes one clean predictor of the difference (e.g., in this case a form of stereotype threat), which I don't think is really tenable. These solutions are unlikely to shock the social dynamic to a new equilibrium, so to maintain outcome you'll have to continue applying the "solution." The other alternative is to engage in radical social engineering and flip a host of parameters. I am skeptical that most people have the stomach for that, so what you're going to continue to see are "solutions" which will never address the underlying causes but apply a band-aid upon the "problem."

7) In the most general and big picture sense James F. Crow's observation that when you extract a set of individuals highly deviated from means across a wide range of traits the likelihood that intergroup differences will emerge are going to be very high. In other words, to be a world class sprinter or mathematician requires a joint set of traits where the mean for the candidate population is highly deviated from the central tendency. Even if the distribution of said traits differs only minimally across groups it is extremely likely that different groups will yield very different numbers of individuals who match the appropriate criteria.

Finally, if you are going to comment on Chris' blog, be civil. He's had my back before, so I am not intending to send hecklers his way.