What's my point?

On Facebook last week, a friend posted a note regarding the study published in Science magazine
that females have caught up with males in standardized testing on math and science. The note was posted with some sense of satisfaction, and a lot of the same feeling was in most of the various news accounts. The positive news was centered on this:

The researchers looked at the average of the test scores of all students, the performance of the most gifted children and the ability to solve complex math problems. They found, in every category, that girls did as well as boys.

My first reaction, without reading it too closely I admit (that seems to be a common theme for me) was to wonder how much of the change was male regression versus female progression. Given the handwringing over primary education in the U.S., was it a good thing, or a bad thing that the sexes were equal?

Today, however, I read some counterpoints to the study. Or more specifically, disagreement with how the outcomes of the study were reported. The point of contention is that the news accounts of the study centered on the focus on the testing mean (boy versus girl average) instead of variance (dispersion of scores). In news reports, it was first mentioned in the Wall Street Journal:

Girls and boys have roughly the same average scores on state math tests, but boys more often excelled or failed, researchers reported. The fresh research adds to the debate about gender difference in aptitude for mathematics, including efforts to explain the relative scarcity of women among professors of science, math and engineering.

And it's since been discussed on Marginal Revolution, which was then mentioned on the Freakonomics blog.

The main point of contention is the shape of achievement of boys and girls in math and science. The average amongst a group only tells you so much. If one group scores 100, 95, 90, 70, 60 and the other group scores 90, 85, 85, 80, 75, the mean is the same, but the level of achievement is different. A starker example would be if the first group was 100, 100, 100, 60, 55. If one presumes a high level of accomplishment in math/science is necessary for technical fields, the general increase by girls may not be enough to cause that bump in advanced education/career path. Furthermore, there's the issue of why is there such variance among boys.

This variance is something that occurred to me a long time ago--that the difference in intelligence of the sexes was negligible, but guys pushed more to the extremes. One of the comments in the blogs above mentioned that intelligence is believed to be tied to the X chromosome, so girls get the average of 2, while boys get just one, increasing male variance. I'm not sure if that's true or right, but it's a theory.

I would think some variance, or perceived variance would be sociological. Lower male achievement may be condoned to some degree because "boys will be boys", athletic achievement, an outgoing personality (or however you'd describe Bart Simpson) which leads to the belief one is smart, but just just doesn't test well, or just a greater propensity to get into trouble (also Bart). Girls seem to be less prone to these pitfalls. In regard to athletics, for example, I think I've read that female athletes score above averages, whereas male athletes are well below.

On the flip side, there's the thought that boys garner more attention, which means more direction, which could be important to the high variance. When I think back to elementary and high school, my recollection is that in the former, there were more smart girls but the smart kids were all at the same general level. Except for me. I was brilliant. Everyone told me so (oh, how the mighty have fallen). Middle school was much the same.

High school was a little different. Some people slid out of the "smart" group. More of those might have been female, hard to say for sure--I might just have been more aware of their lack of presence. But the general mix in the various AP classes junior and senior year was still fairly evenly split. The one thing that struck me (as it did in college) was that the smart girls seemed to work a helluva lot harder than the guys, but there wasn't a whole lot of difference in grades. I think the smartest people in my grade were considered guys, but that may have been the smartest girls were quiet and reserved and the smartest guys thought they were brilliant, so perceptions may have been shaped by those personality traits.

Still, that's all anecdotal experience. The blogs/discussions linked above get into more detail about the statistical relevance of the study and the meaning of the variance. In response to my subject, I guess my point is, in the words of Winston Wolf, "Well, let’s not [pat each other on the back] quite yet. " It would be misguided of educators, public officials, business and other stakeholders to treat the problem (female underperformance in math and science) as solved without looking deeper into the issue. That is, if it is an important enough issue to address outside of efforts to generally increase STEM education.