I apologize to my readers for recycling so much old material, but certain crucial issues must be resolved before we can move forward knowledgeably.
In this post, I summarize all I have learned to date about how much high SAT performers regress to the mean when faced with official IQ tests and what this implies about the SAT’s correlation with said tests. Some of the data may contradict previous posts, as new information has come to light, causing me to revise old numbers.
Study I: New SAT vs the Raven
A study by Meredith C. Frey and Douglas K. Detterman found a 0.48 correlation between the re-centered SAT and the Raven Progressive Matrices in a sample of 104 university undergrads, but after correcting for range restriction, they estimate the correlation to be 0.72 in a less restricted sample of college students. I don’t buy it, but I’m not interested in how well the re-centred SAT would correlate with the Raven among college students, but among ALL American young adults. (including the majority who never took the SAT).
Using the Frey and Detterman data, I decided to look at the Raven scores of those who scored 1400-1600 on the re-centred SAT, because 1500 on the new SAT (reading + math) corresponds to an IQ of 143 (U.S. white norms), which is 46 points above the U.S. mean of 97. Now if the new SAT correlated 0.72 or higher among ALL American adults, we’d expect their Raven scores to only regress to no less than 72% as far above the U.S. mean, so 0.72(46) + 97 = IQ 130.
I personally looked at the scatter plot carefully and did my best to write down the RAPM IQs of every single participant with an SAT score from 1400-1600. This was an admittedly subjective and imprecise exercise given how small the graph is, but I counted 38 top SAT performers and these were their approximate RAPM IQs: 95, 102, 105, 108, 108, 110, 110, 113, 113, 113, 113, 113, 117, 117, 117, 117, 117, 120, 120, 120, 122, 122, 128, 128, 128, 128, 134, 134, 134, 134, 134, 134, 134, 134, 134, 134, 134, 134
The median IQ is 120, and it does not need to be converted to white norms because the Raven was normed in lily white Iowa circa 1993, but as commenter Tenn noted, I should have perhaps corrected for the Flynn effect since the norms were ten years old at the time of the study. Correcting for the Flynn effect reduces the median to 118 (U.S. white norms) which is 21 points above the U.S. mean of 97.
For people who are 46 IQ points above the U.S. mean on the new SAT to regress to only 21 points above the U.S. mean, suggests the new SAT correlates 21/46 = 0.46 with the Raven in the general U.S. population.
Study II: New SAT vs the abbreviated WAIS-R
Harvard is the most prestigious university in the World with an average SAT score in the stratosphere, thus it’s interesting to ask how Harvard students perform on an official IQ test. The best data on the subject was obtained by Harvard scholar Shelley H Carson and her colleagues who had an abbreviated version of the WAIS-R given to 86 “Harvard undergraduates (33 men, 53 women), with a mean age of 20.7 years (SD 3.3)… All were recruited from sign-up sheets posted on campus. Participants were paid an hourly rate…The mean IQ of the sample was 128.1 points (SD 10.3), with a range of 97 to 148 points.”
It should be noted however that the WAIS-R was published in 1981, and that the norms were collected from 1976 to 1980. Carson’s study was published in 2003, so presumably the test norms were 25 years old.
James Flynn cites data showing that from WAIS-R norms (circa 1978) to WAIS-IV norms (circa 2006) the vocabulary and spatial construction subtest (used in the abbreviated WAIS-R) increased by 0.53 SD and 0.33 SD respectively. These gains would result in the composite score of the abbreviated WAIS-R becoming obsolete at a rate of 0.26 IQ points per year, meaning the Harvard students’ scores circa 2003 were 6.5 points too high. This reduces the mean IQ of the sample to 121.6 (U.S. norms) which is about 120 (U.S. white norms); 23 points above the U.S. mean of 97 (white norms).
However Harvard’s median re-centered SATs of 1490 equate to IQ 143 (U.S. white norms) which is 46 points above the U.S. mean of 97. Assuming the sampled Harvard students were cognitively representative of Harvard and assuming Harvard is cognitively representative of all 1490 SAT Americans, the fact they regressed from being 46 IQ points above average on the SAT to 23 IQ points above average on the abbreviated WAIS-R, suggests the re-centered SAT correlates 23/46 = 0.5 with the abbreviated WAIS-R.
Study III: Old SAT vs the full original WAIS
Perhaps the single best study was referred to me by a commenter named Andrew. In this study, data was taken from the older more difficult SAT, and participants took the full-original WAIS. In this study, six samples of seniors from the extremely prestigious Dartmouth (the 12th most selective university in America) averaged 1357 on the SAT just before 1974. Based on my latest research, an SAT score of 1357 circa 1974 would have equated to an IQ of 144 (U.S. norms); 143 (U.S. white norms). Because this is much higher than previously thought; the degree of regression is quite devastating.
Assuming these students are typical of high SAT Americans, it is interesting to ask how much they regress to the mean on various subtests of the WAIS.
Averaging all six samples together, and then adjusting for the yearly Flynn effect from the 1950s through the 1970s (see page 240 of Are We Getting Smarter?) since the WAIS was normed circa 1953.5 but the students were tested circa 1971.5, then converting subtest scaled scores to IQ equivalents, in both U.S. norms and U.S. white norms (the 1953.5 norming of the WAIS included only whites), we get the following:
|iq equivalent (u.s. norms)||iq equivalent (u.s. white norms)||estimated correlation with sat in the general u.s. population inferred from regression to the mean from SAT IQ 44 points above U.S. mean.|
|sat score||144||143||44/44 = 1.0|
|wais information||128.29||127.2||28.29/44 = 0.64|
|wais comprehension||122.22||120.9||22.22/44 = 0.51|
|wais arithmetic||120.37||119||20.37/44 = 0.46|
|wais similarities||119.16||117.75||19.16/44 = 0.44|
|wais digit span||117.37||115.9||17.37/44 = 0.39|
|wais vocabulary||125.93||124.75||25.93/44 = 0.59|
|wais picture completion||105.87||104||5.87/44 = 0.13|
|wais block design||121.82||120.5||21.82/44 = 0.50|
|wais picture arrangement||108.33||106.55||8.33/44 = 0.19|
|wais object assembly||113.65||112.05||13.65/44 = 0.31|
|wais verbal scale||126||125||26/44 = 0.59|
|wais performance scale||116||114||16/44 = 0.36|
|wais full-scale||123||122||23/44 = 0.52|
In three different studies (New SAT vs Raven, New SAT vs abbreviated WAIS-R, Old SAT vs WAIS), people averaging exceptionally high SAT scores averaged only 46%, 50%, or 52%, respectively, as far above the U.S. mean on the official IQ tests as they did on the SAT, suggesting the SAT (old or new), only correlates about 0.5 with official IQ tests. Correlations in the range of 0.5 are about all you’d expect most educational measures (school grades, years of school) to correlate with IQ, but it’s a surprisingly low correlation given that some consider the SAT to be more than a mere education measure, but an IQ test itself. So either the SAT is NOT equivalent to an IQ test, or it’s only equivalent to an IQ test among people with similar educational backgrounds, or my method of inferring correlations from the degree of regression is giving misleading results (perhaps because Spearman’s Law of Diminishing Returns is flattening the regression slope at high levels or because of ceiling bumping on the tests involved).
The potentially low correlation between the SAT (and presumably other college admission tests like the GRE, LSAT, etc) with official IQ has some positive implications. It means that to whatever extent IQ and success are correlated in America, the correlation is a natural consequence of smart people adapting to their environment, and not the artificial self-fulfilling prophecy of a man-made testocracy.
It also suggests that there’s no substitute for a real IQ test given by a real psychologist with blocks, cartoon pictures, jig-saw puzzles, and open-ended questions. I can see David Wechsler, chuckling from the grave, saying “I told you so.”