This should be straightforwardly testable by standard statistics
Agreed.
That may require prohibitively large sample sizes, i.e. not be testable.
With regards to measuring g, and high IQs, you need to keep in mind regression towards the mean, which becomes fairly huge at the high range, even for fairly strongly correlated variables.
Other more subtle issue is that proxies generally fare even worse far from the mean than you’d expect from regression alone. I.e. if you use grip strength as a proxy for how quick someone runs a mile, that’ll obviously work great for your average person, but at the very high range—professional athletes—you could obtain negative correlation because athletes with super strong grip—weightlifters maybe? - aren’t very good runners, and very good runners do not have extreme grip strength. It’s not very surprising that folks like Chris Langan are at very best mediocre crackpots rather than super-Einsteins.
That may require prohibitively large sample sizes, i.e. not be testable.
At least for certain populations the sample sizes should be pretty large. Also a smaller-than-desired sample size doesn’t mean it’s not testable, all it means is that your confidence in the outcome will be lower.
proxies generally fare even worse far from the mean than you’d expect from regression alone
Yes, I agree. The tails are a problem in general, estimation in the tails gets very fuzzy very quickly.
Yes, I agree. The tails are a problem in general, estimation in the tails gets very fuzzy very quickly.
And it seems to me that having studied math complete with boring exercises could help with understanding of that somewhat… all too often you see people not even ballpark by just how much necessary application of regression towards the mean affects the rarity.
That may require prohibitively large sample sizes, i.e. not be testable.
With regards to measuring g, and high IQs, you need to keep in mind regression towards the mean, which becomes fairly huge at the high range, even for fairly strongly correlated variables.
Other more subtle issue is that proxies generally fare even worse far from the mean than you’d expect from regression alone. I.e. if you use grip strength as a proxy for how quick someone runs a mile, that’ll obviously work great for your average person, but at the very high range—professional athletes—you could obtain negative correlation because athletes with super strong grip—weightlifters maybe? - aren’t very good runners, and very good runners do not have extreme grip strength. It’s not very surprising that folks like Chris Langan are at very best mediocre crackpots rather than super-Einsteins.
At least for certain populations the sample sizes should be pretty large. Also a smaller-than-desired sample size doesn’t mean it’s not testable, all it means is that your confidence in the outcome will be lower.
Yes, I agree. The tails are a problem in general, estimation in the tails gets very fuzzy very quickly.
And it seems to me that having studied math complete with boring exercises could help with understanding of that somewhat… all too often you see people not even ballpark by just how much necessary application of regression towards the mean affects the rarity.