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.
Indeed if rationalists were entirely selected by IQ and nothing else, and there were no other confounders, and height was +1.85 SD, IQ would be +9.25 SD. In the real world this instead provides a Bayesian update that you were wrong in assuming rationalists were purely selected for by IQ, and not e.g. gender.
The fact that going from 2.42 SD to 3.03 SD is nonsensical does not in anyway make it more sensible to go from 2.42 to 1.93. Your response to faul_sname is completely irrelevant because it assumes rationalists are selected for on SAT, which is clearly false. The correct calculation is impossible to make accurately given we are missing key information, but we can make some estimates by assuming that rationalists are selected for something that correlates with by IQ and SATs and guessing what that correlation is.
Or to put it another way: these SAT scores are compatible with an average IQ anywhere between + 1.93 to + 3.03 SD. Insofar as your prior lies somewhere between these two numbers, and you don’t have a strong opinion on what precisely Lesswrong selects for it’s not going to update you very much in either direction.
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.
Indeed if rationalists were entirely selected by IQ and nothing else, and there were no other confounders, and height was +1.85 SD, IQ would be +9.25 SD. In the real world this instead provides a Bayesian update that you were wrong in assuming rationalists were purely selected for by IQ, and not e.g. gender.
The fact that going from 2.42 SD to 3.03 SD is nonsensical does not in anyway make it more sensible to go from 2.42 to 1.93. Your response to faul_sname is completely irrelevant because it assumes rationalists are selected for on SAT, which is clearly false. The correct calculation is impossible to make accurately given we are missing key information, but we can make some estimates by assuming that rationalists are selected for something that correlates with by IQ and SATs and guessing what that correlation is.
Or to put it another way: these SAT scores are compatible with an average IQ anywhere between + 1.93 to + 3.03 SD. Insofar as your prior lies somewhere between these two numbers, and you don’t have a strong opinion on what precisely Lesswrong selects for it’s not going to update you very much in either direction.