Commenter Deeru asked me to convert GMAT scores to IQ equivalents.  This is always tricky because while IQ tests are normed on the general population of Western countries, college admission tests are normed on only the educated segment of a population, so converting from one type of norming to another requires some assumptions.

According to Wikipedia:

It’s ironic how they deny the GMAT is an intelligence test, while in the next sentence describing it is a test of “problem-solving abilities” because one of the most common definitions of intelligence is the (cognitive) ability to problem solve.  It’s clear that the people who make the GMAT are trying to have their cake and eat it too.  They want the predictive validity of an IQ type test, while at the same time, want to be seen as good liberals who don’t believe in IQ.

Of course any test that measures literacy and numeracy  will tend to correlate substantially with g (the general factor of all cognition, measured by IQ tests) whether the test manufacturers intended it to be an IQ test or not because symbolism itself (words and numbers) is a defining feature of the human intellect.

Here’s some basic GMAT data:

My first observation is that from about 300 to 700, GMAT scores are more or less normally distributed with a mean of 551.94 and a standard deviation (SD) of 120.88.

GMAT scores of 300 to 700

If we assume that the GMAT population is roughly equivalent to the U.S. college graduate population (mean IQ 111, SD = 13.5), compared to the general U.S. population (mean IQ 100, SD = 15), then the following formula equates GMAT scores to IQ equivalents (U.S. norms):

Formula one (for GMAT scores of 300 to 700):

IQ = [(GMAT score – 551.94)/120.88](13.5) + 111

GMAT scores of 700 to 800

However much like the pre-1995 SAT, GMAT scores seem to become much more rare than the Gaussian curve would predict at the highest levels (perhaps because of ceiling bumping or even Spearman’s Law of Diminishing Returns reducing the correlation between sub-sections).  For example, a score of 800 is 2.05 SD above the GMAT mean, which on a Gaussian curve, predicts one in 52 GMAT testees should score 800.  Instead Deeru claims only one in 6,667 scores this high!

But in order to map this to the IQ scale, we need to know how many people  would score 800 on the GMAT if all four million 22-year-old Americans took the GMAT every year (including college dropouts, high school dropouts etc).

I begin with the assumption that the higher you would score on a graduate school admission test, the more likely you are to actually take such a test (given the correlation between academic talent and education level). and so roughly 100% of U.S. 22-year-olds who would score perfect on a graduate school admission test, actually take such a test, and whatever shortfall there may be is roughly balanced by perfect scoring foreign-test takers, or test-takers from other age groups.

Thus people who score perfect on graduate school admission tests did not merely score higher than those who are applying to graduate school, but they scored higher than all 22-year-olds in America, if all 22-year-olds took these tests.

So if only 30 people a year score perfect on the GMAT, does that mean that only 30 of the four million 22-year-olds in America each year would score 800 on the GMAT?  No, because there are many genius 22-year-olds who would have scored 800 on the GMAT had they decided to major in business, but instead are busy acing the LSAT or the GRE or the MCAT etc.

Only 23.6% of advanced degrees are in business, thus I estimate that only 23.6% of people who write graduate school admission tests are writing the GMAT.  But if 100% of aspiring grad students wrote it, then the number scoring perfect each year should jump from 30 to 127.

So assuming roughly 100% of U.S. 22-year-olds who would have scored perfect on grad school admission tests actually take said tests (and whatever shortfall is roughly balanced by foreigners and other age groups), and assuming only 23.6% of said testees take the GMAT in particular, then:

if all four million U.S. 22-year-olds took the GMAT, only 127 would score 800, which means that an 800 is a one in 31,497 level score.  This equates to an IQ of 160 (U.S. norms).

So given that:

GMAT 800 = IQ 160

and given that 700 = IQ 128 (per formula one), then the following formula equates high GMAT scores to IQ (U.S. norms):

formula two (for GMAT scores 700 to 800):

IQ = 0.32(GMAT score) – 96

I do not consider the GMAT or any other college admission test to be a particularly good measure of intelligence, however when scores from actual IQ tests are not known, the above conversions are a useful proxy.

THEY SHOULD NOT HOWEVER BE USED TO ESTIMATE THE MEDIAN IQ OF ELITE BUSINESS SCHOOLS BECAUSE SUCH STUDENTS ARE SELECTED BASED ON GMAT SCORES WHICH MEANS GMAT PERFORMANCE IS NOT A RANDOM SAMPLE OF ELITE BUSINESS SCHOOL INTELLIGENCE. THIS SUBTLE CONCEPT HAS PROVEN EXTREMELY HARD FOR MANY READERS, BLOGGERS AND SCHOLARS TO GRASP!  YOU’RE EITHER HAVE A STATISTICALLY INTUITIVE BRAIN OR YOU DON’T.  IT’S GENETIC!