# NYT v. WSJ on Girls and Math

Consider the following two characterizations of the recent study published in Science regarding gender and performance on standardized math tests. According to the NYT:

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.

### 9 Responses

1. Isn’t this equality of mean but inequality of variance exactly the sort of thing that Larry Summers suggested it was worth investigating? You know, the thing that torpedoed his career?

2. TZ says:

You’re being too generous to the Times. The article starts off this way:

Three years after the president of Harvard,

Lawrence H. Summers, got into trouble for questioning women’s “intrinsic aptitude” for science and engineering — and 16 years after the talking Barbie doll proclaimed that “math class is tough” — a study paid for by the National Science Foundation has found that girls perform as well as boys on standardized math tests.

The article later notes that women are underrepresented, “as noted by Dr. Summers, who resigned in 2006, in the highest levels of physics, chemistry and engineering, which require advanced math skills.”

Yet the study doesn’t contradict Summers’ actual point about the gap at the top of the profession possibly being due to intrinsic differences, and the author of the Times articles fails to even mention the greater variability of male achievement. Perhaps not a lie, but intentionally misleading, with a rather obvious bias with regard to the story’s hook.

3. keeping my head low says:

I was watching the TED lectures on Youtube (which, if you haven’t seen them, are really worth watching). Helen Fisher, the famous anthropologist, casually tossed out the “greater variance at the top and bottom” point as if there is no controversy about it, and she didn’t even feel the need to wrap it, as Summers did, in the context of “speculation.” Since then, I’ve watched how the issue gets reported and when I saw this new study come out I knew right away that some media outlets would not report on that finding. And so it goes.

4. bill says:

Nate says: “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 . . .”

This is the money passage of this blog post. The study looked at Minnesota public-school 11th graders (age 16)? If you’re going to be “the next Fermat,” or even just the next person to be denied tenure in a flagship state U math department, it seems very likely that, male or female, at age 16 you may already be in college, studying math. If you’re in NYC or something, you may still be in a public school (Stuy/Hunter/Bronx Science), but for most of the country, the relevant group would be to a significant degree omitted from this study.

Instead, they studied the kids “left behind.”

5. Mike McDougal says:

Nate, please explain to me how the following quotation is not a completly worthless comment: “smart girls are just as smart as smart boys.”

It’s true by definition. 100 degree water is just as hot at 100 air. 20 pound cats are just as heavy as 20 pound dogs.

6. sex shop says:

intent. a joke, even if it’s a really really really bad joke, doesn’t get you intent. of course, you don’t need to be an attorney to figure this out. you just have to be able to read english

7. mikrofiber says:

Nate, please explain to me how the following quotation is not a completly thanks

8. geciktirici says:

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9. i think girls have sharp minds for maths..