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private_messaging comments on 2013 Survey Results - Less Wrong
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For non-Americans, what's the difference between SAT 2400 and SAT 1600 ?
Averaging sat scores is a little iffy because, given a cut-off, they won't have Gaussian distribution. Also, given imperfect correlation it is unclear how one should convert the scores. If I pick someone with SAT in top 1% I shouldn't expect IQ in the top 1% because of regression towards the mean. (Granted I can expect both scores to be closer if I were picking by some third factor influencing both).
It'd be interesting to compare frequency of advanced degrees with the scores, for people old enough to have advanced degrees.
The SAT used to have only two sections, with a maximum of 800 points each, for a total of 1600 (the worst possible score, IIRC, was 200 on each for 400). At some point after I graduated high school, they added a 3rd 800 point section (I think it might be an essay), so the maximum score went from 1600 to 2400.
Yes, it's a timed essay.
The correlation is the slope of the regression line in coordinates normalised to unit standard deviations. Assuming (for mere convenience) a bivariate normal distribution, let F be the cumulative distribution function of the unit normal distribution, with inverse invF. If someone is at the 1-p level of the SAT distribution (in the example p=0.01) then the level to guess they are at in the IQ distribution (or anything else correlated with SAT) is q = F(c invF(p)). For p=0.01, here are a few illustrative values:
The standard deviation of the IQ value, conditional on the SAT value, is the unconditional standard deviation multiplied by c' = sqrt(1-c^2). The q values for 1 standard deviation above and below are therefore given by qlo = F(-c' + c invF(p)) and qhi = F(c' + c invF(p)).
There are subtleties though. E.g. if we take some programming contest finalists / winners, and take their IQ scores, those are regressed towards the mean from their programming contest performance. Their other abilities will be regressed towards the mean from the same height, not from IQ. This might explain the dramatic cognitive skill disparity between, say, Mensa and some professional group of same IQs.