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private_messaging comments on 2013 Survey Results - Less Wrong
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It's very interesting that the same mistake was boldly made again this year... I guess this mistake is sort of self reinforcing due to the uncannily perfect equality between mean IQ and what's incorrectly estimated from the SAT scores.
Actually, I just ran the numbers on the SAT2400 and they're closer; the average percentile predicted from that is 99th, which corresponds to about 135.
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 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.
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.
One reason SAT1600 and SAT2400 scores may differ is that some of the SAT1600 scores might in fact have come from before the 1994 renorming. Have you tried doing pre-1994 and post-1994 scores separately (guessing when someone took the SAT based on age?)
SAT1600 scores by age:
Average SAT for LWers 30 and under (217 total): 1491. (27 1600s.)
Average SAT for LWers 31 to 35 (74 total): 1462.7 (9 1600s.)
Average SAT for LWers 36 and older (81 total): 1437. (One 1600, by someone who's 56.)
I'm pretty sure the 36 and above are all the older SAT, suspect the middle group contains both, and pretty confident the younger group is mostly the newer SAT. The strong majority comes from the post 1995 test, and the scores don't seem to have changed by all that much in nominal terms.
Which creates another question, why do the SAT 2400 and SAT 1600 differ so much?
2210 was 98th percentile in 2013. But it was 99th in 2007.
I haven't seen an SAT-IQ comparison site I trust. This one listed on gwern's website for example seems wrong.
If I remember correctly, I did SAT->percentile->average, rather than SAT->average->percentile; the first method should lead to a higher estimate if the tail is negative (which I think it is).
[edit]Over here is the work and source for that particular method- turns out I did SAT->average->percentile to get that result, with a slightly different table, and I guess I didn't report the average percentile that I calculated (which you had to rely on interpolation for anyway).
It's only accurate up to 1994.
According to Vaniver's data downthread, SAT taken only from LWers older than 36 (taking the old SAT) predicts 140 IQ.
I can't calculate the IQ of LWers younger than 36 because I can't find a site I trust to predict IQ from new SAT. The only ones I get give absurd results like average SAT 1491 implies average IQ 151.