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Journal by Arik
Departing only slightly from the overtly political musings, let me put it to you that statistics are almost always misunderstood, by almost everyone.
Or, perhaps a bit more precisely, I would say that almost everyone misunderstands common statistics - but not in the same ways!
So we'll pull in sex for an example. There's a school of thought that says that there's virtually no difference between men and women, statistically, on anything important. There's another school of thought that says they're so incredibly different, statistically, on virtually everything important, they almost don't look like the same species! And to make this even funnier, these two schools of thought can often point to the SAME data to support their diametrically opposed conclusions!
Ok, so let me break this down for you with just a little more detail. Let's pick an attribute we test for, aggressiveness is a good one here, because the statistical differences between the sexes are about as dramatic on this measure as you'll find anywhere.
So, if I pick out two individuals randomly, and I tell you nothing other than their sex - one is male, the other is female - and ask you to guess which one is more aggressive, what's your guess?
If you guessed the male, of course that was the better guess statistically. But your edge isn't very big, you're only 60% likely to be right. If I answered female I still have a 40% chance to get the question right - you've only got a little edge, not a solid distinction of kind.
In fact, if you go select a group of women who are just a little more aggressive than average, and set them up against a group of males who are just a little less aggressive than average the women are absolutely going to use the guys as footstools and doormats.
This is the no significant differences argument simplified a bit for easy digestion. And it's valid. It's true. On average, women are only a little bit less aggressive than men, and many women are more aggressive than many men. So it's ignorant prejudice to say that men are the aggressive ones and women are not aggressive. It's radically contrary to the facts! And if that's true in terms of aggressiveness it's much more true on most other metrics.
BUT, there are more facts than have been mentioned. What if we look beyond the average, at the distribution?
What if, instead of randomly selecting a male and a female from the general population, we FIRST randomly select 100 individuals, 50 males 50 females, THEN select the most aggressive individual of the bunch. This time, we guess which sex that individual is. Again, you say male, leaving me with the contrary position.
This time the odds are entirely different. There's virtually no chance I'll win.
The average woman is only slightly less aggressive than the average male, and more aggressive than many. Many women are more aggressive than the average male. But the most aggressive man on the planet will be a male. In fact, if we could rank every individual on earth, something like the top 5-6 million people would be males. Only after that would you start seeing females.
A really neat thing is this actually works almost as well in the opposite direction as well. Lots of women are fairly low on the aggression scale but if you want to find someone that is really freakishly low on it, yeah, that's probably going to be a male. Imagine that!
The middles of the distributions aren't far off. But the shape is different, and there are a lot more males waaaaay out on the limbs. On lots of different metrics, not just aggression.
Or, perhaps a bit more precisely, I would say that almost everyone misunderstands common statistics - but not in the same ways!
So we'll pull in sex for an example. There's a school of thought that says that there's virtually no difference between men and women, statistically, on anything important. There's another school of thought that says they're so incredibly different, statistically, on virtually everything important, they almost don't look like the same species! And to make this even funnier, these two schools of thought can often point to the SAME data to support their diametrically opposed conclusions!
Ok, so let me break this down for you with just a little more detail. Let's pick an attribute we test for, aggressiveness is a good one here, because the statistical differences between the sexes are about as dramatic on this measure as you'll find anywhere.
So, if I pick out two individuals randomly, and I tell you nothing other than their sex - one is male, the other is female - and ask you to guess which one is more aggressive, what's your guess?
If you guessed the male, of course that was the better guess statistically. But your edge isn't very big, you're only 60% likely to be right. If I answered female I still have a 40% chance to get the question right - you've only got a little edge, not a solid distinction of kind.
In fact, if you go select a group of women who are just a little more aggressive than average, and set them up against a group of males who are just a little less aggressive than average the women are absolutely going to use the guys as footstools and doormats.
This is the no significant differences argument simplified a bit for easy digestion. And it's valid. It's true. On average, women are only a little bit less aggressive than men, and many women are more aggressive than many men. So it's ignorant prejudice to say that men are the aggressive ones and women are not aggressive. It's radically contrary to the facts! And if that's true in terms of aggressiveness it's much more true on most other metrics.
BUT, there are more facts than have been mentioned. What if we look beyond the average, at the distribution?
What if, instead of randomly selecting a male and a female from the general population, we FIRST randomly select 100 individuals, 50 males 50 females, THEN select the most aggressive individual of the bunch. This time, we guess which sex that individual is. Again, you say male, leaving me with the contrary position.
This time the odds are entirely different. There's virtually no chance I'll win.
The average woman is only slightly less aggressive than the average male, and more aggressive than many. Many women are more aggressive than the average male. But the most aggressive man on the planet will be a male. In fact, if we could rank every individual on earth, something like the top 5-6 million people would be males. Only after that would you start seeing females.
A really neat thing is this actually works almost as well in the opposite direction as well. Lots of women are fairly low on the aggression scale but if you want to find someone that is really freakishly low on it, yeah, that's probably going to be a male. Imagine that!
The middles of the distributions aren't far off. But the shape is different, and there are a lot more males waaaaay out on the limbs. On lots of different metrics, not just aggression.
The Fine Print: The following comments are owned by whoever posted them. We are not responsible for them in any way.
squatcho, n.:
The button at the top of a baseball cap.
-- "Sniglets", Rich Hall & Friends
(Score: 2) by Tara Li on Friday September 14 2018, @04:04PM
It's not really my field - my days of taking sadistics classes are decades in the past. But the bell curve is an ideal, and real-world things will always affect some of this. Especially if you really have two populations hiding in one.
Check this simulation out: https://anydice.com/program/117d7 [anydice.com]
While the two component bell curves are very symmetric, if you look carefully, the combined curve is *not* symmetric. (You can see it in the table data numerically, but if you switch to graph, you can see the curves overlaid and see it there visually).
I don't know if there's something akin to Fourier Transforms to decompose bell curves similar to using them to decompose composites of sine waves, but I imagine there pretty much has to be - and that it would reveal the number of sub-populations in a larger population.