[Doctor Stochastic]

Correct. That's the way things are supposed to proceed. As a rule of thumb, high correlation usually means that there is a causation, but the obvious one may not be correct (storks and babies.)

[Alamo-Girl]

Thank you for the explanations and the follow-up!

One example that pops into my mind is that statistics might show a high correlation of math abstraction aptitude among Chinese entering college in the U.S. But the cause might be the education system in China or its culture rather than genetic inheritance. I suspect that is the case with the classic WWII "German scientist", i.e. the education system or culture in Germany at the time might have been particularly fertile.