There is far greater psychological variation within each sex than there is between the sexes, is there not?
It depends on what you’re measuring. Let me illustrate with a toy example. Consider some quantitative trait such that the trait value is normally distributed within each sex, and say that both distributions have the same standard deviation (call it s) but different means (call them x1 and x2). (Imagine two bell curves plotted on the same chart, partially overlapping.) We can measure the difference between the means in terms of s; this statistic is known as Cohen’s d:
d = (x1 - x2)/s
So if d is less than one, then there’s a sense in which we can say that the variation within a sex (as operationalized by the standard deviation s) is larger than the variation between sexes (as operationalized by the difference in means x1 - x2). But there’s nothing intrinsically special about d<1; if we chose some other way to operationalize the claim “more variation within a sex than between sexes,” we would get a different result.
As it turns out, d=1 is actually very large, as sex differences go: Janet Hyde reviewed a number of studies (PDF) and found d<1 for every trait measured except for throw velocity and throw distance (which aren’t even psychological).
Given that there is a large amount of overlap for every psychological trait measured, it’s tempting to conclude that there is there is therefore no such thing as psychological sex. Ultimately, however, I don’t think this inference is quite justified.
Why? Well, consider this diagram. In the diagram, if you look at any one particular trait in isolation, there is substantial overlap between groups, but if you look at the entire configuration space, the groups don’t overlap at all. I suspect this kind of phenomenon to apply to real-world psychological sex differences: the difference mostly isn’t in any one exclusive trait, but is buried in the correlations between traits.
If there were no psychological sex differences, you could learn any number of things about a person’s psychology, and yet still do no better than chance in trying to guess their physiological sex. But if there’s a statistical difference in some [ETA: statistically independent] traits, then as you learn more about a person, your probability of guessing wrong goes down exponentially. It might be an instructive exercise to explicitly construct a model and play around with the numbers a bit. Like, suppose hypothetically there were a sex difference of d=0.6 in ten different [independent] psychological traits, and consider a hypothetical individual who has the female mean value for all of these traits. The normal distribution peaks at a probability density of 1/sqrt(2pi) = 0.3989, and has a probability density of 0.3331 at plus-or-minus 0.6 standard deviations, so (if I understand the relevant math) we can predict that our hypothetical individual is female with probability (0.3989/0.3331)^10/(1 - (0.3989/0.3331)^10) = 0.86. Of course, this is only a model, and different choices of parameters will give us different results. What I like about this view is that we’ve reduced the issue to a quantitative one; the claim that there is such a thing as psychological sex can be interpreted as meaning that the probability of guessing a person’s sex correctly given adequate psychological information is close to one.
Is it even possible to reliably tell the difference between an XX brain and an XY brain just by looking at the structure of neurons?
I do not possess detailed familiarity with the neuroscience literature, but in my current state of incomplete information, my guess would be yes. See, e.g., this summary, which claims differences in white matter/gray matter ratios and in the relative sizes of different brain regions.
Has anything ever actually been found that was exclusive to one or the other?
As explained in my commentary above, I don’t think this question is as relevant as it first appears: it could be possible to classify brains by sex given a sufficiently large number of sufficiently large statistical differences, even if there is no particular feature possessed by all and only brains of one sex.
It depends on what you’re measuring. Let me illustrate with a toy example. Consider some quantitative trait such that the trait value is normally distributed within each sex, and say that both distributions have the same standard deviation (call it s) but different means (call them x1 and x2). (Imagine two bell curves plotted on the same chart, partially overlapping.) We can measure the difference between the means in terms of s; this statistic is known as Cohen’s d:
d = (x1 - x2)/s
So if d is less than one, then there’s a sense in which we can say that the variation within a sex (as operationalized by the standard deviation s) is larger than the variation between sexes (as operationalized by the difference in means x1 - x2). But there’s nothing intrinsically special about d<1; if we chose some other way to operationalize the claim “more variation within a sex than between sexes,” we would get a different result.
As it turns out, d=1 is actually very large, as sex differences go: Janet Hyde reviewed a number of studies (PDF) and found d<1 for every trait measured except for throw velocity and throw distance (which aren’t even psychological).
Given that there is a large amount of overlap for every psychological trait measured, it’s tempting to conclude that there is there is therefore no such thing as psychological sex. Ultimately, however, I don’t think this inference is quite justified.
Why? Well, consider this diagram. In the diagram, if you look at any one particular trait in isolation, there is substantial overlap between groups, but if you look at the entire configuration space, the groups don’t overlap at all. I suspect this kind of phenomenon to apply to real-world psychological sex differences: the difference mostly isn’t in any one exclusive trait, but is buried in the correlations between traits.
If there were no psychological sex differences, you could learn any number of things about a person’s psychology, and yet still do no better than chance in trying to guess their physiological sex. But if there’s a statistical difference in some [ETA: statistically independent] traits, then as you learn more about a person, your probability of guessing wrong goes down exponentially. It might be an instructive exercise to explicitly construct a model and play around with the numbers a bit. Like, suppose hypothetically there were a sex difference of d=0.6 in ten different [independent] psychological traits, and consider a hypothetical individual who has the female mean value for all of these traits. The normal distribution peaks at a probability density of 1/sqrt(2pi) = 0.3989, and has a probability density of 0.3331 at plus-or-minus 0.6 standard deviations, so (if I understand the relevant math) we can predict that our hypothetical individual is female with probability (0.3989/0.3331)^10/(1 - (0.3989/0.3331)^10) = 0.86. Of course, this is only a model, and different choices of parameters will give us different results. What I like about this view is that we’ve reduced the issue to a quantitative one; the claim that there is such a thing as psychological sex can be interpreted as meaning that the probability of guessing a person’s sex correctly given adequate psychological information is close to one.
I do not possess detailed familiarity with the neuroscience literature, but in my current state of incomplete information, my guess would be yes. See, e.g., this summary, which claims differences in white matter/gray matter ratios and in the relative sizes of different brain regions.
As explained in my commentary above, I don’t think this question is as relevant as it first appears: it could be possible to classify brains by sex given a sufficiently large number of sufficiently large statistical differences, even if there is no particular feature possessed by all and only brains of one sex.