I agree. You only multiply the SAT z-score by 0.8 if you're selecting people on high SAT score and estimating the IQ of that subpopulation, making a correction for regressional Goodhart. Rationalists are more likely selected for high g which causes both SAT and IQ, so the z-score should be around 2.42, which means the estimate should be (100 + 2.42 * 15 - 6) = 130.3. From the link, the exact values should depend on the correlations between g, IQ, and SAT score, but it seems unlikely that the correction factor is as low as 0.8.
Your argument assumes a uniform prior, but a Gaussian prior is more realistic in this case. In practice, IQ scores are distributed normally, so it's more likely that someone with a high SAT score comes from a more common IQ range than from a very high outlier. For example, say the median rationalist has an SAT score of +2 SD (chosen for ease of computation), and the SAT-IQ correlation is 0.80. The IQ most likely to produce an SAT of +2 SD is 137.5 (+2.5 SD). However, IQs of 137.5 are rare (99.4%-ile). While lower IQs are less likely to achieve such a high SAT score, there are more people in the lower IQ ranges, making it more probable that someone with a +2 SD SAT score falls into a lower IQ bracket.
This shift between the MLE (Maximum Likelihood Estimate) and MAP (Maximum A Posteriori) estimates is illustrated in the graph, where the MLE estimate would be +2.5 SD, but the MAP estimate, accounting for the Gaussian prior, is closer to +1.6 SD, as expected. (You may also be interested in my reply to faul_sname's comment.)
Here’s the breakdown: a median SAT score of 1490 (from the LessWrong 2014 survey) corresponds to +2.42 SD, which regresses to +1.93 SD for IQ using an SAT-IQ correlation of +0.80. This equates to an IQ of 129.
I don't think that works unless Less wrong specifically selects for high SAT score. If it selects for high IQ and the high SAT is as a result of the high IQ then you would have to go the other way and assume an SD of 3.03.
If, as seems more likely, Less wrong correlates with both IQ and SAT score, then the exact number is impossible to calculate, but assuming it correlates with both equally we would estimate IQ at 2.42 SD.
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.
I like that new Scott Alexander estimate of 128, 130+ always stroke me as too high, just from knowing a bunch of people irl who range from 85 to 147, and meeting a bunch of rationalists irl. The average rationalist is definitly considerably smarter than those I know who test around 120, but not as bright as the 140+ people.
The odd thing is I have met a few people in the 130ish range who had way higher computing power than normal for their IQ, so I think there probably is something like effective IQ, which is your raw base IQ (or g for that matter), multiplied by how effective your thought doctrines are. Someone with a good grasp on Bayesianism or another very good logic framework can run circles around someone with a 5 points higher IQ and less formal training in thought.
The second paragraph puts into words something I've noticed but not really mentally formalized before. Some anecdotal evidence from my own life in support of the claims made in this paragraph: I've met individuals whose tested IQ exceeds those of other, lower but not much lower, IQ individuals I know who are more educated / trained in epistemological thinking and tangential disciplines. For none of the individual-pairs I have in mind would I declare that one person "ran circles around" the other, however, the difference (advantage going to the lower but better "trained" IQ individual) in conversational dynamics were notable enough for me to remember well. The catch here is the accuracy of the IQ claims made by some of these individuals, as some did not personally reveal their scores to me.
Honestly, this fits my intuition. If I think of all the rationalists I know, they feel like they are on average near 120 IQ, with what feels like a standard distribution around it, though in reality it's probably not quite normal with a longer upper tail than lower tail, i.e. fewer 90s than 150s, etc. Claims that the average is much higher than 120 feel off to me, relative to folks I know and have interacted with in the community (insert joke about how I have "dumb" friends maybe).
are you correcting for the year the test was taken? The SAT grading has shifted dramatically over time.
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.
a median SAT score of 1490 (from the LessWrong 2014 survey) corresponds to +2.42 SD, which regresses to +1.93 SD for IQ using an SAT-IQ correlation of +0.80.
I don't think this is a valid way of doing this, for the same reason it wouldn't be valid to say
a median height of 178 cm (from the LessWrong 2022 survey) corresponds to +1.85 SD, which regresses to +0.37 SD for IQ using a height-IQ correlation of +0.20.
Those are the real numbers with regards to height BTW.
These both seem valid to me! Now, if you have multiple predictors (like SAT and height), then things get messy because you have to consider their covariance and stuff.
That reasoning as applied to SAT score would only be valid if LW selected its members based on their SAT score, and that reasoning as applied to height would only be valid if LW selected its members based on height (though it looks like both Thomas Kwa and Yair Halberstadt have already beaten me to it).
Eric Neyman is right. They are both valid!
In general, if we have two vectors and which are jointly normally distributed, we can write the joint mean and the joint covariance matrix as
The conditional distribution for given is given by ,
defined by conditional mean
and conditional variance
Our conditional distribution for the IQ of the median rationalist, given their SAT score is
(That's a mean of 129 and a standard deviation of 9 IQ points.)
Our conditional distribution for the IQ of the median rationalist, given their height is
(That's a mean of 106 and a standard deviation of 14.7 IQ points.)
Our conditional distribution for the IQ of the median rationalist, given their SAT score and height is (That's a mean of 131 and a standard deviation of 8.9 IQ points)
Unfortunately, since men are taller than women, and rationalists are mostly male, we can't use the height as-is when estimating the IQ of the median rationalist (maybe normalizing height within each sex would work?).
In The Mystery Of Internet Survey IQs, Scott revises his estimate of the average LessWrong IQ from 138 to 128. He doesn’t explicitly explain how he arrived at this number, but it appears to be an average of the demographics norm method (123) and the SAT method (134). However, using the information in his post, the SAT method doesn’t actually yield 134 but rather 123.
Here’s the breakdown: a median SAT score of 1490 (from the LessWrong 2014 survey) corresponds to +2.42 SD, which regresses to +1.93 SD for IQ using an SAT-IQ correlation of +0.80. This equates to an IQ of 129. Subtracting 6 points (since, according to the ClearerThinking test, the IQs of people who took the SAT and remember their score is ~6 points higher than the group average) brings the adjusted IQ estimate to 123.
The ClearerThinking test also provides a way to adjust self-reported IQs. Subtracting 17 points (because people who report having taken an IQ test claim an average score of 131, but their tested average is only 114) gives an adjusted IQ of 121, based on a self-reported average of 138.
Aggregating the data across all LessWrong and SSC surveys[1] with available information, the estimates consistently cluster around 122. While some might think this is too low, it’s worth noting that an IQ of 122 is at the PhD level.