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December 06, 2006
The Glass Ceiling
Something of a logical fallacy here:
Our research shows that it doesn't stop there: when you look at the
behaviours needed for high performance leadership in the business world
- strategic thought, relationship-building, influence, power and
communication - women actually have a higher overall average capability
than men. So why aren't the equally, if not more capable, people in
society running the show?
Because looking at average capability when trying to find the 0.001% who'll get to the very top isn't very useful. What we actually want to do is look at the variation around that average. This is the thing that got Larry Summers into such trouble. It is said that men show greater variation around that average on almost all tests one might care to use. IQ (for whatever little that is actually worth), aggression, etc etc. If we are sorting for the top 0.001% of whatever set of talents actually being looked for (to the extent that talent does indeed rise to the top, something that Chris Dillow isn't all that sure about and nor am I) then we'd expect to find a preponderance of men: just as we would at the other end of the tail, amongst the hopelessly incompetent at the same things.
Now, I'm not all that sure about how much talent does in fact lead to the top: I'm sure that luck has at least as much to do with it, so also one's starting point in the society. But that isn't Julia's point, it is that the average level of talent should explain the distribution of the prizes at the very top. No, it won't, if rewards are determined by talent then the the very top ones will be determined by the distribution of talent at the very tip of the distribution tail.
December 6, 2006 in Politics | Permalink
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Comments
Would have to be a really huge difference in variance to outweigh even a small difference in the mean.
Posted by: dsquared | Dec 6, 2006 9:29:50 AM
> strategic thought, relationship-building, influence, power and communication
IME it's more
emotional thinking, bitching, back-stabbing, bitchyness and gossip.
Posted by: AntiCitizenOne | Dec 6, 2006 10:27:54 AM
Would have to be a really huge difference in variance to outweigh even a small difference in the mean.No, dsquared, you've missed the point entirely. He's talking about a deviation that need not affect the mean at all. The data says that women are more talented on average but the few most and least talented are usually men.
Posted by: newparadigm | Dec 6, 2006 10:36:47 AM
The fact you cite (higher variation among men) does not prove your conclusion. Higher variation does not necessarily imply more outliers. Men could have a broad spectrum with thinner tails (like a bowler hat), and women a high, narrow spectrum with fatter tails (like a sombrero) - the standard deviation might still be higher for men even though there were more women above some high cutoff point.
Also, your cited fact would still suggest that there should be a lot more women among "average-level" math-related jobs. I'm not convinced that math PhDs represent "the 0.001% who'll get to the very top", or even that the top 0.001% will get to the top, but even so, there should be a lot more women economics PhDs, or teaching math at the high-school level and in engineering, accounting, policy analysis, computer programming, and similar jobs - but women are under-represented in most of those fields as well. So by your own explanation for the dearth of women "at the top", there is no good explanation for the dearth of women in the remaining 99.999% of jobs.
Posted by: Kevin T. Keith | Dec 6, 2006 3:34:31 PM
Just as there are very, very few sportswomen who can compete with sportsmen (even in non-physical sports) there will always be significantly fewer women in numerate and geo-spatial professions and trades. That's just biology.
The problem this creates is that those women who have the abilities are likely to be put off by the predominantly male environment and whose talents are therefore lost to the economy.
And getting to the top of just about any professin or organisation is largely to do with aggression, competitive instinct and having no concern for your personal popularity. Again these are predominantly male failings so men will always predominate in top jobs.
Posted by: towcestarian | Dec 6, 2006 3:52:14 PM
Kevin Keith: you are right as far as your assertion goes. But do we have any evidence that the distributions in question for men and women deviate from normal? You're describing kurtosis: what is the kurtosis for the variables in question? Is the curve for men platykurtic or leptokurtic? What is the skewness? I don't know the answer to these questions, but I would hazard a guess that if the distributions for men and women have non-zero kurtosis, then that for men is likely to be leptokurtic (positive kurtosis) and that for women platykurtic (negative kurtosis), contrary to your thought experiment. This is consistent with the 'more outliers' description of male distributions.
Posted by: David Gillies | Dec 6, 2006 4:45:07 PM
[He's talking about a deviation that need not affect the mean at all. The data says that women are more talented on average but the few most and least talented are usually men. ]
"more talented on average" means "have a higher mean ability". If you have two distributions centred around different means, then the one with the higher mean will have a larger probability mass above any point far from the mean, unless the difference in variances is quite large.
Posted by: dsquared | Dec 6, 2006 6:00:33 PM
Is there are cure for kurtosis?
Posted by: AntiCitizenOne | Dec 6, 2006 6:00:56 PM
"f you have two distributions centred around different means, then the one with the higher mean will have a larger probability mass above any point far from the mean"
Nope, not true, at least for normal distributions. If by 'probability mass' you mean cumulative distribution function then for two distributions d_1 and d_2 with μ_1 < μ_2 and σ_1 > σ_2 where μ_i, σ_i are the means and standard deviations respectively, then there is a point at which CDF(d_1) = CDF(d_2) and is lower thereafter. The same is true on the low side. Higher S.D. always wins.
Posted by: David Gillies | Dec 6, 2006 9:28:41 PM
"Again these are predominantly male failings": characteristics, surely, not failings. Whether they are failings depends on the circs.
Posted by: dearieme | Dec 6, 2006 11:27:48 PM