Gender difference in math ability variability driven by social inequality, not biology – study

Gender gap in maths driven by social factors, not biological differences (Not Exactly Rocket Science):

Since 1894, some scientists have suggested that men have a greater variability in intellectual ability than women, a simple statistical quirk that would result in more male prodigies. This was the controversial hypothesis that Lawrence Summers mentioned in his now-infamous speech at the National Bureau of Economic Research Conference in 2005:


To test that, Hyde looked at data from maths tests in Minnesota and compared the numbers of boys and girls who scored in the top 5% of their year. The ratio was 1.45, meaning that for every two girls in this elite group, there were around three boys. In the top 1%, the ratio was 2.06, meaning two boys for every girl. That seems to vindicate the Variability Hypothesis, but those figures only applied to white American children. In other ethnic groups or, indeed, in other countries, the picture was very different.

For Asian-Americans the ratio was actually 0.91, meaning more girls than boys in the top 1%. International studies have found similar trends. One analysis of tests from the Program for International Student Assessment (PISA) showed that 15-year-old girls matched or outnumbered their male peers in the top tiers within Iceland, Thailand and the UK. Two studies found that 15-year-old boys and girls were equally varied in their mathematical skills in most of the countries taking part in PISA and the Trends in International Mathematics and Science Study (TIMSS). In some, like the Netherlands, girls actually turned out to have the wider range of ability.

So much for the idea that a greater variation in ability underlies the larger number of men in the top ranks of mathematics – if that had any biological basis, it should apply to all populations regardless of ethnicity or nationality. Clearly, that’s not the case. Instead, the evidence suggests that whatever gender differences exist are mostly down to social factors.

There’s plenty of evidence to suggest that, given the right social environment, the gender disparity in maths becomes vanishingly narrow. Various studies have found that countries with the poorest degrees of gender equality also have the widest gulfs between male and female mathematical performance. And in their own analyses, Hyde and Mertz found that a country’s gender inequality gap significantly correlates with the ratio of boys to girls in the top 5% of PISA test scorers, and the proportion of girls competing in the International Mathematics Olympiad – an incredibly challenging competition where the top scorers have one-in-a-million ability.

It’s no coincidence that countries like Denmark, the Netherlands, the UK and Iceland, where equal numbers of girls and boys populate the top 1% of the PISA results, are also in the top dozen countries in terms of gender equality. (The US, for the curious among you, is ranked 31st, between Estonia and Kazakhstan) These international comparisons point the finger at gender inequality, rather than greater male variability or aptitude, as the main reason behind the lack of women at the highest levels of maths in some countries.

Obviously, that includes a multitude of sins that will need to be addressed – lack of attention or encouragement, the effects of stereotypes, a lack of female role models, wilful misogyny and unconscious biases, hostile work environments, and so on. Addressing these issues is no easy task but at the very least, this review summarises firm evidence that attempts to do so will see female mathematicians rivalling their male counterparts at every level of the discipline.

Of course, it takes more than facts and empirical evidence to change the opinions of most male geeks about female inferiority in math. The Slashdot community’s reaction to the story is an example of this.

Slashdot’s reaction

Let us ignore the first comment joking that the study cannot be trusted because it was done by a team of female mathematicians/statisticians, as well as the comments assuming that women in CS are useful because they increase the chances of men in CS getting laid. In addition to submissions about women triggering general sexist comments, the study that disproves innate female inferiority in math becomes an opportunity for male geeks to rehash old, obsolete arguments about innate female inferiority in math.

Note that most of the Slashdot comments I repost below were modded up with a score of 5 (out of a maximum of 5).

“Girls are barely passing math. It doesn’t come naturally to them.”

In a comment titled “Taking vs Excelling”, modded up with “Score:5, Interesting”, Tanktalus writes:

Taking the course is not the same thing as passing or excelling. It’s an important metric, but not the only one. Perhaps we have a “traditionally disadvantaged” group being pushed, in the name of equality, into an area they dislike because it doesn’t come natural, and they’re barely passing. That’s not success – that’s a failure because these people probably would be more successful in life playing to their strengths rather than weaknesses.

In other words, this commenter didn’t bother to RTFA, but felt confident anyway in asserting that women are probably barely passing their math courses.

“Perhaps women are biologically inferior in math, and the appearance of equal ability is produced by cultural factors.”

In a comment titled “Just a thought”, modded up with “Score:5, Insightful”, Xeth writes:

(not meant to necessarily have any correlation with reality)

People seem to assume that what is happening is that previously, cultural norms dictated gender inequality when there was no biological basis, and now that those norms have changed, biological equality is restored. Couldn’t it be the other way around? I.e. that there is a biological inequality, that is being altered by cultural factors to produce equality?

Confronted with the study’s suggestion that women are not biologically inferior in math ability, Xeth offers an alternative interpretation: perhaps women are biologically inferior to men in math ability, but modern cultural factors are producing the external appearance of women having equal math ability.

“But men have greater variance!”

In a comment titled “Simply doesn’t address the real issue”, modded up with “Score:4, Interesting”, an Anonymous Coward writes:

This is an extremely dishonest story which does not address the most basic issues involved. What Summers said at Harvard is supported by the evidence and remains the best explanation for the “gender gap.” Indeed, he felt confident that he could “get away” with his statements because the evidence is so overwhelming and the facts so obvious.


for virtually all traits the STANDARD DEVIATION of the male distributions is somewhat larger than the female distribution — although not by much. Again this makes some intuitive sense — men are biological more expendable then women so more variation in male traits can be tolerated.

I can hardly be expected to believe that physical traits (the measurement of which is generally not controversial) are unique in having property (4). Especially when the observable data available for mental traits exhibits a difference in standard deviation.

This difference in standard deviation predicts what we see in practice — if we set a high threshold and look at the number of men and women with ability above that threshold we expect the ratio of men to women to be large. Because this is an effect of differences in standard deviation, it is not observable near the middle of the distribution — only at the tails.

There are many many articles which conclude that there is no gender gap in mathematical ability because the mean of the male and female distributions are the same or similar. I am not familiar with every such article, but every one I have read — including the two famous Science articles — presents observational data showing a difference in STANDARD DEVIATION. An issue none of them seem to address.

Once again, the commenter didn’t bother to RTFA, which has already addressed and debunked the “greater male variability hypothesis”. He is already convinced that the study is flawed, that he is more clever than the female researchers, and that women are biologically incapable of excelling in math.

“Females can learn math, but they have difficulty applying it, because their brains are not equipped to do so.”

In a comment titled “The article is confused”, modded up with “Score:5, Interesting”, j. andrew rogers writes:

The article is confused about where most of the real differences are purported to be.

No one credible claims that females have less ability to learn mathematics or crunch numbers in most cases, which is what this article is contesting. In other words, they built themselves a strawman. The differences involve application, not learning.

What *is* credibly claimed, in the sense that there is not insignificant quantities of direct and indirect evidence in literature, is that females are markedly poorer at certain classes of applied mathematical problems, notably applications involving complex, high-dimensionality metric spaces. Females understand the mathematics just fine, they have relative difficulty applying it to real-world problems when system complexity exceeds a certain threshold. This is largely attributed to male brains having more neurons dedicated to conceptualizing and manipulating spatial relationships.

There are real differences, but it is mostly in specific areas of the applied side and there is a relatively straightforward causal theory related to brain structure. That people feel it necessary to repeatedly trot out the strawman that women have less ability to learn math while conveniently ignoring supportable arguments for differences in practical ability reeks of a political agenda. There are other biases in application spaces strongly favoring females that also have straightforward causal links related to differences in brain structure but which say nothing about the ability of males to learn.

There is evidence of a gender difference in ability to manipulate spatial relationships, but there is no consensus that this difference is innate. Some of the indirect evidence used to support this hypothesis is a gender difference in math performance of school-age children and the scarcity of women in math, science, technology, and engineering—which is what this very study addresses.

As for math application and complexity, the paper notes (p. 8802):

Thus, girls have now reached parity with boys in mathematics performance in the U.S., even in high school where a gap existed in earlier decades.

However, coding of the test items on these examinations for cognitive level indicated that none of them tapped complex problem solving at most grade levels for most states (13). Thus, it was impossible with these NCLB data sets to investigate whether a gender gap existed in complex problem solving. Therefore, the researchers also examined data from the National Assessment of Educational Progress (NAEP), a federally managed program that tests a random sample of U.S. students each year (14). Items from 12th grade data categorized by NAEP as hard and by the researchers as requiring complex problem solving were analyzed for gender differences; effect sizes were found to average d = 0.07, a trivial difference. These findings provide further evidence that U.S. girls have now reached parity with boys, even in high school, and even for measures requiring complex problem solving.

“Women are mentally differently-abled. The Politically Correct regime denies innate gender difference even in the face of hard evidence.”

In a comment titled “There is and always will be differences.”, modded up with “Score:5, Insightful”, JustNiz writes:

Whether you like to accept it or not, women and men are psychobiologically different. Meaning, there are observable, quantifiable and consistent physical differences in the brain and its chemistry based solely on gender.

As a result, women consistently perform worse at spatial-based tasks than men. Women consistently perform better at communications-based tasks than men. There are millions of well-conducted experiments and studies that re-prove the existence of these and other gender-based differences over and over again.

It frustrates the hell out of me that the loony ‘Politically Correct’ regime is so enforced on us and continues to reduce to denial any innate gender difference even in the face of hard evidence.

Most ‘normal’ people now feel they can’t even openly raise the possibility, much less the FACT that we actually are mentally differently-abled BECAUSE of gender.

Society as a whole will not properly develop until we accept the existence of gender-based ability differences, including mental, as a fact and move on.

Ironically, this commenter accuses the ‘Politically Correct’ regime of denying innate gender difference in the face of hard evidence, while denying in the face of hard evidence. If he doesn’t like the results, he concludes that the study is biased.

“Women do well in math because they work harder. Men do well because of innate ability. Estrogen and testosterone have different effects on the brain and body.”

In a comment modded up with “Score:5, Insightful”, CorporateSuit writes:

Chemically, testosterone and estrogen have different, powerful effects on the brain and body. Be careful not to call people “bigots” because they celebrate this diversity and seek out the advantages it contains, or you must call yourself a bigot for your intolerance toward anyone who thinks that any notable differences are an evil that needs to be squashed. Yes, with extra effort, one sex can almost always measurably outperform the opposite sex where the opposite sex is more fitted, biologically, to a purpose — but that doesn’t reinforce your point; it contradicts it. If a woman and a man can perform equally at math, but the woman has to study n% longer, then the man is inherently better at math. That’s what inherency means. It’s not politically correct, but it’s nature… however, I vehemently agree that the product of nurture and identity should always have the /choice/ to agree with nature or to struggle to see if it can obtain something better. If a woman chooses to study n% longer than the man to perform equally at math, her identity shows that she would be the better mathematician — because she’s more willing to put forth the necessary effort– but don’t hate or belittle people because they accept what nature has given us as a gift, rather than viewing it as a curse.

The commenter believes that if women do as well as men in math, it must be because they work harder, since they cannot possibly have innate math ability. Of course, he has no evidence for this, except his prior conviction that women are biologically weaker in math, his rationalization being that women have higher levels of estrogen.

Conclusion & How It Works

Sexism, not learning, is the general male geek reaction to the study. Apparently, the mere suggestion that men are not innately superior is a vicious attack on men that must be responded to with hysteria, defensiveness, and mental gymnastics.

Once again, men use sexism to argue that sexism no longer exists. For most male geeks, it is unfathomable that there could be sexism or hostility towards women among male geeks. Sexism is such a constant in male geek culture that it is invisible to them.

How it Works by XKCD
(How it Works comic by XKCD. (Randall Munroe knows that sexism is a problem.))

Related links:

20 Responses to “Gender difference in math ability variability driven by social inequality, not biology – study”

  1. thewhatifgirl Says:

    This comment: “This is largely attributed to male brains having more neurons dedicated to conceptualizing and manipulating spatial relationships.” – makes me laugh. I’m willing to bet that this guy would readily agree that women are better at interior design, which also requires an ability to “conceptualize and manipulate spatial relationships.”

    Though my own case is anecdotal, of course, I blame my own difficulties with math on my high school math teacher, who just couldn’t believe that I was doing huge chunks of math in my head and basically told me that I had to write it all out or he would automatically flunk me for cheating. Whether or not he made that assumption on the basis of my gender, I’ll never know, but I do know that after a year of writing out every math step, I could no longer do it in my head.

    I also was raised, in many ways, more like a boy than most other women I’ve known and have consistently done better at spatial reasoning problems on tests than most other women do.

    And finally, if I might be anecdotal just a little bit more, the best teacher I had in college math was female, and I think I understood her better than the majority of the males in that class, who were constantly asking each other what was going on while I was happily – and comprehendingly – doing my work. Which makes me think that perhaps it isn’t just female role models that young girls need but also different forms of teaching that more women might be able to provide.

  2. Kathy Says:

    I think little girls are still encouraged to play with dolls, and boys get toys that encourage spatial thinking, leggos, or putting train sets together, reading instructions on how to put things together, so I personally have tried to search out toys that encourage thinking, my daughter is a high honor student with excellent math grades, and she doesn’t even try. I did notice, however, that her interest in boys had a negative effect on her math grades, I talked to her about it, and she resumed with the excellent grades in math, she made top honor grades in New York State Science exams as well.
    I did well in math until high school, there were only two girls in my class, I also had trouble remembering what seemed to me to be useless long theorems where the resulting answer was already clear to me.

  3. thelady Says:

    On the SAT I scored 100 points higher on the Verbal section than the math. In college I majored in engineering. Within a year of graduation I took the GRE. My scores had reversed and my Math score was now 100 points higher than my Verbal. People have to be trained to think mathematically and logically. You have to exercise that part of your brain.

    Most of my peers in engineering commented that they now think completely differently than they used to and find themselves randomly adding/multiplying/dividing numbers they see on addresses or license plates. We are all now comfortable doing calculations such as tips in our head.

    This is not about innate ability, it is about repetition.

  4. NancyP Says:

    thelady is right. I used to be good at math, now I have to write out equations. I just don’t use math enough.

  5. Brinstar Says:

    Those Slashdot comments are priceless. And so sad.

  6. Therese Says:

    For most male geeks, it is unfathomable that there could be sexism or hostility towards women among male geeks.

    omg… that explains… so… much!

  7. Chris Diaz Says:

    The racists and sexists have been trying to justify white male hegemony for centuries. It just goes to show that constant vigilance is needed. Their like the little game, they keep popping up incessantly and have to be whomped back down over and over.

  8. Mechie Says:

    I have a hard time believing that gender differences in such things as spatial ability are innate and hardwired.

    Look at the toys children are given. Boys get toys which develop spatial ability such as toy trains, Meccano, etc. Girls mostly get toys which develop nurturing behaviour such as baby dolls. All that play in childhood surely influences brain development.

  9. jwbe Says:

    I was always bad in geometry, algebra and physics, but good in analysis (math) and chemistry.
    One of my teacher said that it was her observation that people good in geo. and alg. are good in analysis and reverse. I am an autodidact when it comes to learning something.
    As to gender roles and toys, I am definitely not somebody who defends ‘typical’ gender roles, but nature made us that way, equality is for me not to be the same like man and to have all the same skills

  10. Mirra Says:

    I wonder at how people can believe that mathematical ability at an extremely high level can be so clearly measured. I find it very difficult to gauge my own mathematical ability. I’m okay at it (I’m doing a postdoc in pure mathematics) but I have my doubts. I didn’t get the best grade at school, but I never had any trouble with it either. I’ve always found it quite addictive.

    When I learnt about the alleged higher variability in mathematical ability among males I have to admit it did make me think “maybe I’m just not that good at mathematics after all and I shouldn’t be doing it”, which I know is an irrational response to something that is just a statistical variation on the whole population.

    But mathematical research can be hard and it gets me down sometimes.

    So many guys confidently assert their own ability, and I always wonder “how do they know they’re so good?” Some people are obviously fantastic and their brilliance can go unquestioned, but not all of these guys seem to fall into that category.

  11. Restructure! Says:


    So many guys confidently assert their own ability, and I always wonder “how do they know they’re so good?” Some people are obviously fantastic and their brilliance can go unquestioned, but not all of these guys seem to fall into that category.

    See Men overestimate their intelligence in all 12 countries, research finds and This is why white males are so confident in themselves (Men are raised in an environment in which they are regularly assured of their superiority. The experts are usually men, like them).

  12. “Easterners” are not collectivist automatons who are poor at analytical reasoning. « Restructure! Says:

    […] (Note that the article’s author, Ed Yong, also wrote the excellent post Gender gap in maths driven by social factors, not biological differences at Not Exactly Rocket Science, which was also covered on this blog.) […]

  13. a girl Says:

    Yeah I agree that a lot of guys overestimate their ability and math can be hard. I certainly think getting a PhD would be hard. And at the undergraduate level I prefer math to writing, as it is not as easy to confuse people with some good solid calculus as with an essay. That’s just a preference. I’m better at economics. I have been really adhd lately and I find algorithm creation in economics is something I can do in my head. It’s a lot of people watching. I use a lot of math theory in my economic analysis though, it helps me shape my thoughts.

  14. Male geeks reclaim masculinity at the expense of female geeks. « Restructure! Says:

    […] male and female brains that make success in science, math, and technology exclusive to men. Thus, arguments and studies that suggest otherwise are perceived as a direct attack on the masculinity and male identity of male geeks. According this male geek worldview, if women […]

  15. Misogyny: Geeks vs. Jocks - The Sexist - Washington City Paper Says:

    […] male and female brains that make success in science, math, and technology exclusive to men. Thus, arguments and studies that suggest otherwise are perceived as a direct attack on the masculinity and male identity of male geeks. According this male geek worldview, if women […]

  16. Alas, a blog » Blog Archive » Open Thread & Link Farm, Baleful Stare Edition Says:

    […] The gender gap in math is driven by social factors, not biological differences. […]

  17. Männliche Geeks behaupten ihre Maskulinität auf Kosten weiblicher Geeks — Says:

    […] Erfolge in Wissenschaft, Mathematik und Technologie exklusiv Männern vorbehalten. Daher werden Arguments und Studien, die auf das Gegenteil hinweisen, als direkter Angriff auf die Maskulinität und männliche Identität der männlichen Geeks wahrgenommen. […]

  18. m Andrea Says:

    What a fantastic blog, thank you!!

  19. Across the calculus sections, women outperformed men on grades. « Restructure! Says:

    […] other male geeks who insist that there are hard-wired brain differences in men and women, and argue that women’s brains are hard-wired against understanding math and science as well as men (instead of hard-wired against enjoying math and science), this part of the article should be […]

  20. Across the calculus sections, women outperformed men on grades. | Geek Feminism Blog Says:

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