By this logic, if rationalists are selected based on IQ and not height, and the average rationalist height is +1.85 SD, then we’d have to assume that rationalists’ IQ is +9.25 SD (assuming an IQ-height correlation of 0.2), which is, of course, impossible.
For another example of why this logic doesn’t work, consider this: if you have a variable that is uncorrelated with IQ (r = 0), and rationalists are just slightly above average for that variable, then we’d be forced to conclude that rationalists are infinitely smart (or, if they’re below average, infinitely dumb) depending on the direction of the deviation. This is clearly nonsensical.
For an explanation of why this logic doesn’t work, see my reply to Unnamed’s comment. And for the correct calculations, see my reply to faul_sname’s comment.
This is a good point. I don’t think it should make that much of a difference given how young LessWrong is on average, but it can’t hurt to try.
My two problem are 1) finding SAT statistics for nationally representative samples, and not just seniors that take the SAT (the latter are obviously selected) is difficult, and 2) I’d need more detailed data than just the SAT averages—I’d have to adjust each person’s SAT z-score based on the year they took the test.