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Let's use height as a neutral example.
Men are taller then women - this is true, but what does it mean, and how can we deal with disputes?
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Some women are taller than some men - so we are - perhaps - talking about averages?
But the average healthy and well-nourished woman would be taller than the average disease-ridden and mal-nourished (seriously mal-nourished) man; and the average modern Dutch woman is certainly taller then the average pygmy.
So nutrition, disease and heredity are relevant - and there are other factors too.
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How to sort this out? Are men taller than women, or not?
Simple: we can easily imagine a situation in which all relevant variables that influence height are controlled: so we could look only at equally well-nourished, equally healthy men and women of identical genetics (identical except in sexually differentiated features) and we could control all other relevant variables.
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What would we find?
One of two things:
1. All men and women would have identical height, or
2. All men and women would have different height.
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And what we would find is number 2. - every single man would be taller than the tallest woman.
There would be no overlap between the sexes.
So, that is the answer: men are taller than women (all else being equal - all relevant factors being controlled).
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(Now apply the same reasoning mutatis mutandis to controversial psychological and physical traits.)
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Note:
It is impossible that men and women would be exactly the same height, since men and women differ physically in so many ways.
Or, to put it another way, it is a grossly improbable prior hypothesis to assume no-difference in height between men and women; it flies in the face of everything we know about biology.
Or, to put it another way, it is grossly improbable that men and women would have ended-up identical, having experienced such different selection pressures (such differentiated environmental and social niches) throughout their evolutionary history - when this different evolutionary history is relevant to the adaptiveness of the trait in question.
Now apply the same reasoning mutatis mutandis to controversial psychological and physical traits.
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I favor a standard deviations approach myself. If the means between the two groups in question differ by around a standard deviation, it is proper to say group A is more of whatever quantity is under discussion e.g. men are taller than women. If it's 2 standard deviations or so, then some kind of amplifier in language is appropriate---e.g. Jews are much smarter than blacks or men are MUCH stronger than women.
ReplyDeleteThat's how people talk in areas that aren't political minefields.
@Jehu - but, if you read my post, you will see the limitations of that way of talking.
ReplyDeleteHow many SDs apart are the means depends on the population being sampled, and on how the variables are differentially operating on men and women.
If men and women have very different experiences in a society then this could change or even reverse the average difference in height expressed in terms of SD.
(For example, if men were protein starved and women well-fed, it would be possible to make women on average taller than men.)
In other words, this is a question for science, not statistics.
BGC,
ReplyDeleteIn such a society, it would be correct to say that women are taller than men. Most people when making comparisons are talking about present values, at least when they're not in a political minefield.
Yes - I am familiar with this matter, as I was a lecturer in epidemiology for three years.
ReplyDeleteThe purpose of this posting was to show how to deal with the common objections to the simple (and broadly correct) statement that men are taller than women.
When we went to live in South Australia we noticed that the men were no taller than we were used to, but the women were. My wife said "They must have been rich for so long that even the girls were properly fed."
ReplyDelete