Lumifer comments on Innate Mathematical Ability - Less Wrong
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In your hypothetical there would be a lot of warning signs -- for example all IQs above 145 would be random, that is, re-testing IQs above 145 would produce a random draw from the appropriate distribution tail.
And I suspect that it should be possible to figure out real-world distributions (the fatness of the tails, in particular), by looking at raw, non-normalized test scores.
Yes, you and I are on the same page, I was just saying that IQ shouldn't be defined to be normally distributed.