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.

sat

Such formulas are useful, 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 on an official IQ test. Note, 123 is NOT their SAT score converted to an IQ equivalent, it’s their expected IQ on a different test, given their score on the SAT, and thus there is severe regression to the mean.

A predicted IQ of 123 remarkably similar to the mean IQ of 122 a sample of Harvard students actually obtained when tested on the WAIS. Some readers might be wondering why I’m not equating the predicted IQ to white norms as I normally do. The answer is that the RAPM was normed in Iowa (one of the 5 whitest states in America) so converting to white norms would be redundant.

One possibility is that this formula underestimates the expected intelligence of high SAT people because the scatterplot 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 line prediction of 123 was not too low.

An RAAPM IQ of 123 is 26 points above the U.S. mean IQ of 97. An SAT score of 1490 equates to an IQ of 139…or perhaps 137 if a many SAT takers are tested repeatedly and use their best score as commenter Lion of the Judah-sphere suggested… about 40 points above the U.S. mean of 97. Dividing 26 by 40 suggests the SAT and RAPM correlate 0.65. If we assume that the correlation between the SAT and Raven is entirely caused by g (general intelligence)…a reasonable assumption given they have little in common but reasoning.. and if we further assume that the RAPM has a g loading of 0.85, then we can deduce that the SAT has a g loading of 0.76 (0.65/0.85).