Just checking, but verbal and mathematical reasoning skills are positively correlated, right? This assertion seems to be supported by the fact that many (I’d go so far as to say nearly all) LW users have high verbal intelligence (as evidenced by the general quality of the comments here) and most of them seem to have high mathematical intelligence as well (as evidenced by the many posts on decision theory, game theory, and other fields of mathematics). If the two are correlated, do you know the coefficient of correlation?
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.)
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.)
One reference that also comes to mind is this box from Deary 2001. If we assume “verbal intelligence” to correspond to the “verbal comprehension” group factor in the diagram, and “mathematical reasoning” to correspond to its “perceptual organization” factor (since perceptual organization’s associated subtests of picture completion, block design, matrix reasoning, and picture arrangement sound the most similar to Raven’s matrices; though “arithmetic” is in the working memory factor) then if I’m thinking about this correct, those two group factors would share 65% (100 0.86^2 0.94^2) of their variance.
Just checking, but verbal and mathematical reasoning skills are positively correlated, right? This assertion seems to be supported by the fact that many (I’d go so far as to say nearly all) LW users have high verbal intelligence (as evidenced by the general quality of the comments here) and most of them seem to have high mathematical intelligence as well (as evidenced by the many posts on decision theory, game theory, and other fields of mathematics). If the two are correlated, do you know the coefficient of correlation?
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.
One reference that also comes to mind is this box from Deary 2001. If we assume “verbal intelligence” to correspond to the “verbal comprehension” group factor in the diagram, and “mathematical reasoning” to correspond to its “perceptual organization” factor (since perceptual organization’s associated subtests of picture completion, block design, matrix reasoning, and picture arrangement sound the most similar to Raven’s matrices; though “arithmetic” is in the working memory factor) then if I’m thinking about this correct, those two group factors would share 65% (100 0.86^2 0.94^2) of their variance.