I think that the way that Scott estimated IQ from SAT is flawed, in a way that underestimates IQ, for reasons given in comments like this one. This post kept that flaw.
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.)
I think that the way that Scott estimated IQ from SAT is flawed, in a way that underestimates IQ, for reasons given in comments like this one. This post kept that flaw.
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.)