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I recently indulged in a little smack-talk about how Math majors have higher SAT verbal scores than English majors, but now it's bothering me that I don't even know what the correlation is between SAT math and verbal scores ... and I'm not even sure how to find out! Google searches and AI summaries seem to be so polluted with stat questions about correlations in hypothetical SAT results that I can't quickly find anything with results for the correlation in actual SAT results. Even the College Board's annual report, which is at least statistically literate enough to define and report standard deviations for each subtest, doesn't report the correlation between subtests. They have other reports of correlations between paper and digital SATs, between SAT results and future college grades... They'll even report separate correlations of subtest scores with other tests and with HS GPA without mentioning the subtests' correlation with each other!
Well wait I do find this: A report from Connecticut estimates a 0.89-0.9 correlation based on an observed 0.82-0.85 correlation. N=1,343 but I'll take it. Then with the bivariate normal distribution CDF from Octave/Matlab, I ask for
0.1-bvncdf([norminv(0.1, 0, 1) -norminv(0.1, 0, 1)], [0 0], [1 0.9; 0.9 1]), which is ... 1.5e-10? About one person in seven billion? (as opposed to the one person in a hundred we'd get if there was no correlation). If I go with that 0.82 correlation I still only get one person in 2 million, so that kind of test score would probably be a thing that's happened before, but only because the kid was having a lucky day with math and bad luck with reading simultaneously, not because you'd expect to see a score like that again on a retest.Of course SAT scores aren't actually a Gaussian distribution, but I think that thought experiment still strongly suggests you're right, and anyway there's no way we're finding data with higher moments. Even if we got our hands on raw data, I'd bet that a kid with 650+ math and sub-380 reading is much more likely to be a recent immigrant who's still struggling with English, not someone who's actually got poor verbal reasoning skills in general.
Among a more range-restricted sample set, and likely even more affected by the low-quant ceiling and high-quant low-verbal foreign test-takers than the SAT, the GRE still reports a Quant-Verbal correlation of 0.45.
Not only among this sample is the Quant-Verbal correlation not distinctly negative as would be wish-casted by those who propose a tradeoff between supposed various intelligences—it's Noticeably positive, despite the wishes of those who hope there are multiple intelligences and that stat-points are equally distributed across intelligences. For many Westerners, especially Americans, there are some headwinds to admitting that some people are smarter than others, much less that some groups of people are smarter, on average, than other groups of people.
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Available in the technical manual appendix:
https://satsuite.collegeboard.org/media/pdf/sat-suite-assessments-technical-manual-appendix-pt-1.pdf
Page 136, Table A-6.9.1.
Found via Gemini. Interestingly, I'm told it drops significantly for students who attend elite schools, to around 0.6, due to restriction of range effects.
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