Steve Sailer asks:
Converting SAT scores into IQ scores: From the Boston Globe:To convert SAT scores from 1996 through this year to an IQ score, Professor Douglas Detterman of Case Western Reserve University provides this formula: (.095 X SAT Math) + (.003 X SAT Verbal) + 50.241 = IQ
For SAT scores before 1996 — before the “recentering,” which raised the average SAT back to 500 — Detterman provides this formula: (.126 X SAT Combined Score) – (.0000471 X SAT Combined Score X SAT Combined Score) + 40.063 = IQ. The first formula, Detterman says, was based on a highly selected sample and may not predict the full range of IQ as accurately as the second.
Unfortunately, neither of these formulas seems to make much sense. Why is the new formula almost wholly dependent on the Math score? And in the old formula, which is based more sensibly on the combined score, IQ doesn’t seem to go up fast enough as the SAT score rises.
Perhaps the newspaper fouled up the formulas. Does anybody know a better version?
The paper the article is referring to is 2003 Frey and Detterman paper, which we blogged on last year.
Much more inside:
Scholastic Assessment or g?The Relationship Between the Scholastic Assessment Test and General Cognitive Ability
There is little evidence showing the relationship between the Scholastic Assessment Test (SAT) and g (general intelligence). This research established the relationship between SAT and g, as well as the appropriateness of the SAT as a measure of g, and examined the SAT as a premorbid measure of intelligence. In Study 1, we used the National Longitudinal Survey of Youth 1979. Measures of g were extracted from the Armed Services Vocational Aptitude Battery and correlated with SAT scores of 917 participants. The resulting correlation was .82 (.86 corrected for nonlinearity). Study 2 investigated the correlation between revised and recentered SAT scores and scores on the Raven’s Advanced Progressive Matrices among 104 undergraduates. The resulting correlation was .483 (.72 corrected for restricted range). These studies indicate that the SAT is mainly a test of g. We provide equations for converting SAT scores to estimated IQs; such conversion could be useful for estimating premorbid IQ or conducting individual difference research with college students.
Here is the full text PDF version for those without an academic subscription.
A couple of things to note…
They look at two different measures of IQ. The first is from the Armed Services Vocational Aptitude Battery, selected from the National Longitudinal Study of Youth (yes, that NLSY). The second is vs. the Raven’s progressive matrices (RAPM) tests.
The fact that the RAPMs are designed to be nonverbal tests is probably why their second equation has such a low regression coefficient for the verbal component.
Overall, the Frey and Detterman study is really just an (important) special case of a known truth: all measures of human cognitive ability tend to strongly intercorrelate with each other. That’s the highly nontrivial and nonobvious fact at the core of the study of human (and, now, mouse) intelligence. Frey & Detterman’s contribution was in assessing the strength of the contribution – which is quite strong.
So – yes – the equations cited in the article are (surprisingly enough) the same as in the paper. I too had expected a misprint because the values for a 1600 seemed too low – giving only about 120 in their formula. But if you look at their data set, this is because they were sampling from the vast middle:
They obtain two equations via nonlinear regression, one for SAT vs. g-derived IQ and one for the SAT vs. Raven’s matrices-derived IQ scores. You can also use the fact that the linear correlation between SAT and g-derived IQ is .82 and use a simple linear regression equation, but that is less accurate than the nonlinear fit. You could write this equation if you knew the mean and standard deviation of the SAT scores in the first sample. Then you’d have:
(IQ – 100)/15 = .82 * (SAT – mean)/std
I would just use the mean (=1025) & standard dev data (=209) from the 2003 recentered scores, but I know that they are not one-for-one comparable with the older SATs. But having dug up this info, I thought it’d be of interest. Here is the 2003 homepage for the SAT. Here is the raw data for all SAT test takers in 2003, and here is a raw data text version suitable for analysis in R, Matlab, or what have you. Here’s a plot of the distribution of scores:
As you can see, it pretty well approximates a normal distribution – the difficulty is calibrated so that this happens.
Posted by godless at 04:43 PM