On SAT, ACT, IQ, and other psychometric test correlations

Although I touched on this topic briefly before, I seem to have forgotten some relevant plots and data and don’t feel like editing the last one, so this post is somewhat redundant…

Both the SAT and ACT are quite well correlated with IQ tests, so much so that you can make good guesses about someone’s IQ if you know their SAT/ACT score and vice versa.

sat_composite_by_asvab_iq

asvab_by_sat

satv_by_asvab satm_by_asvab


The SAT – ASVAB correlation is quite strong and it is probably weakened by range restriction effects.  People with lower IQ scores and/or lower HS GPA are much less likely to sit for the SAT.   If the SAT is significantly influenced by the degree to which people actually apply themselves in school (almost surely to some degree) and IQ is only weakly correlated with conscientiousness and related characteristics, both will tend to significantly reduce the apparent strength of the correlation


act_prob_by_hsgpa sat_prob_by_hsgpa act_prob_by_iq sat_prob_by_iq

sat_prob_by_aidx

act_prob_by_aidx


sat_by_aca_idx


splom_sat_misc

test_correlations_by_year


The ASVAB/AFQT is effectively an IQ test and it is certainly well correlated with “official” IQ tests like Wechsler Adult Intelligence Scale (WAIS) and Stanford-Binet.

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Given the strength of the correlation between ASVAB and SAT/ACT and similarities in design, the correlations between these “aptitude” tests and WAIS or Stanford-Binet are probably very similar, especially without range restriction effects and without these tests being spaced apart by several years in some cases (consider that the ASVAB-SAT r=0.85 whereas PSAT-SAT r=0.90…. pretty close).  Of course, there is not one true “IQ test” and different tests have different strengths and weaknesses.

Other people have studied this question using NLSY79 (the older NLSY study) and compared to other psychometric tests too.

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Of course, just because these tests are well correlated in general does not mean that one cannot make incrementally better predictions with additional information or, at least, adjust the confidence level accordingly.  It seems to me that people that “slack off” in school, as determined to lousy GPAs despite high IQ, are significantly less likely to earn SAT scores commensurate with their intelligence (especially at the upper ability levels).

sat_by_q_grouped_by_hsgpa_tercile

That’s not to say that that makes the SAT a worse predictor for admissions purposes though!

Likewise, there are some modest differences by the student’s father’s education level:

Or by parents income level (1997)

sat_by_q_grouped_by_pincome_b4

(which doesn’t necessarily means these tests are biased as there are also average differences in GPA controlling for IQ, not to mention regression to the mean, etc)

hsgpa_by_iq_grouped_by_income

gpa_by_iq_grouped_fed

(and, in practical terms, the higher SES GPA usually means more due to more higher average grading standards and larger average course loads)

Notes:

  • I used the NLSY97 dataset, which provides test scores and a lot of other information at an individual level for a (mostly) nationally representative cohort of people born between 1980 and 1984, for this analysis.   I converted the ASVAB score percentiles to IQ scores whereby 50th percentile = 100 IQ, SD = 15.  NLSY97 oversampled some lower-IQ groups, but the percentiles were set according to national norms (which is somewhat lower than the white or the asian means in this and other data)..
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6 thoughts on “On SAT, ACT, IQ, and other psychometric test correlations

  1. On the other thread, you linked me to the GCSE study that showed that variation in scores can be attributed as follows: 62% genetics, 26% shared environment, 12% nonshared environment. This seems to be broadly consistent with the education research that I have seen, such as the Coleman Report. It seems that the results are usually that the socioeconomic status of the student matters the most, the socioeconomic status of the peers matters second most, and teachers matter third most. Beyond that, there seem to be few factors that make a big difference. It’s very much possible to me that the socioeconomic status of the student is partially a proxy for parenting and culture, and I see relatively little that policy can do to change that. On the second one, Richard Kahlenberg has done substantial work showing that integrating schools by class helps the disadvantaged children by ensuring that the majority of kids are focused on learning. http://www.aft.org/sites/default/files/periodicals/Kahlenberg.pdf He also shows that it has no effect on the middle class kids if the disadvantaged kids are below a certain level. I imagine you probably disagree with this research. If so, could you explain why? As for the third factor, I think the Chetty value added model is pretty convincing. We can debate endlessly how to get good teachers, but I know that the research shows that poorer kids usually get the worst teachers. If you integrated the schools, that problem would be addressed.

  2. You argue repeatedly that the socioeconomic benefit is primarily (or perhaps exclusively?) through parental education. Can you explain the mechanism for this? Is it just the best proxy for culture (how the child is raised)? It must be more than genetics because this relationship exists even after controlling for test scores.

    • I should have mentioned, Coyle’s extraction of the g factor using SEM was from the ASVAB subtest scores of those in the NSLY97.

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