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by abeppu 358 days ago
The methodology at the page you link to seems really sketchy and inappropriate to the kinds of groups under discussion.

> Suppose PA(x) and PB(x) differ only by a translation in x, such that fB(x) = fA(x - Δ), where Δ is the mean difference in x between the groups.

... but you can't really just assume that the variance within two groups is the same. Especially when comparing a small group like the Nandis (a "subtribe of a half million") vs a large and diverse group like "Europeans", as they do in the "Augmentation of Small Differences" section, it seems pretty cavalier to just assume that the variance is the same.

But for comparing stuff between sexes, the "variability hypothesis" about men having greater variability across a range of traits dates back to Darwin, and has a pile of research results. It would seem especially irresponsible to rely on an assumption that the variance was equal between the sexes. One might have prior reason to expect otherwise, and differences in variance may materially contribute to different fractions above or below an extreme threshold.

Further, given the kind of selection effects you were alluding to before, it may not even be safe to assume these distributions are normal. While the endurance of the broader population ought to be normally distributed, if there are various hurdles on the path to participating (e.g. the organizers say you should probably have completed a 50 mile race at a given pace before signing up for their 100 mile race?) one might well see a different overall shape.
1 comments
thaumasiotes 358 days ago
> But for comparing stuff between sexes, the "variability hypothesis" about men having greater variability across a range of traits dates back to Darwin, and has a pile of research results. It would seem especially irresponsible to rely on an assumption that the variance was equal between the sexes.

That would imply a much larger advantage for men. If you were seeking to show that women outperform men, you'd gloss over that point as much as you thought you could get away with.

(In a little more detail: if you determine that it takes an athleticism factor of 10.8 to run 200 miles, greater male variability immediately implies that among all people who have that much athleticism, the average male athleticism will be quite a bit higher than the average female athleticism. The average of a thresholded normal distribution is quite close to the threshold, but it gets farther away as the standard deviation increases.)

> Further, given the kind of selection effects you were alluding to before, it may not even be safe to assume these distributions are normal. While the endurance of the broader population ought to be normally distributed, if there are various hurdles on the path to participating (e.g. the organizers say you should probably have completed a 50 mile race at a given pace before signing up for their 100 mile race?) one might well see a different overall shape.

...you don't seem to have understood the method. The assumption is that the broader population is normally distributed - you know, what you already said it was safe to assume - and that the selected population consists of that part of the broader population's normal distribution that exceeds some threshold.

Or in pictures, we assume that the population looks like this:

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and the running-200-miles population looks like this:

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