I’ve discussed this topic before, but in light of my revised formula for converting new SAT scores to IQ equivalents, some of my old conclusions require revision.

The average Harvard student has a post-1995 SAT score of 1490, which according to my latest estimate, equates to an IQ of 145 (U.S. norms), or 143 (U.S. white norms).

However according to my  analysis of a Harvard study, Harvard undergrads have an average Wechsler IQ of 124 (U.S. norms) or 122 (U.S. white norms).  This might be an underestimate because of sampling error or ceiling bumping,  but taking the figure at face value, if students selected largely by the SAT to have an IQ equivalent 45 points above the U.S. mean on the SAT, average only 24 points above the U.S. mean on the Wechsler, a 0.53 correlation between SATs and Wechsler IQ in the general U.S. population is crudely implied: 24/45 = 0.53.

There is reason to believe this result is not anomalous.

Scientists Meredith C. Frey and Douglas K. Detterman came up with a formula for predicting how one would score on an official IQ test from their performance on the post-1995 SAT. The formula was presumably derived from regression predicting IQs on the Raven Advanced Progressive Matrices (RAPM) from scores on the SAT (see scatter-plot C below) of 104 students at a selective private university.

Such formulas have value, because if you ever hit your head, a psychologist might administer an IQ test to see if you have brain damage. But if you score low, it doesn’t necessarily prove any damage; it could just be that you’re naturally dumb. Thus knowing your statistically expected performance on an official IQ test from your past performance on tests like the SAT is diagnostically useful.

The formula is as follows:

X’IQ = (0.095 * SAT-M) + (-0.003 * SAT-V) + 50.241

It is interesting to apply this formula to the average Harvard student who scored 1490 on the SAT (reading + math). Assuming the typical Harvard undergrad scored 745 on both the reading and the math section, the formula predicts they will score 123 119 on the Raven IQ test (the Raven was normed in lily white Iowa so 123 119 reflects U.S. white norms, which are equivalent to 125 121 in U.S. norms). Remarkably close to the actual IQ of Harvard students on the Wechsler!

So  people who have an IQ equivalent 45 points above the U.S. mean on the new SAT, scoring only about 25 21 points above the U.S. mean on the Raven, once again implying a post-1995 SAT-IQ correlation that is only in the mid 0.50s: around 0.5:

25/45 = 0.56    21/45= 0.47

One possibility is that this formula underestimates the expected intelligence of high SAT people because the scatter-plot clearly shows a pile up of scores at the ceiling of the RAPM, however this pileup only seems to consist of 12% of the sample (not enough to significantly flatten the regression line, especially since some of them would have scored the same even if the test had more hard items).

In addition, I personally looked at the scatter plot carefully and did my best to write down the RAPM IQs of every single participant with an SAT score from 1400-1600. This was an admittedly subjective and imprecise exercise given how small the graph is, but I counted 38 top SAT performers and these were their approximate RAPM IQs: 95, 102, 105, 108, 108, 110, 110, 113, 113, 113, 113, 113, 117, 117, 117, 117, 117, 120, 120, 120, 122, 122, 128, 128, 128, 128, 134, 134, 134, 134, 134, 134, 134, 134, 134, 134, 134, 134.

While the mean RAPM IQ of the top SAT performers was likely reduced by ceiling bumping, the median wold not have been, and that median was 120, suggesting the regression prediction of 123 119 was not too low.

If we assume that the correlation between the SAT and Raven is entirely caused by g (general intelligence)…a  somewhat reasonable assumption given they seem at least superficially to have little in common but reasoning.. and if we further assume that the RAPM has a g loading of about 0.8, then we can deduce that the new SAT has a g loading of 0.7 (0.56/0.8)  0.59 (0.47/0.8).  That’s hardly bad, but not as good as the Wechsler IQ tests which are thought to have g loadings of 0.9-0.95.  I guess there’s a reason beyond political correctness why Mensa stopped accepting SAT scores for admission.