The SAT is normally taken by the most academically successful third of U.S. 17-year-olds. The two thirds of American teens who don’t take the SAT have either dropped out of high school long before the SAT is given, or they have no plans to go to a selective college.
However in order to convert SAT scores to IQ equivalents, it helps to know how all American teens would do on the SAT if they took it.
In a series of rare little-known studies, the college board gave a short version of the SAT to a representative sample of all American high school juniors and then statistically adjusted the scores to predict how the would have done at 17 (I think). They could have just waited until they were 17, but by then a lot of them would have dropped out of high school, and thus could not be tested.
Here are the results from 1974 (remember, the SAT got a lot easier in April 1995):
One of the first thing we notice is that the distribution is not perfectly Gaussian at the extremes. For example a verbal score of 650 is at the 99 percentile which on a normal curve, is 2.33 standard deviations (SD) above the mean (IQ 135; U.S. norms), but according to the actual mean and standard deviation (368 and 111 respectively), it’s 2.54 standard deviations above the mean (IQ 138). That may sound like a trivial difference but it occurs on the math section too. The normal curve says a math score of 700 (99 percentile) would be 2.33 standard deviations above the mean (IQ 135) but the actual mean and standard deviation put 700 at +2.66 SD (IQ 140). These differences add up in the composite score.
I suspect this departure from the normal curve is because some kids attend schools that better prepare them for the SAT than others.
Of course at the very, very high end of the SAT you get the opposite problem. The normal curve under-predicts how rare scores are. I suspect this happens because normally on the SAT, if you fail an item that is beneath you, you can recover by solving at item that is above your head. But when there are no items that are above your head, you can’t compensate for silly mistakes with lucky guesses, making perfect scores especially rare.
Pumpkin Person 
perfect scores post ’95 aren’t that rare as it’s possible to miss a few and still make a perfect scaled score.
a perfect 1600 was very rare prior to ’95…like no more than 2 people per administration.
so in terms of the difficulty of the test and the level of selection (of test takers), my GRE verbal of 800 is my most outstanding test score…even though iirc one could miss 4 and still get an 800.
It should match up to these, for both to be correct;
http://www.iqcomparisonsite.com/iqtable.aspx
http://www.iqcomparisonsite.com/SATIQ.aspx
According to this, a mathematical score of 650 (multiplied by two for conversion on his chart) would mean a Score of 1300 would give a 133 Stanford-Binet* score, which is in the 98th percentile! This confirms Jara’s numbers.
*http://www.iqcomparisonsite.com/GREIQ.aspx
You can’t just multiply by two because the correlation between math and verbal isn’t perfect. Someone in the top 1% in both would be above the top 0.5% in the composite
Just estimating 🙂
I never considered that getting 98th percentile, for example in both Verbal and Mathematics and sections would yield a composite ABOVE the 98th percentile. I guess that fewer people would do well in BOTH sections? That is very fascinating indeed.
Or of course as you put it, the 99th percentile in both would yield 99.5th percentile for composite.
I have a math question: can you add up the standard deviation of each section to get the standard deviation of the total, or would it be less because there is a correlation between the sections?
Intuition tells me that it would be less, but whenever I see the actual data from the sat for example, it seems very close to what you would expect adding them up,
Intuition tells me that it would be less,
Your intuition is right
but whenever I see the actual data from the sat for example, it seems very close to what you would expect adding them up,
Either the correlation between the two subtests is very high, and/or the test score distribution is not very Gaussian, making the standard deviation misleading.
https://www.google.com/?gws_rd=ssl#q=Correlation+strength+between+Math+and+Critical+Reading+SAT+scores&start=0
Fourth link, from an google book
“the correlation(between Math and Critical Reading) is not given but is known to be quite high”…..
To test how posting works
My impression is that larger fractions of high school students are taking the SAT and ACT in recent years.
Steve, great to hear from you!
On page 691 of The Bell Curve they note that in 1952, only 6.8% of high school grads took the SAT, but by 1963, the percentage increased to 47.9%..
On page 184 of his book Real Education Charles Murray notes that 47% of (U.S.) high school grads and 35% of all (U.S) 17-year-olds took the SAT in 2005.
Of course these figures are hard to interpret without knowing what percentage were taking the ACT in these years and what percentage graduated from high school in 1952 and 1963.