khafra comments on Even if you have a nail, not all hammers are the same - Less Wrong
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I think the complaint here is less that higher order moments would've produced higher quality results, and more that when testing for adverse effects on health, they used mean dosages already known to be toxic, which is a pretty thorough screening out of any evidence collected.
It would be confidence-inspiring to see the raw data, and some better analyses of it, of course.