Aleks sends in a striking example of a news story presented in two completely different ways:

I [Aleks] was looking at the NYT and WSJ today, and one particular discrepancy struck me. The NYT story, “Math Scores Show No Gap for Girls,” by Tamar Lewin, says:

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. . . . “Now that enrollment in advanced math courses is equalized, we don’t see gender differences in test performance,” said Marcia C. Linn of the University of California, Berkeley, a co-author of the study. “But people are surprised by these findings, which suggests to me that the stereotypes are still there.” . . . Although boys in high school performed better than girls in math 20 years ago, the researchers found, that is no longer the case. . . . 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 NYT story had absolutely no mention of the girl/boy variance whatsoever. Compare to the

WSJ version (girl/boy variance in the headline), “Boys’ Math Scores Hit Highs and Lows,” by Keith Winstein: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.

In the 1970s and 1980s, studies regularly found that high- school boys tended to outperform girls. But a number of recent studies have found little difference. . . . [The recent study] 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. . . . The study found that boys are consistently more variable than girls, in every grade and in every state studied. That difference has “been a concern over the years,” said Marcia C. Linn, a Berkeley education professor and one of the study’s authors. “People didn’t pay attention to it at first when there was a big difference” in average scores, she said. But now that girls and boys score similarly on average, researchers are taking notice, she said.

Here’s some context from a few years back (I looked it up, because I wasn’t sure exactly what Summers said, and the NYT article referred to him. From the NYT a few years ago:

Dr. Summers cited research showing that more high school boys than girls tend to score at very high and very low levels on standardized math tests, and that it was important to consider the possibility that such differences may stem from biological differences between the sexes. Dr. Freeman said, “Men are taller than women, that comes from the biology, and Larry’s view was that perhaps the dispersion in test scores could also come from the biology.

What’s amazing is that the two newspapers quote the same researcher but with two nearly opposite points. I assume she made both points to both newspapers, but the NYT reporter ran with the “stereotypes are still there” line and the WSJ reporter ran with “researchers are taking notice.” It must be frustrating to Linn to have only part of her story reported in each place. (Yeah, yeah, I know that newspapers have space constraints. It still must be frustrating.)

I would be really interested to see researchers look more indepth at the "the population of boys has higher variance than the population of girls" hypothesis.

For an analysis of sex difference in mathematical aptitude read this http://www.lagriffedulion.f2s.com/math.htm

Many of the studies are flawed because of small sample sizes, unrepresentative samples and low g loading on mathematical aptitude tests. However as pointed out by La Griffe du Lion, the Project Talent study did use a representative large sample of American 15 year olds. The mathematics scores from Project Talent show mean shift of .12 SD and variance ratio of 1.2. Thus boys have a slight edge in the mean, and somewhat more dispersed scores. Thus we should not be surprised that the 4 sigma and above region is mostly populated by men.

The "No Child Left Behind" math tests are also too easy leading to poor g loading and lack of discrimination among the really high achievers. Both newspapers are pretty remiss in not pointing out these problems.

Newspapers don't understand variances, only means.

One possible source of higher variance for boys is that they have only one X chromosome, whereas girls have two. With two X chromosomes, any variance due to effects of variable genes on the X will be reduced due to averaging of the effects of the two chromosomes. (This is complicated by the fact that in any individual cell, one of the X chromosomes is inactivated, but which one is inactivated varies from cell to cell.)

Some years ago, not long after the Summers controversy, Nature published a paper showing that many genes relating to intelligence reside on the X chromosome. The accompanying commentary (by Nature staff, not the authors of the paper) made snide remarks about how since X relates to intelligence, and women have twice as many X's, one can see how stupid Summers remarks were. Of course, the paper actually shows the exact opposite – providing a specific reason why the variance of intelligence for boys could be greater than for girls.

Andrew, my journalist friend argued that WSJ actually argued the opposite of what this study said:

Gender Similarities in Mathematics and Science

Janet Shibley Hyde and Marcia C. Linn

Boys and girls have similar psychological traits and cognitive abilities; thus, a focus on factors other than gender is needed to help girls persist in mathematical and scientific career tracks.

While the paper noted consistent (small)

variance differences (variance ratios around

1.1), they also explicitly made the point that

the male:female ratio above the 99th percentile

of around 2:1 among whites does not explain

(e.g.) the 4:1 ratio in engineering programs …

"The male:female ratio above the 99th percentile

of around 2:1 among whites does not explain

(e.g.) the 4:1 ratio in engineering programs …"

That 2:1 would be be 2.62:1. If the ratio of 4 for engineering programs (where does that number come from?) is true, than the discrepancy is likely attributable to male preference for subjects like engineering. Indeed why would we expect men and women to have exactly the same preferences in everything? Nor would we expect them to have exactly the same abilities or IQs. There are a lot more ways for things to be different than the same. We know from the work reported by Steven Pinker that many personality traits are sex linked.

It's hard for me to believe there's anything new here – I was in a gifted class in my youth, some 15 years ago, and when we queried about the unbalanced sex ratio (remember! we were clever!), the answer we got was just this: that men and women average at about the same, but men are more variable, hence they will do both better and more poorly in the tests.

So what's new?

Because the author of the research study has her own gender similarities hypothesis that says so.

Are you really amazed that the NYT would ignore relevant facts to put a PC slant on a story?

Keith Winstein is an MIT alum, so he knows what a variance is without having to look it up in a dictionary and failing to grok. If we had more reporters like him, we wouldn't be riding this handbasket. (Hi, Keith!)

"The "No Child Left Behind" math tests are also too easy leading to poor g loading and lack of discrimination among the really high achievers. Both newspapers are pretty remiss in not pointing out these problems."

Actually, why is the WSJ remiss? It appears that the WSJ is more on target than the times article, but why would they mention anything previous research.

I'm not sure how differing variances demands a genetic explanation any more than a difference in average. If we can assume that the gene pool has not changed wrt math ability, the disappearance of the average difference suggests that it was a product of non-genetic factors. Why should the same not be true for the difference in variability we still see?

It's easy for me to imagine (and recall, as a female high math achiever) cultural pressures which tend to either push boys towards the margins, or are more tolerant of atypical boys than atypical girls. The mean is not enough to completely characterize the distribution of math achievement, and i think it probably doesn't completely describe the effects of sexism on math students.

I wrote about this on my own site.

The point many on the pro-egalitarian side seem to miss is this: the fact that there's a somewhat skewed number of men with an interest in something doesn't mean we shouldn't be encouraging and welcoming girls to enter these fields, or that we shouldn't be opposing historical patterns of discrimination. It just means that we don't automatically need to freak out if the distribution isn't 50-50 or a close approximation thereof.

You don't have to stop being a liberal just because you think it's all right for it turn out 70% boys in some MIT class.

From Lewin's article in the Times: "On the ACT, another college entrance test, the study said, the gender gap in math scores disappeared in Colorado and Illinois after the states began requiring all students to take the test."

In fact, this isn't true. The authors note in the online supplement that the gender gap in

Compositescore, not math score, disappeared. Once all Colorado and Illinois students began taking the ACT, the "boy advantage" in Mathematics (and Science) did shrink a little, but it's still very much there. The "girl advantage" in English and Reading, on the other hand,grew, and it's now notably larger than the boys' advantage in math and science.Based on the detailed data on the ACT web site, it seems to me that the Illinois and Colorado experiment proves that (on average) girls really are better than boys in reading and english. But everyone knew that (right?), so it's not newsworthy.

The bigger social issue is the bias and stereotypes that ultimately affect individuals, whether its girls who wish to pursue engineering or boys that wish to pursue nursing. Ironically, our perverse fascination with gender and racial group achievement statistics might in this case help quell irrational behaviors that same fascination once stoked. But sometimes we'd be wiser not to make so much of these group statistics, and instead just try to be fair to people.

2.6:1 would be normal for an engineering programme. But this could surely be exacerbated if large numbers of women found engineers and mathematicians slightly repellent.

Let's face it, maths and engineering faculties aren't exactly suave, are they?

It may be a little more complicated. First, the equalization of the averages is evidence that gender bias was involved. Second, Lucy makes a good point that the variance may be gender bias, though the equalization of the averages is suggestive, but certainly not conclusive, evidence that this may not be.

My hunch is that the phenomenon of "top end males" has less to do with aptitude than with motivation. Men may be more motivated than women to be at the very top and more likely to abandon the effort once their limitations become clear. But is this genetic or cultural? Could be societal reward structure or could be genetic desire to get more mates, being the best. Being the best mathematician probably isn't the best mating strategy, but it may be an artifact of a broader genetic motivation to stand out.

The Times also has an MIT grad on staff (physics) in the Science section — Dennis Overbye. But the difference is — you're not going to find him reporting an education story. Keith Winstein at the Journal does both Science and Education stories.

Tamar Lewin, who wrote the Times article and completely missed the part about variance, has a Barnard bachelors and a Columbia masters, which just screams "liberal arts tradition." Sometimes I wonder if newspapers should require all references to scientific writing to be vetted by a dedicated scientific reader.

I couldn't resist throwing in this straw man.