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lucidfox comments on Transsexuals and otherkin - Less Wrong
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It means taking averages over such an extremely diverse sample that the results end up having no real meaning - like literal average temperature per hospital, which includes sampling over corpses in the morgue and severe fever sufferers. So if the average temperature hospital 1 turns out to be 0.1 degrees higher than in hospital 2, it tells us nothing about the relative distribution of patient traits in each hospital.
That's your hypothesis over the results, not inherent in the testing procedure. If that is the case it would show up as a specific result not be mistake for somehting else.
I'd say there being very clear trends is orders of magnitude more probable.
The way I described the experiment means the raw data would be very rich, and you should be able to see very clear things like some people being better at distinguishing than others, people being better at distinguishing between people who are otherwise similar to their culture, some people being better at pretending than others, some of the "typicals" being a lot more or less typical than others, etc. There's lots of redundancy.
That expression would require less explanation if it were "average body temperature in a hospital".
Somehow the Russian version is more suggestive of that, without explicitly saying "body temperature". Languages are funny that way.