Why Care If There Are Innate Gender Differences?

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?

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As far as I’m aware, it’s not quite true that “once you actually have some evidence about a person’s mathematical/scientific ability (like you’ve talked to them) their gender isn’t relevant.” The point of a statistic is that it provides information about the individual (or at least, what they are like most likely). Presuming some kind of innate difference between the genders here, the same piece of data - in this case, maybe some statement the other person makes indicating their abilities - does not push your truth-value probability inference to the same point taking into account gender, because the fact that the other person is male or female (and the corresponding gender effect) biases the inference.

The point is that conditioning on the information you have availible can totally change the effect of various factors on your rational estimate of ability. In fact it can even reverse the effect of a given factor.

For instance suppose (totally randomly) than women tend to be better at reading comprehension tasks. Now if you knew nothing about someone and were told they were a woman this should make you increase your expectation of their reading comprehension. Now suppose also that women tend to test better than men, e.g., statistically they take tests more seriously and score higher relative to their inherent ability than men.

Now suppose you know only that someone got a 700 on the language section of the SAT. In this case further discovering that the individual is a woman should likely reduce your estimate of their reading comprehension since the effect of knowing that their SAT score is an overestimate will swamp the effect of knowing they are innately more likely to have a higher reading comprehension.


Now this point may apply just as well in the reverse. For instance if women are more intimidated by math exams than men (which some studies suggest is true) in fact finding out an applicant for math grad school is a woman should actually increase one’s expectation of their ability.

Ultimately I have no idea which way these conditionalization effects will fall but I do think we have good reason to believe these will overwhelm any innate factors. In short if we want to learn what effect knowledge of gender should rationally have on our judgment of someone we need to look to the interaction of gender and the information we are likely to get about them not the innate effects of gender.

 
 
 

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