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Notes -
It’s somewhat of a false dichotomy: “overlapping curves with long tails” and “bimodal distribution” are often pam_theyre_the_same_picture.jpg, especially with natural data.
“Overlapping curves with long tails” can result in bimodal distributions, and bimodal distributions are frequently the result of mixing two overlapping curves, long tails or not. A common case is a bimodal distribution being a mixture of two normal distributions.
That being said, it’d be fallacious to conclude that, if a unimodal (or, at least, non-obviously bimodal) distribution results from the mixture of two populations, that means the difference between the two populations is not significant or substantial. Especially since even modest differences in mean can produce amplified effects on the tails.
As described by the paper linked in the Wikipedia article above, a population mixture between men and women is unlikely to be bimodal in height, despite human height between the sexes often serving as a canonical example for a bimodal distribution in statistics textbooks. And, might I add, its status as a canonical example is probably because the average height difference between men and women is well-accepted, observable, and uncontroversial in spite of there being readily noticeable variance in the heights of both men and women.
The authors suggest a rule of thumb of the difference in mean being greater than the sum of the two population standard deviations for producing a bimodal distribution. Such a difference would be akin to a difference of greater than 30 IQ points for two populations with a standard deviation of 15.
The paper also hilariously (not sure if the authors find it as amusing as I do) Notices that the male heights in a previous study have far more 5’10” and 6’0 men than would be expected relative to 5’11”-ers. This immediately made me think of classic OKCupid dating statistics, where there is a dearth of reported 5’11”-ers due to potential 5’11”-ers rounding up to satisfy the female demand for male height and round numbers. I would remark, "5'11 versus 6'0: the meme to academia pipeline." However, it might actually be "5'11 versus 6'0: the academia to meme pipeline."
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