NYT v. WSJ on Girls and Math
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.
The WSJ, however, told an apparently different story:
The researchers, from the University of Wisconsin and the University of California, Berkeley, didn’t find a significant overall difference between girls’ and boys’ scores. But the study also found that boys’ scores were more variable than those of girls. More boys scored extremely well — or extremely poorly — than girls, who were more likely to earn scores closer to the average for all students.
So who is right? What does the study itself, actually say?
Here’s the money passage:
The variance ratio (VR), the ratio of the male variance to the female variance, assesses these differences. Greater male variance is indicated by VR > 1.0.All VRs, by state and grade, are >1.0 [range 1.11 to 1.21 (see top table on p. 494)]. Thus, our analyses show greater male variability, although the discrepancy in variances is not large. Analyses by ethnicity show a similar pattern (table S2).
Does this greater variability translate into gender differences at the upper tail of the distribution (13)? Data from the state assessments provide information on the percentage of boys and girls scoring above a selective cut point. Results vary by ethnic group. The bottom table on p. 494 shows data for grade 11 for the state of Minnesota. For whites, the ratios of boys:girls scoring above the 95th percentile and 99th percentile are 1.45 and 2.06, respectively, and are similar to predictions from theoretical models. For Asian Americans, ratios are 1.09 and 0.91, respectively. Even at the 99th percentile, the gender ratio favoring males is small for whites and is reversed for Asian Americans. If a particular specialty required mathematical skills at the 99th percentile, and the gender ratio is 2.0, we would expect 67% men in the occupation and 33% women. Yet today, for example, Ph.D. programs in engineering average only about 15% women.
So is the NYT being misleading here? Not quite. They claim that the study found that “in every category, that girls did as well as boys.” Given the variances at the top of the range, however, this statement seems false, leading The City Journal to opine today “This statement is simply wrong” and either “the Times is deliberately concealing the results of the study or its reporter cannot understand the most basic science reporting.”
Notice, however, that prior to the offending statement, the Times article says, “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.” Given these categories – average test scores, performance of gifted kids, and the ability to solve complex math problems – that statement that “in every category, that girls did as well as boys” is correct. Average scores were comparable, as was the performance of top students and average performance of complex problems. In other words, boys and girls have the same average score, smart girls are just as smart as smart boys, and as a whole boys and girls do about the same on complex problems. On the other hand, these claims are also consistent with the finding that at the top and bottom ends of a given distribution there are a statistically significant variations between the performance of boys and girls as groups.
In English: while there are lots of girls who do extremely well at math, there are more boys who do extremely well. Likewise, while there are lots of girls who do extremely poorly at math, there are even more boys who are mathematical dunces. In short, the NYT didn’t lie but they did fail to mention a potentially interesting result from the study.
Of course, as the Science article points out, the variation is not big enough to account for the disparity that one sees, for example, in engineering programs or on the math faculties of universities. There are a number of possible reasons for this. Obviously, bias of various kinds may be at work here. It is also possible that once one looks at results from more difficult tests – the Science study was looking at standardized tests given to public school students, which is hardly the sort of instrument that is likely to differentiate between the next Fermat and someone who is bit better at calculus than the person in the next seat – the difference could become big enough to account for the differences. Finally, there is the possibility of self-selection. In part this could simply be another chapter in the bias story, i.e. girls don’t become math majors because of the hostile environment in math departments, etc. It is also possible, however, that preferences break down differently by gender.
Just because you are good at math doesn’t mean that you want to become an engineer.