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?