[NOTE: Pumpkin Person does not endorse the SAT (old or new), as a great measure of IQ, BUT, if one wants to express their old SATs on the IQ scale, here are simple ways of doing so]

I have previously cited a rare study showing that if all American young adults (in the early 1970s) had taken the old SAT (pre-1995), not just the college bound elite, the mean verbal score would have been 368 with an SD of 111, and the mean math score would have been 402 (SD = 112). Thus converting old SAT verbal and math scores into IQ equivalents (U.S. norms) was simply a matter of converting them to Z scores, then multiplying by 15 and adding 100.

So,

formula 1:

verbal IQ (U.S. norms) = [(verbal SAT – 368)/111] + 100

formula 2:

math IQ (U.S. norms) = [(math SAT – 402)/112] + 100

Now what happens if you want to convert the composite old SAT score (verbal + math) to IQ.  Well we know the mean score if all Americans had taken the test would have been about 770 (the mean verbal + the mean math), but we don’t know the standard deviation.

On page 779 of the book The Bell Curve by Herrnstein and Murray, they cite the formula for calculating the standard deviation of a composite score. r is the correlation between the two tests that make up the composite and σ is the standard deviation of the two tests.

Herrnstein and Murray also claim that for the entire SAT population, the correlation between SAT verbal and SAT math is 0.67.  Of course we’re interested in the correlation if ALL American young adults had taken the old SAT, not just the SAT population.  If they had, it’s possible the correlation would have been higher than 0.67 given less range restriction in the general population compared to the college bound population.  On the other hand, the college bound population had studied verbal and math skills more diligently during high school, thus perhaps inflating the correlation.  Assuming these two factors cancel out, and the correlation was probably the same for the college bound population as for the general population, then applying the above formula gives a general population combined standard deviation of 203.77.

So,

formula 3:

full-scale IQ (U.S. norms) = [(combined SAT) – 770)/203.77] + 100

This formula appears to give fairly good results, at least up to the mid 1550s.  For example, scholar Ron Hoeflin claimed that out of a bit over 5,000,000 high-school seniors who took the SAT from 1984 through 1988, only 1,282 had combined scores of 1540+.

Hoeflin has argued that even though only a third of U.S. teens took the SAT,  virtually 100% of teens capable of scoring extremely high on the SAT, did so, and whatever shortfall there might be was negated by bright foreign test-takers.

Thus, a score of 1540+ is not merely the 1,282 best among 5 million SAT takers, but among ALL fifteen million Americans who were 17 years-old anytime from 1984 through 1988.  In other words, 1540 was a one in 11,700 score, which on the normal curve, equates to an IQ of 157 (sigma 15).

Using formula 3, 1540 also equates to exactly IQ 157.

However above 1560, the formula seems to yield IQs that are too low, given their actual rarity.  This is because people who scored above 1560 typically hit the ceiling on the math section and approach the ceiling on the verbal, so people capable of scoring well above 1600 if the test had more hard items, tend to cluster in the high 1500s.