Ann Coulter is one of the many people I promised to estimate the IQ of in the near-future, which got me thinking about a recent comment she made:

Trump graduated from the Wharton School of Business and went on to make $11 billion. Carson went from Yale to the University of Michigan Medical School and was the first man to separate twins conjoined at the brain. Fiorina graduated from Stanford University and then earned $80 million in business.

By contrast, look up the educational achievement of the average pundit sneering at Trump’s idiocy and the ordinariness of his supporters. I won’t be as nasty as they are, but wow! – people who went to bush-league schools shouldn’t throw stones. There’s nothing wrong with attending a bush-league college. But maybe ease up on holding yourself out as a great intellectual appalled by the dirty masses if you went to a third-rate college in the era of need-blind admissions.

Actually authoritative Forbes magazine puts Trump’s net worth at $4.5 billion, which is unbelievably impressive, but it’s nowhere near $11 billion.  But Coulter’s larger point is that where you went to college is a good proxy for intelligence.  Trump himself seems to share this view.  I remember an episode of The Apprentice where a contestant was bragging about college credentials, and Trump’s sidekick George H. Ross noted that where you went to college didn’t matter.  But Trump rather obnoxiously cut Ross off saying something like “I disagree.  It means a lot.  It’s very very important”  I wonder what Trump’s 80% non-college base would think of that.

In order to test Coulter’s assertion, I looked at some SAT stats for a few colleges:

college sat range (25 percentile to 75 percentile) CR + M iq equivalent estimated standard deviation
caltech 1450-1580  141-152  8.25
harvard 1400-1590  137-153  12
harvey mudd 1390-1570  136-151  11.25
yale 1380-1550  136-149  9.75
stanford 1360-1550  134-149  11.25
princeton 1360-1540  134-149  11.25
georgia tech 1220-1415  123-138  11.25


SATs were converted to IQ equivalents using my formula:  IQ equivalent = 23.835 + 0.081(post-1995 SAT score: CR + M).  Standard deviations (SD) were estimated for each college by multiplying the IQ equivalent gap between the 75th and 25th percentile by 0.75.  This was done because assuming a roughly normal curve in each college, the SD should be 3/4 as large as the gap between these two percentiles.  For example, the IQs of all Americans are normally distributed with an SD of 15, which is 3/4 of the 20 point gap between the 25th percentile (IQ 90) and the 75th percentile (IQ 110).

Analysis of variance

The average SD of the seven colleges above is 10.71.  Squaring 10.71 to get the variance gives 114.7.  But if we square the SD for Americans as a whole (15) we get 225.  This suggests 51% (114.7/225) of the variance in IQ (as measured by SAT) exists within a given college, which means that 49% (0.49) of the variance in U.S. IQ must exist between colleges (and non-college).  The square root of 0.49 suggests a potent 0.7 correlation between where you went to college (assuming you did) and how well you did on the SAT (or for those who didn’t take it, how well you would have done).

In order to test whether the correlation really is 0.7, it helps to look at two extremes.  The most selective and least selective colleges in America.

The most selective college in America

In terms of median SAT scores, Caltech is the most selective college in America.  There are about 224 freshman a year (excluding foreign students) out of 4.413 million 18-year-olds in America.  Cutting the number of freshman in half, we see the median freshman is in the top 112 out of 4,413 million, or roughly the top one in 39,402 in terms of selectivity of college attended.  Thus, if there were a perfect correlation between IQ and college attended, the median Caltechie would have an IQ of 161 (U.S. norms).  Their actual median SAT (CR + M) is 1515 to 1525 (depending on the source) which equates to an IQ of 147, and we should probably reduce this by 5 points to 142 because I suspect many students inflated their scores by taking the SAT multiple times to get the best combination of scores (a procedure known as superscoring and it is by no means unique to Caltech)

The least selective colleges in America

The least selective colleges in America are no college at all or colleges that don’t require the SAT.  65% of all American late teens do not take the SAT, so the median non-SAT taker is in the bottom 33% of American late teens in college attended (or not attended).  Thus if there were a perfect correlation between IQ and college attended, non-SAT takers would have a mean IQ of 93 (U.S. norms).

What is the actual IQ of non-SAT takers?  We know that the average SAT score of the 2/3rd of U.S. late teens who take the SAT is about 1016 (IQ 106), and we know the average IQ of all U.S. teens is 100 (by definition), thus the 2/3rds who didn’t take the SAT must have a mean IQ (on the SAT) of 97.

Slope of standardized regression line

As mentioned above, if there were a perfect correlation between IQ and college attended, then Caltechies would have a median IQ of 161 and non-SAT takers would have a mean IQ of 93: A gap of 68 points.

But the actual IQs (as measured by the SAT) are 142 and 97 for Caltechies and non-SAT takers respectively (a gap of 45 points).

In a bivariate normal distribution (which this may not be), the slope of the standardized line of best fit in a scatter plot equals the correlation between X and Y.  As you’ll recall from grade 9 math, slope = rise/run.  Rise = increase along the Y axis, run = increase along the X axis.

In this case, the increase on the Y axis is estimated at 45 points (the actual IQ gap between Caltechies and non-SAT takers) and the increase on the X axis is 68 points (the theoretical IQ increase if the correlation were perfect).  Dividing 45 by 68 gives a slope of 0.66, or roughly 0.7, which is the same correlation as inferred from the analysis of variance performed earlier in this post.

Does correlating college attended with SAT overestimate the correlation between IQ and college attended?

The answer is yes.  Because colleges, especially competitive colleges, actively select students based on SATs, said students would regress precipitously to the mean on an IQ test not used to select them.  Assuming a 0.72 correlation between the SAT and the Wechsler intelligence scales, I’d expect the correlation between college attended and IQ to drop from 0.7 to 0.7(0.72) = 0.5 if a neutral IQ test were used.  Thus, where you went to college is only a very rough proxy for IQ, unless the IQ was measured by the SAT (or similar tests) in-which case it’s a somewhat strong proxy.