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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.

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