[keithflower]

The January 2012 issue of the Notices of the American Mathematical Society presents a comprehensive review article disagreeing that there is "plenty of evidence" women are less likely to be very good at math based on "natural causes" (whatever the hell that kind of nonsense phrase is supposed to mean), and provides plenty of evidence that any disparity is due to attitudes toward women and other sociocultural factors:

"Debunking Myths about Gender and Mathematics Performance" http://www.ams.org/notices/201201/rtx120100010p.pdf

Now for the anecdotes: in my experience there has been plenty of outright racial and gender discrimination in computing, science, math, and even medicine. I've seen it. I suspect most if not all of you have seen it. It persists into the 21st century.

That needs to continue to change.

[yummyfajitas]

Did you read the article?

It agrees completely with the data I cited. It shows a variance ratio of 1.1-1.2 across many countries (though not all).

Interestingly, it also shows very little correlation between gender equity and gender disparities in math performance. The strongest correlation it shows is that gender equity is positively correlated with math performance disparities! Gender equity seems to increase [1] math performance of both boys and girls, but it increases boy's scores more.

[1] Of course, the article only shows correlation, not causation, but I didn't feel like rephrasing what I wrote.

[bermanoid]

It agrees completely with the data I cited. It shows a variance ratio of 1.1-1.2 across many countries (though not all).

This was the most glaring example of statistical dishonesty in this paper: their data shows with perfect clarity that there's a > 1.0 male/female variance ratio for almost every country in the set, and I encourage anyone interested in this to look at their graphs and draw your own conclusions (http://imgur.com/39pja). To me, it looks like a typical noisy measurement (the authors note that the variation within a single country was about 20% from test to test, so we should expect a decently wide distribution (well, the authors don't actually admit that - as a first mathematical blunder in a series of many, they claim that 20% variation is very small and means we should expect a tight distribution)) with a mean somewhere between 1.12 and 1.15, a variance of maybe .1 (just about right for a measurement with around 20% variation, no?), and a decent bit of skew. Pretty good jumping off point for some analysis and explanation, I would think...

But not in this article. The authors merely point to those graphs and claim that they obviously disprove the greater male variance hypothesis. In other words - they point to a distribution of admittedly noisy measurements that is clearly centered around ~1.13 or so, with almost zero density below 1.0, and claim that it proves that the mean of the distribution is 1.0, (with an implicit "STFU Larry Summers"). When I first read this, I thought they were trolling me, the result is so clearly wrong.

[As an aside, it's worth noting that a variance ratio in the 1.1 to 1.2 range is enough to explain away most, if not all, of the gender imbalance in mathematics, if we make the assumption that the variance ratio is the same throughout all of mathematics education (which is not likely true - IIRC these measurements were all at the 8th grade level)]

Their argument? Because the measured variance ratios are not identical, we should ignore the mean of the distribution. Seriously, that's it. I'm not talking about a statistical calculation showing that the null hypothesis (that the variance ratio is 1.0) should not be rejected, mind you (because such a calculation would not allow us to accept the null hypothesis - a quick look at the graph is enough to be sure of that), or in fact any statistical argument at all. They quite literally claim that any variation in the measured variance means that the entire distribution is meaningless.

They also try to confuse the issue a little bit by pointing out that there's a bit of correlation between the variance ratio and the variance; while interesting and certainly worthy of further explanation (not done in this paper), this is completely and utterly irrelevant to the variance hypothesis, yet they imply that it somehow disproves it as well.

Quite frankly, the referees should have caught this, I can't remember the last time I've seen such bad statistical reasoning in a legitimate math journal. There are glaring issues all over the rest of the paper, too, where they've filtered and re-filtered data many times until they obtain the correlations that they want, where they chop data into bins in suspect ways, etc., but to actually enumerate all these errors in detail would make this a much longer rant.

It's a shame, too, because it appears that some of the article is solid, and it presents some interesting data that definitely warrants more investigation; unfortunately, they went absolutely bananas in several places, drawing completely unfounded conclusions from the data they generated, so I would be hesitant to cite this paper as proof of anything.

[bermanoid]

Just an additional FWIW:

While I do think the variance ratio in math is significantly different from unity (without speculating as to the cause), it's worth pointing out that while this does explain a lot of the gender imbalance in math, it doesn't come close in computing. Off the top of my head, in math it's something like 35% women, a 1:2 ratio, whereas in tech it's closer to 10%, or 1:9.

To explain a gap that wide based on variance, we'd have to assume that men are way more than 10% more variable in computer ability than women, probably more on the order of 100%, and that seems very unlikely to me (there's not really any data to look at there because CS performance is not as commonly measured as math is).