Thursday, November 08, 2007

Gender differences in "extreme" mathematical ability

Since the Larry Summers debacle I've kept my eye out for relevant data on gender differences in mathematical ability. Finally I've found some analysis of results from a nationally representative study of elementary school children (K-5). Interestingly, the larger variance in male math performance is already observed at the beginning of kindergarten -- yes, before formal schooling has begun. By 3rd grade males are outperforming throughout the distribution, but the advantage at the high end is roughly unchanged. Note the authors consider 95 percentile to be "extreme" ability, which is kind of funny. You have to go quite a bit further out on the tail to find the talent pool from which professors of math, computer science, physical science and engineering are drawn.

Taking a quick look at their numbers, it appears that at the beginning of kindergarten the male distribution has standard deviation about 8 percent greater than the female distribution (larger variance -- both tails are overpopulated by males), although means and medians are pretty much the same. This implies that, already at age 5, at the 1 in 1000 talent level there will be roughly 2.5 times as many boys as girls. This ratio becomes larger and larger as one looks at more elite groups -- for 1 in 10k talents the ratio is something like 4 to 1 male to female. (I am extrapolating the normal distribution here, which might be a source of error.)

If subsequent societal effects were exactly gender neutral after age 5, one still might expect to find a strong asymmetry in gender representation in certain fields. Therefore, gender asymmetry in outcomes is not by itself evidence of discrimination at higher levels of the selection process. Removing gender bias at all levels, starting from kindergarten and continuing through grade school, high school, undergraduate, graduate and postdoctoral training, and, finally, faculty hiring, will not correct for the effect which is already present at age 5!

Note, I'm not claiming that the male advantage at age 5 is necessarily biological in origin -- it might be due to environmental causes. If one believes the causes are entirely environmental, and if one wants to equalize the numbers of male and female math geniuses, then intervention had better begin quite early -- extending to how mommies and daddies raise their infants.

In some other research by the same authors (I don't have a web link), international scores on the TIMSS examinations show that at the 90th percentile in math ability among seniors in high school, the ratio of males to females varies between roughly 2-3. This is a much larger discrepancy than the kindergarten numbers (strongly apparent already at only the 90th percentile), although it would be hard to know whether it is due to biological causes such as hormones and differences in male/female development, or to societal causes. The fact that there is some variation between countries does suggest at least a significant societal component.

If you read this post carefully, you will see that I have done little more than interpret the results of the nationwide testing examined in the paper below. Nevertheless, I anticipate I might get into trouble for having the temerity to perform this simple analysis. Let me therefore state, for the record, that I do believe that societal effects tend to discourage women from achievement in math and science, and that we can do much better than we currently are in promoting female representation in math-heavy fields. However, I do not think that there is any data supporting a complete absence of gender differences in the distribution of cognitive ability.

Gender Differences in Kindergartners Mathematics Achievement! Evidence from a Nationally Representative Sample

Paper presented at the annual meeting of the American Sociological Association (to appear in Social Science Research)

Paret, M. and Penner, A., Dept. of Sociology, UC Berkeley (2006, Aug)

Abstract: Gender differences in mathematics achievement are typically thought to emerge at the end of middle school and beginning of high school, yet some studies have found differences among younger children. Until recently the data available to examine gender differences among young children consisted of small non-nationally representative samples. This study utilizes data from the Early Childhood Longitudinal Study, Kindergarten Class of 1998-99 to analyze differences in a nationally representative sample of kindergarteners as they progress from kindergarten to third grade. Using quantile regression techniques to examine gender differences across the distribution, differences are found among students as early as kindergarten. Initially boys are found to do better at the top of the distribution and worse at the bottom, but by third grade boys do as well or better throughout the distribution.

Alex said...

Uh oh! Now you've really gone and put your foot in it... :D

Kea said...

Go jump off a cliff, asshole.

Mark said...

If this is true, it has a rather unfortunate side effect.

I expect you've probably heard of the experiment where identical CVs were submitted to different hiring committees (in science fields). In half the cases the applicant's name was male, and in half female. What they found was that when the application was very strong, the applicant's sex had no effect on the committee's decision, but when the application was borderline, the committees were biased towards the men.

Now, the problem here is that, if there genuinely is a skewed talent distribution between males and females, then the decisions of these hiring committees is perfectly Bayesian. On the other hand, it seems terribly unjust to the female applicants - they have to be better than the men to succeed (which is what women in science often report).

Anonymous said...

Why do social and genetic explanations have to be mutually exclusive? The fact that blind symphony auditions increase the success rate for female candidates shows that gender discrimination exists, and that we should be vigilant in trying to prevent it.

At the same time, mental retardation is significantly more likely among boys than girls, and boys are approximately 3-4 times as common in special education programs. While the latter could be a social bias, the former certainly is not, and I think it shows that (as if anyone disagreed) there are gender-based cognitive differences. If you assume that the mean intelligence is the same for men and for women, men must outnumber women *somewhere* above the mean in the intelligence distribution, though it does not have to be in the tails.

Mal

Anonymous said...

I was looking at "Gender differences in mathematics achievement: Exploring the early grades and the extremes" by Penner and Paret, work by the same authors as mentioned above.

There is a lot of nuance here. Let's start with this observation by the authors:

"Initially boys are found to do better at the top of the distribution and worse at the bottom, but by third grade boys do as well or better than girls throughout the distribution"

and they further add that,

"The male advantage at the top of the distribution among entering kindergarteners is largest among families with high parental education, suggesting gender dynamics in middle and upper class families have important implications for continuing gender segregation in science occupations."

On page 10, you will find the table of ability in kindergarten by subpopulation. Mostly you will find males doing slightly better than girls, with a 0.15 standard deviation male advantage at the 95% and above ability level (about the same advantage males as a whole will have by third grade), although Latino females outperform Latino males. The authors comment that "male advantages in math are mediated by parental education and in particular that the male advantage is most pronounced among students with higher parental education"

I think if we couple this with the fact that tutoring actually produces two standard deviations better performance in students than formal education. (Read: "The 2 Sigma Problem: The Search for Methods of Group Instruction as Effective as One-to-One Tutoring" by Bloom) I think we can have a reasonable hypothesis that the educated people might be tutoring their kids, leading to higher reprensation in the high ability samples.

I find it hard to believe that if the typical parent of a 95% and above scoring child is middle class and highly educated, that the educational exposure of the 95% and above cohort is identical to those below 95%.

I will end by quoting one more comment from the paper "simple biological theories are unlikely to be as helpful as social and cultural factors in explaining these differences."

I disagreed that the ability of mature scientists could be reasonably related with the ability of those scientists during their first months of kindergarten. In other words, the statement that we had to go 'out on the tail to find the talent pool from which professors of math, computer science, physical science and engineering are drawn" made no sense to me. If I met Gauss at 5 then I think I would believe he was going to be a very good scientist when he grew up. If we are talking about Einstein at 5, given that he started talking late and then slowly, I am not sure I would have made the same determination.

steve said...

Anonymous:

Good comments. Note, I don't think any of my arguments really depend on how the gender disparity arises (nature/nurture) -- the main point is that they are present already quite early. Given that, it is naive to think that they will be easy to correct much further down the pipeline.

"If I met Gauss at 5 then I think I would believe he was going to be a very good scientist when he grew up. If we are talking about Einstein at 5, given that he started talking late and then slowly, I am not sure I would have made the same determination."

Admittedly the correlation may be weak (although the correlation between adult IQ and IQ measured at age 4 is statistically significant), but imagine there are two populations, one with 10x as many Gauss-like child prodigies as the other. Do you not imagine that there might also be an asymmetry in the number of adult geniuses produced?

Also, I suspect that if you actually tested Einstein's math ability as early as age 5-10 you might have been quite impressed.

Yonatan said...

Wow, you'd better pack you bags and run. Eugene, Oregon isn't the kind of place where you can say such things!!