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Agreed - you see the same effect in the talent search pool.

The College Board says you need to see scores 60 points apart to be sure that you're really seeing a difference in ability, and not just measurement error.

I think I can explain some of the weirdness in scores on the math SAT.

According to a quick search, the SAT math section consists of 44 multiple choice questions, and 10 grid-ins. When you get a multiple choice question wrong, you lose points. When you get a question right, you gain points. When you don't answer a question, you fail to gain points. When you get a grid-in question wrong you don't lose points, but you fail to gain points.

If we look at the distributions for the top math scores from Val's link, we see that 770 and 740 are more popular scores than 760 and 730 respectively. This is most likely an indication that answering 1 multiple choice questions wrong results in a score of 770. Skipping 1 multiple choice question, or answering 1 grid-in question wrong probably results in a 780. I still haven't figured out how a score of 790 is possible, so my answer probably isn't entirely accurate. But following my logic, answering 2 multiple choice questions wrong probably results in a 740.

At any rate, I agree with Val's initial assertion that the SAT isn't a very good IQ test. I'm sure performance on the SAT correlates somewhat strongly with IQ, but I think it's measuring other things that are related, such as processing speed, accuracy (carefulness), focus and attention span, and retention. When I take an IQ test, I usually have to think. When I took the SAT, specifically the math part, I simply had to carefully regurgitate problem solving techniques I had been taught several years before. I also had the opportunity to take the SAT before I had been taught many of the appropriate problem solving techniques, and I didn't fair as well. It was quite evident to me in 7th grade (without any exposure to algebra or geometry) that the test wasn't measuring my intelligence by asking me geometry problems with vocabulary I'd never heard before.

Regarding the ceiling, I will say that it's lower than I would like. It would be nice for some of the people scoring perfect or nearly perfect to be able to differentiate themselves from some of the other people scoring perfect or nearly perfect. But I guess that's what SAT subject tests are for.

No, it's because different versions of the test have different scaled score results for the same raw score. http://media.collegeboard.com/digitalServices/pdf/SAT-RAW_Score_Scaled-Score_Ranges_2011.pdf

(You lose 1/4 of a point for each wrong answer on the multiple choice, but your score is rounded up in calculating the raw score. So getting 3 wrong produces the same raw score as leaving 3 blank, but getting 4 wrong produces the same raw score as leaving 5 blank.)

AlexsMom, did you link the right thing? I'm not seeing a lot of specifics, and nothing about the range between 720 and 800.

I linked to two different things - which one were you looking at?

There's nothing magic about that range. A given SAT raw score maps to multiple scaled scores, depending on the test version (if you're looking at the second link), and the weird score distribution is attributable to that.

If you're looking at the first link, scroll way down to the bottom, and look at the notes for Standard Error of the Difference.

On page 422 of The Bell Curve there is a table of SAT scores (actually derived from the PSAT) from national norm studies conducted by the ETS in various years. "The results are summarized in the table below, adjusted so as to represent the mean score that all American juniors would have received on the SAT had they stayed in school for their senior years and had they taken the SAT."

year verbal_mean math_mean
1955 348 417
1960 374 410
1966 383 395
1974 368 402
1983 376 411

The SAT has been normed to have average verbal and math scores of test-takers equal to 500, so at least through 1983 there was a large difference between the average SAT-taker and the general high school population. As the proportion of students taking the SAT has increased, this difference has shrunk, but I think it is still significant.

Here is some more recent evidence along the same lines.
Mean SAT scores by state along with participation rates are shown at http://www.commonwealthfoundation.org/policyblog/detail/sat-scores-by-state-2011 . Maine has the lowest average SAT score of 1391 for the three sections combined, because it uses the SAT as the high school NCLB test and therefore has a participation rate of 93%. On the NAEP, Maine is about average.

I wonder if he's heard of the Flynn Effect.

Yessss! Exactly that. Thank you.

IQ is measured relative to one's cohort. If people born in 2000 have higher raw scores on an IQ test administered in 2010 than people born in 1970 did on the same test in 1980, the IQ test will be re-normed to maintain a constant average IQ of 100. The Flynn effect is compatible with mean reversion of IQ.

Here is an analogy. People in 1980 were on average richer than in 1950, but there was still some mean reversion in income in the sense that not every child born into a richest (poorest) 10% household in 1950 belonged to a richest (poorest) 10% household in 1980.

The population consisting of (or closely representing) the offspring of the latest several generations of ancestors of the children sampled.