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JonahSinick comments on Innate Mathematical Ability - LessWrong
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Yes, the two are correlated. I'm surprised at not being able to find a really good reference, but doing linear regression on this dataset of SAT scores from a class of 162 high school seniors gives a correlation of 0.68 between math and verbal.
Wow. A correlation coefficient of 0.68 is... actually pretty highly correlated. That's much higher than I was expecting. (I thought the correlation would be at most 0.5 or so.)
What does an anticipated 0.5 correlation coefficient between two variables feel like?
I said at most 0.5, not exactly 0.5. The latter requires a level of predictive confidence that I don't have, so if you're asking what the latter feels like, then I don't know. If you're asking what the former feels like, it basically means I didn't expect the correlation to be more than, say, the correlation between someone's SAT scores and their ACT scores.
No, the correlation between SAT and ACT is higher than the correlation between SAT-M and SAT-V. Of course it is. You should be shocked if it isn't. The small correlation between SAT and ACT in that sample is due to restriction of range. If the same sample had been polled on component scores, the M-V correlation would have been even smaller. For a larger sample, the SAT-ACT correlation is 0.9 (p5/10) [and if that's a self-selected sample of people who took both, the correlation on the whole population is probably higher]. Also from that source, SAT-M correlates 0.9 with ACT-Math, though SAT-V only correlated 0.8 with ACT-Reading and ACT-English.
This book claims an M-V correlation of only 0.56, but I haven't determined what the sample was. (I find Jonah's 0.68 more plausible, but this seems like a better source.)
That makes sense. Thank you.