As I’ve said before the existence of any innate statistical difference between men and women in mathematical/scientific ability is of no real practical importance. As far as public policy goes we should be looking at what would be most effective in increasing the number of capable graduates in math and science related fields. However, I blog about what irks me not what matters and articles like this one on arstechnica and this summary at science NOW that falsely suggest some study provides a clear cut answer to the nature/nurture debate really annoy me.

For starters I think it’s fairly irresponsible for a publication of the AAAS to offer a statement like this as unqualified commentary

The results “essentially confirm” earlier studies–and they should finally put to rest the idea that girls aren’t going into technical fields because they can’t do the math, says Ann Gallagher, a psychologist who studies testing at the Law School Admission Council in Newtown, Pennsylvania.

The casual reader will certainly understand this claim as saying that women are not innately disadvantaged relative to men in technical fields. Yet this research doesn’t even come close to proving this claim and in light of broader trends in male/female school performance that came up previously this result is perfectly compatible with girls being innately statistically worse at doing mathematics. Given that girls tend to outperform boys generally in academics before college we must either conclude that girls have greater innate intellectual talent or that some other factor, such as a greater willingness to study or pay attention to the teacher, accounts for this general academic superiority and must be accounted for to accurately compare innate ability. While the former hypothesis shouldn’t be dismissed out of hand the later one seems more likely¹ meaning that this study is essentially useless in comparing the innate abilities of boys and girls in math/science. While the authors of the research article might have reasonably expected their audience to be aware of the generally higher performance of girls in pre-college schooling leaving these considerations out of interpretive articles for the lay reader is at best unacceptable sloppiness.

True, the sentence I quoted is technically true. Girls have the literal capability to do technical fields but the obvious implication is that they have statistically equal innate ability which simply isn’t demonstrated by this piece of research. Unfortunately the article on ars is no better.

Thus, the gender gap in math performance seems to be insignificant in grade school, which is good news. Unfortunately, that does not help explain why the gender gap widens later in life. It is possible that pressure from society eventually catches up to women and makes it difficult to stay in certain fields, as the problem certainly doesn’t seem to be innate intellectual capability.

Once again this is a technically correct claim that is nevertheless extremely misleading. For starters, just like the piece in Science NOW this remark plays to the false idea that there is a sharp well-defined distinction between nature and nurture while also implying that whatever social effects cause the gender bias in the sciences must be negative. It’s equally possible that women are relatively more likely to be drawn away from math/science by other interests (child rearing, law, other non-technical pursuits). Even discouraging social pressures aren’t necessarily bad. If women leave technical subjects because they find math/science nerds less hot or simply don’t like hanging out with them that’s not a harm against women². Moreover, there are a vast number of explanations that don’t fall clearly on either the socialization nor innate differences side, e.g., suppose women are innately less rebellious and more eager to please authority figures and thus our educational system is more likely to snuff out their interest and ability to think critically. Fallaciously suggesting that social effects must be harmful barriers to women is almost as bad as what the sexist individuals on the nature side of the debate do when they conflate evidence of innate differences with female incapacity.

As if this wasn’t enough the arstechnica article casually dismisses the results from the article about greater male variation in performance and the Science NOW article ignores them entirely. Interestingly the study found that different races favored different genders at the high end of the tests, e.g., more Asian girls than Asian boys scored at the very high end while more white boys than white girls scored at the top. Still, while both ars and the original journal article dismiss the effects found as small in a discipline requiring mathematical ability at the 99th percentile these data suggest we should find 67% women and only 33% men. Pointing out that some engineering fields have only 15% women as the journal article does only tells us there are other factors at work but it doesn’t downplay the significance of this one. In fact given that math and physics Ph.D.s are probably almost exclusively chosen from the top half percent in mathematical ability this effect on it’s own might account for much of the observed gender gap. Moreover, in combination with the normal tendency of people to clump with others of the same gender and the role of friends/acquaintances in determining classes and majors it’s certainly plausible that even relatively minor differences in gender ratio could be magnified into something larger even if everyone acted in a fair and reasonable fashion.

Ultimately, however, any conclusions you might have been tempted to draw from the results in this article are undone by the fact that none of the questions asked in the standardized tests required serious thought. I stand with the researchers in bemoaning the sorry state of standardized testing in pre-college education but unfortunately for them this undermines any conclusions they might wish to draw about gender and innate ability. Quite simply how well you can memorize the quadratic formula and plug in numbers is totally irrelevant to your ability to do higher mathematics. I’m about to get my Ph.D. in mathematics despite being almost held back a grade because I wasn’t fast enough at my multiplication tables and regularly losing a fair number of points on math tests in high school because I didn’t memorize their stupid rules.

Of course there is nothing here to suggest that the gender differences we see in technical fields are the result of any innate differences but this research certainly doesn’t show otherwise so it shouldn’t be presented as doing so. Frankly I’m quite disturbed at the persistent bias in lay scientific articles about this subject. While I wholeheartedly agree about the importance of disabusing the public about their simpleminded stereotypes about gender differences and strongly support efforts to root out remaining discriminatory treatment covering up the complexities of the issue as these articles do feels too close to being propaganda for the desired answer for my taste.

I know I’m beating this issue to death so I will try to keep this post short but reading slashdot today I ran across this awful article from the Wall Street Journal Blogs saying women write better code than men. Now in and of itself the idea that statistically women write better code than men is neither absurd nor offensive but this article might as well have been ripped out of a 1950s era stereotype about women’s inferiority at math¹.

Emma McGrattan, the senior vice-president of engineering for computer-database company Ingres–and one of Silicon Valley’s highest-ranking female programmers–insists that men and women write code differently. Women are more touchy-feely and considerate of those who will use the code later, she says. They’ll intersperse their code–those strings of instructions that result in nifty applications and programs–with helpful comments and directions, explaining why they wrote the lines the way they did and exactly how they did it.

This remark is shortly followed by an equally over broad statement to the effect that men are too interested in showing off how clever they are to write readable code. Now while it’s certainly possible that (of the people who program) women are somewhat more likely to write better code (though I know of no evidence to this effect) this article adopts the sweeping tones of stereotype and bias to suggest that individual hiring decisions should favor women on these grounds. It is exactly this sort of unwarranted assumption that group characteristics make a difference even after individual factors (like say looking at previous code they have written, interviewing them) that distinguishes outright prejudice and discrimination from mere scientific hypothesizing. Well that plus the tendency to offer totally unsupported explanations that play into gender stereotypes (women are more touchy-feely).

If the conclusion had been the other way around and suggested that women were too touchy-feely to program well this vice-presidenty would probably quickly find themselves out of a job. This is why I blame faux feminism for this sort of attitude. It is exactly the confusion of feminism with the idea that we should cheer on women like they were a sports team that creates the impression this kind of harmful remark is reasonable. Despite obviously validating the idea that we should hire people based on unproven stereotyped generalizations about their gender instead of individual accomplishment this remark is seen as ‘ok’ because it favors hiring women. Another good example of this effect is how acceptable it has become to advocate for single sex education when coached in terms of helping women, even when the underlying theory would make Larry Summers cringe.

Now if the only harm these attitudes inflicted was a bit of discrimination against men you might reasonably think it wasn’t a huge deal². However, you simply can’t train people to accept traditional gender stereotypes and discriminate based on those only when it gives a certain kind of result. If you convince people to hire women for coding jobs because they are more touchy-feely you can’t avoid the fact that they are going to turn around and favor men for jobs in math, physics or the military where being touchy-feely is perceived as a negative (perhaps with some justification). Hell, even being good team players and leaving clear directions are going to be negatives for some job.

In fact I think what we are seeing right now is the harm of being touchy-feely about gender equality. The point is that deciding what views/people are good based on who sounds like they are on your side might have been fine when discrimination was primarily overt but when the primary concern is the affect of societal gender roles and semi-conscious stereotypes the greatest danger comes from the people encouraging that type of thinking and behavior, especially if they do so while claiming the `feminist’ moral high ground.

So in a recent post I argued that we really shouldn’t care at all if there are innate gender differences because such differences would be irrelevant to our judgments about any individual’s ability. In that post I simply took it for granted that the presence of innate gender differences really shouldn’t affect our judgment of people’s ability but now I see this is a point I need to explore at greater length. In particular I think there are three major fallacies that people fall into which leads them to assume that the question of whether there are innate statistical differences in men and women’s proclivity for math and science makes a difference in people’s daily lives. These fallacies lead people to think that the existence of innate gender differences would somehow justify gender discrimination and bigoted stereotypes. Of course not liking the consequences of a theory is no reason to reject it but in this case it’s certainly worthwhile to repudiate the fallacious thinking that makes people care so much about this issue.

The three fallacies that I’ve noticed are the following.

1. The confusion of small statistical differences with our intuitive notion of a valid generalization.
2. The belief that innate factors are somehow set in stone while cultural or social effects are temporary and thus justify different inferences.
3. Failure to appreciate the power of conditionalization.

The first fallacy is pretty obvious but very hard to correct. Most people don’t have good quantitative skills, much less experience with statistics so tend to translate claims about small statistical differences into simple stereotypes. Even people who should know better often don’t apply their quantitative training to this domain. This is why you see people respond to claims about innate statistical differences as if someone had claimed that women simply couldn’t do math and science. Once you get beyond this point you tend to run into the second fallacy.

Unfortunately both sides in the nature vs. nurture debate encourage the notion that innate differences are simple matters of ability and social effects are easily overcome issues of confidence. This leads to the fallacious conclusion that somehow innate differences call for a policy of denying women positions in math/science while nurture effects simply call for more encouragement. This couldn’t be further from the truth. One of the largest determiners of math/science achievement is interest and any possible innate differences could just as easily be differences in interest as they are differences in ‘ability.’ Moreover, it’s totally unclear to what extent differences in experience and exposure at young ages make. Thus it’s easily possible that the current gender gap could be the result of some innate difference that makes girls less interested in science as currently presented but small tweaks in science education could grab their attention. Alternatively it’s surely possible that the gender gap is the result of deep cultural forces that are nearly impossible to change and can’t be compensated for by our educational system, e.g., the type of behavior that attracts male romantic interest biases girls away from math and science. Quite simply there is no simple moral or effect on our judgment that one answer to the nature/nurture debate should have as opposed to the other.

The third and last fallacy is perhaps the most problematic, particularly in light of the second fallacy. People tend to assume that if women statistically tend to be worse at task X this is reason to lower their estimate of some particular woman’s (perhaps themselves) ability at task X. Counterintuitively this just isn’t the case. Conditionalizing on the standard information we gather about virtually anyone we meet can eliminate or even reverse the effect that gender should have on our estimation of someone’s ability. If you’ve taken any probability courses you’ve probably seen this point made using the example of the famous berkeley discrimination case. If you haven’t let me give you a simple example.

It’s undoubtedly true that statistically men are worse at nursing than women. This isn’t a claim about innate ability just a simple observation following from the fact that more women than men are nurses hence fewer men have received nursing training. Thus if you know nothing about someone other than their gender you should expect men to have a lower nursing ability. However, this doesn’t entail that you should trust male nurses less than female ones. Nor does it entail that men who aren’t nurses are somehow worse at nursing than women who aren’t nurses. It could even be that men who choose to become nurses despite the stereotypes have particular talent for it and thus conditionalizing on profession reverses the effect gender should have on your expectation of someone’s nursing ability.

The same could very well be true for skill at math/science. Even if there is some innate factor that makes women statistically worse at math/science it’s quite possible that those women who do pursue math/science tend to be more skilled than their male counterparts. In other words once you know that someone is interested in pursuing math/science finding out that individual is a woman might increase the expectation of her ability despite the fact that statistically women were worse than men at math/science. Since we tend to gather all sorts of information about someone we meet or consider for a job it’s totally unjustified to use statistical facts about men vs. women in the general population to reach conclusions about a particular individual.

The issue of nature vs. nurture really, really doesn’t matter that much. It’s almost never justified to use weak group characteristics like this to judge an individual and it’s equally unjustified to take mere statistical differences in a profession as proof of discrimination. So aside from pure scientific curiosity we should forget about nature vs. nurture and concentrate on applied questions like: Does science education unnecessarily make girls feel marginalized or less able? Would greater exposure to female role models in science make more women satisfied with their choice of career? Does rote memorization at the middle school level create barriers that discourage more studious individuals from pursuing math and physics?

In the post before last I pointed out that despite the spin a recent study in science was actually better evidence for biological effects in mathematics ability than it was for the environmental hypothesis. In short showing that girls get better at both math and reading as gender equality increases without shrinking the gap between their math and reading scores is most of the hypothesis that girls simply gain some general academic advantage over boys (for instance they study more) in cultures that don’t oppress them. If this was straightforwardly a matter of discrimination or stereotyping we would expect women’s math and reading scores to equalize as gender equality increased.

Now it was bad enough when some random science summaries spun the study in this fashion but it’s even worse to see ars technica running stories saying things like this about the study:

But a new study suggests that, when it comes to math, we can forget biology, as social equality seems to play a dominant role in test scores.

Ughh, what is it about this topic that causes people to check their reasoning ability at the door? I mean I can understand that the general public might think the suggestion of a statistical difference amounted to a claim that women were incapable of doing math/science but people with a science background should know better. There is no serious doubt that the variation inside the genders is vastly larger than any possible difference in averages. Moreover, once you actually have some evidence about a person’s mathematical/scientific ability (like you’ve talked to them) their gender isn’t relevant. That is we should expect conditioning on actual evidence about someone’s ability should screen off any impact of their gender.

I write about this topic for the same reason I write about other topics. I find fallacious reasoning to be infuriating, especially when it seems to be motivated by a desire to reach certain comforting beliefs. However, it really should be a minor scientific curiosity. It doesn’t matter one jot what the cause of observed differences in gender performance might be. What matters is the effect these differences have on society and what actions we can take to minimize any harms that result from them.

I mean (hypothetically) suppose it turns out that the gender gap in math/science is caused entirely by social conditioning that makes women prefer some disciplines and men others but that those women who do choose to do math/science face no discouragement and those who don’t are made genuinely happy by their choices. In that case there is no compelling reason to force a change to the gender ratio in the sciences, especially if that change could only be brought about by painful social reorganization and reeducation (say by actively punishing women who pursue stereotypical careers to stop them from being role models for next generation).

On the other hand (hypothetically) suppose that the gender gap is the result of some innate difference in cognition but a simple change in the way science is conducted or taught would let many women who want to be scientists contribute productively to the field instead of having their dreams frustrated. Then obviously we should make that change regardless of the fact that the an innate difference was underneath the gender gap.

In short this issue really doesn’t fucking matter but it really really bothers me when I see people, especially scientists, spinning studies so heavily to reach the conclusions they find pleasant to believe. The roots of the gender gap are clearly complicated and almost certainly result from some complex interplay of innate and environmental factors but just think about how differently we would approach this problem if we were studying another species. Instead of prematurely trying to announce the death of either theory we would say the issue was still murky, explain the competing evidence and leave it at that. Why can’t we do that here too?

So my procrastination tonight started early with this interesting article about the proclivities of infants for racial and cultural bias. It’s a good article but I take a bit of an issue with this paragraph.

Spelke’s studies found baby boys and girls have similar mathematical ability, an incidental finding that was at the forefront of her mind in January 2005 when the former Harvard president Larry Summers suggested that the relative lack of female engineers and scientists was down to innate gender differences. ‘When it comes to the basic modules we are born with, they are pretty much the same,’ says Spelke, who was in the thick of the verbal fisticuffs that followed (Summers was ‘wrong, point for point’). Summers resigned as controversy raged. Spelke does not deny that there are differences in the way men and women think but most of this, she believes, is learnt over time, and down to prejudice and the expectations of society.

Of course it’s always easier to repudiate someone’s remarks when you simply assume they said whatever you are itching to reject. But besides mischaracterizing Summers this paragraph also buys into widespread but fallacious assumption that basic computational skills (adding, subtracting etc..) are the skills needed by scientists and engineers; calculation is easy it is the ability to reason abstractly and construct proofs that is hard. I would normally have simply dismissed this as another instance of sloppy journalism but a few minutes later I found the same errors being made in a respectable summary of an article published in the current edition of science, errors seemingly encouraged by the paper itself and it’s lead author.

Tipping off their hand early the summary begins with it’s own (IMO unethical) misquotation of Summers¹ but quickly moves on to reading the result they want to see into this recent study. The study basically plotted gender differences on math tests in a country versus that country’s level of gender equity and concluded that the more equitable the country the smaller the advantage boys enjoyed on math tests. The message the summary takes from this, with support from the study’s lead author, is that gender differences in mathematics are largely a result of enviornmental effects. Of course latter we are given the following qualification.

Having linked social structures to the math gender gap from country to country, Sapienza wonders whether this result rules out biological influences entirely. The answer is no. The biological hypothesis suggests that an average boy would score higher in mathematics than in reading, while for girls the reverse is true. This pattern does not change in more gender equal societies hinting that some aspects of academic performance may be innately different between boys and girls.
Sapienza and colleagues found that boys, regardless of the country and social environment in which they live, typically do better in math than in reading. Similarly, girls are usually better in reading than in math, regardless of the degree of gender equality in their society. As a result, in more gender equal societies, girls will gain an absolute advantage relative to boys.

In short an uncritical reading of either the paper in science or the summary would leave the reader with the impression that we now have even stronger evidence that boys don’t have an innate advantage at mathematics but there are still a few issues that need to be worked out about reading ability. Except the study really shows exactly the opposite. Ignoring for a moment the implicit (but false) assumption that these math tests are good measures of the skills needed to enter math and science professions just try and think about what theory would best explain the fact that cross-culturally boys are better at math than they are at reading while girls are better at reading than they are at math? Seems pretty clear to me that this evidence best supports the idea that their is an innate gender based attraction to math or reading and that in societies with greater gender equity women just perform better in school generally.

Now I don’t actually endorse that theory. It overly simplifies the complex interactions of culture and innate traits and it would be silly to just rely on this evidence while ignoring other evidence supporting larger cultural effects. However, the point remains that the evidence provided actually points in the exact opposite direction of the spin that is provided. Ultimately the point that I take from this is that if you want to have any idea about what’s plausible in this area you really can’t trust anyone’s (except mine of course :-) ) interpretation, even that of the scientists doing the study. You really have to go read the actual papers with a skeptical eye to get something other than spin. In short I worry that their is a bias in the spin given to papers and opinions on this stuff because you get a lot more flak for strident support of one side than the other.