So your theory is that all observed larger number of men at the upper end of any bell curve is due to sexism? And the larger number of men at the lower end of most bell curve, e.g., more men in prison is due to..something?
Most of the data I’ve seen suggests women have lower variance, here Robin Hansen discusses some of the implications about variance in test scores.
There may well be differences in average performance between men and women in various intellectual tasks, in either direction. Indeed, there are some specific categories of tasks where the evidence for such differences seems strong; the most famous example is probably “mental rotation”. The difference for mental rotation is large but not enormous (about 1sd); my understanding is that all other sex differences found in scientific studies are smaller, and there are differences going in both directions.
It seems unlikely to me that there’s a big general cognitive deficit on either side. I believe girls are currently doing better than boys in pretty much all subjects at school in my country nowadays; in the past it was the other way around; so whatever differences there are (in this kind of task) must be smaller than the size of difference that can be induced by cultural effects. Of course this is consistent with deficits in very specific areas, with variance differences that affect how many really stellar performers there are of each sex, etc.
There may well be differences in variance between men and women. These differences might be fairly big, but it seems unlikely to me that they’re large enough to make huge differences at “ordinary” ability levels.
Once you start looking at the tails of the distributions, I expect them to be quite far from being Gaussian or even symmetrical. There are a lot more ways for things to go badly wrong than for them to go exceptionally right, after all. So I am skeptical about inferences from differences at the “low” end to differences at the “high” end.
There are certainly a lot more men than women in prison, especially if you look specifically at crimes of violence. However, lumping this together with variations in ability seems like a wilful embracing of the halo/horns effect; it seems like much of it will come from variations in sociopathy, enjoyment of violence, and other such characteristics that needn’t go along with worse performance as (say) a scientific lab manager.
For those last two reasons, any inference that looks much like “there are more men in prison, so we should expect more men to win Nobel prizes in physics” seems extremely suspect to me. Still more “there are more men in prison, so we should expect more men to make good lab managers”.
Putting all the above together: there may be well be differences in competence between men and women; they may well be bigger at the highest levels; I wouldn’t expect the differences to be enormous except maybe at the very highest levels where variance differences can be a really big deal.
All of that is independent from the question of whether there are sexist attitudes—by which, for present purpose, I mean: whether there are systematic biases that make men get evaluated better than women relative to their actual ability, likely performance, etc. Or, for that matter, worse.
It seems to me that there is a lot of evidence that there are such sexist attitudes, generally favouring men over women. We’ve had a lot of discussion of one study which seems to me like very strong evidence for such attitudes in one domain; I posted some links to some others. There’s a pile of anecdote too, but of course the way that looks may simply reflect what anecdotes I happen to have encountered. (I think the available anecdotage is at any rate evidence that sexist attitudes in both directions exist.)
The possibility of real ability differences has some bearing on how to interpret the apparent evidence for sexist attitudes, but in at least some cases—e.g., the study we’ve discussed so much here—it seems to me that it doesn’t make much difference, because to make the evidence not be strong evidence for sexist attitudes it would be necessary for the ability differences to be (what seems to me to be) unrealistically large.
The relevant question for most practical purposes is not the statistical difference between men and women in some particular kind of ability, but the statistical difference conditional on the information usually available when hiring (or when considering promotion, or when allocating places at a university, or whatever). Nothing I have seen so far gives me reason to think that these differences are large, even though the information in question is limited and unreliable.
(To get quantitative for a moment, let’s suppose everything in sight is normally distributed. Some underlying ability: male and female both have mean 0, but s.d. 1 for men and 0 for women. Some measure of ability equals the actual ability level plus noise with mean 0 and s.d. 1. Actual job performance looks like underlying ability plus other factors with mean 0 and s.d. 0.5. Then conditional on measured ability being +2 (i.e., well above average but not stratospheric), mean predicted job performance is about +1.0 for male applicants (with s.d. 0.87) and +0.8 for female applicants (with s.d. 0.80), a difference of about 0.2 (male) standard deviations. Definitely not zero, but not exactly huge either and a lot smaller than the noise. I have no idea how realistic any of the numbers I’ve assumed here actually are, and would be glad to learn of credible estimates—though of course this is a toy model at best whatever numbers one plugs in.)
Thanks. Though that high likelihood of mindkill makes it (1) more likely that someone will try to correct my obvious stupid errors when in fact I’m right and they’re confused, and (2) more likely that someone will rightly correct my obvious stupid errors when in fact they’re right and I’m confused but I won’t believe them. Still, the best we can do is the best we can do :-).
There are certainly a lot more men than women in prison, especially if you look specifically at crimes of violence. However, lumping this together with variations in ability seems like a wilful embracing of the halo/horns effect; it seems like much of it will come from variations in sociopathy, enjoyment of violence, and other such characteristics that needn’t go along with worse performance as (say) a scientific lab manager.
Note that the number of people who are in jail doesn’t merely depend on how many commit crimes, it depends on how many get caught committing crimes, and that such a statistic would anticorrelate with intelligence is very nearly obvious to me.
Yes, that’s a good point. How big the effect is depends on how the probability of getting caught varies with intelligence: I agree that it will almost always anticorrelate, but the dependence could be very strong or very weak. Anyone got any statistics on that?
Hmm. It might be possible to indirectly get some information about them by comparing the kinds of people that get caught for premeditated crime with the kinds of people that get caught for crimes of impulse, and then adjusting for any correlation of intelligence with self-control. The latter ought to be harder to cover up.
So your theory is that all observed larger number of men at the upper end of any bell curve is due to sexism? And the larger number of men at the lower end of most bell curve, e.g., more men in prison is due to..something?
Most of the data I’ve seen suggests women have lower variance, here Robin Hansen discusses some of the implications about variance in test scores.
Nope. (What did I say to make you think that?)
My position is as follows.
There may well be differences in average performance between men and women in various intellectual tasks, in either direction. Indeed, there are some specific categories of tasks where the evidence for such differences seems strong; the most famous example is probably “mental rotation”. The difference for mental rotation is large but not enormous (about 1sd); my understanding is that all other sex differences found in scientific studies are smaller, and there are differences going in both directions.
It seems unlikely to me that there’s a big general cognitive deficit on either side. I believe girls are currently doing better than boys in pretty much all subjects at school in my country nowadays; in the past it was the other way around; so whatever differences there are (in this kind of task) must be smaller than the size of difference that can be induced by cultural effects. Of course this is consistent with deficits in very specific areas, with variance differences that affect how many really stellar performers there are of each sex, etc.
There may well be differences in variance between men and women. These differences might be fairly big, but it seems unlikely to me that they’re large enough to make huge differences at “ordinary” ability levels.
Once you start looking at the tails of the distributions, I expect them to be quite far from being Gaussian or even symmetrical. There are a lot more ways for things to go badly wrong than for them to go exceptionally right, after all. So I am skeptical about inferences from differences at the “low” end to differences at the “high” end.
There are certainly a lot more men than women in prison, especially if you look specifically at crimes of violence. However, lumping this together with variations in ability seems like a wilful embracing of the halo/horns effect; it seems like much of it will come from variations in sociopathy, enjoyment of violence, and other such characteristics that needn’t go along with worse performance as (say) a scientific lab manager.
For those last two reasons, any inference that looks much like “there are more men in prison, so we should expect more men to win Nobel prizes in physics” seems extremely suspect to me. Still more “there are more men in prison, so we should expect more men to make good lab managers”.
Putting all the above together: there may be well be differences in competence between men and women; they may well be bigger at the highest levels; I wouldn’t expect the differences to be enormous except maybe at the very highest levels where variance differences can be a really big deal.
All of that is independent from the question of whether there are sexist attitudes—by which, for present purpose, I mean: whether there are systematic biases that make men get evaluated better than women relative to their actual ability, likely performance, etc. Or, for that matter, worse.
It seems to me that there is a lot of evidence that there are such sexist attitudes, generally favouring men over women. We’ve had a lot of discussion of one study which seems to me like very strong evidence for such attitudes in one domain; I posted some links to some others. There’s a pile of anecdote too, but of course the way that looks may simply reflect what anecdotes I happen to have encountered. (I think the available anecdotage is at any rate evidence that sexist attitudes in both directions exist.)
The possibility of real ability differences has some bearing on how to interpret the apparent evidence for sexist attitudes, but in at least some cases—e.g., the study we’ve discussed so much here—it seems to me that it doesn’t make much difference, because to make the evidence not be strong evidence for sexist attitudes it would be necessary for the ability differences to be (what seems to me to be) unrealistically large.
The relevant question for most practical purposes is not the statistical difference between men and women in some particular kind of ability, but the statistical difference conditional on the information usually available when hiring (or when considering promotion, or when allocating places at a university, or whatever). Nothing I have seen so far gives me reason to think that these differences are large, even though the information in question is limited and unreliable.
(To get quantitative for a moment, let’s suppose everything in sight is normally distributed. Some underlying ability: male and female both have mean 0, but s.d. 1 for men and 0 for women. Some measure of ability equals the actual ability level plus noise with mean 0 and s.d. 1. Actual job performance looks like underlying ability plus other factors with mean 0 and s.d. 0.5. Then conditional on measured ability being +2 (i.e., well above average but not stratospheric), mean predicted job performance is about +1.0 for male applicants (with s.d. 0.87) and +0.8 for female applicants (with s.d. 0.80), a difference of about 0.2 (male) standard deviations. Definitely not zero, but not exactly huge either and a lot smaller than the noise. I have no idea how realistic any of the numbers I’ve assumed here actually are, and would be glad to learn of credible estimates—though of course this is a toy model at best whatever numbers one plugs in.)
Kudos for explicitly writing out your nuanced position on a high-likelihood-of-mindkill issue.
Thanks. Though that high likelihood of mindkill makes it (1) more likely that someone will try to correct my obvious stupid errors when in fact I’m right and they’re confused, and (2) more likely that someone will rightly correct my obvious stupid errors when in fact they’re right and I’m confused but I won’t believe them. Still, the best we can do is the best we can do :-).
Note that the number of people who are in jail doesn’t merely depend on how many commit crimes, it depends on how many get caught committing crimes, and that such a statistic would anticorrelate with intelligence is very nearly obvious to me.
(I agree with most of the rest of your comment.)
Yes, that’s a good point. How big the effect is depends on how the probability of getting caught varies with intelligence: I agree that it will almost always anticorrelate, but the dependence could be very strong or very weak. Anyone got any statistics on that?
I’d guess people who commit crimes but don’t get caught are very, very hard to get statistics about.
Hmm. It might be possible to indirectly get some information about them by comparing the kinds of people that get caught for premeditated crime with the kinds of people that get caught for crimes of impulse, and then adjusting for any correlation of intelligence with self-control. The latter ought to be harder to cover up.