Might we get an even higher correlation if we tried to take into account the reproductive opportunity cost of raising a child of age X to independent maturity, while discarding all sunk costs to raise a child to age X?
I haven’t done the math, but my intuition says that upon observing the highest! correlation! ever!, surely our subjective probability must go towards a high true underlying correlation and having picked a sample with a particularly high correlation? (Conditioning on the paper not being wrong due to human error or fake, of course—I don’t suspect that particularly, but surely our subjective probability of that must go up too upon seeing the !!!.) If this is correct, it seems that we should expect to see a lower correlation for the modified design, even if the underlying effect is actually stronger.
(If I’m making a thinko somewhere there, please do tell… I hope to Know My Stuff about statistics someday, but I’m just not there yet :))
Do note that the correlation is, IIUC, between the mean Canadian rating for a given age and the mean reproductive value of female !Kung of a given age, meaning that “if the correlations were tested, the degrees of freedom would be (the number of ages) − 2 = 8, not (the number of subjects − 2) as is usually the case when testing correlations for significance”, so IIUC, we expect a large influence of random variation in the sample. (The authors don’t actually provide p-values for the correlations.) That’s not surprising, really; if the highest! correlation! ever! came from an experiment that did not allow for significant influence of random effects (because of really large sample size, say), that should make us suspicious, right? (Because if there were real effects that large, there should be other people investigating similarly large effects with statistically weaker methods, and thus occasionally getting even more extreme results?)
I haven’t done the math, but my intuition says that upon observing the highest! correlation! ever!, surely our subjective probability must go towards a high true underlying correlation and having picked a sample with a particularly high correlation? (Conditioning on the paper not being wrong due to human error or fake, of course—I don’t suspect that particularly, but surely our subjective probability of that must go up too upon seeing the !!!.) If this is correct, it seems that we should expect to see a lower correlation for the modified design, even if the underlying effect is actually stronger.
(If I’m making a thinko somewhere there, please do tell… I hope to Know My Stuff about statistics someday, but I’m just not there yet :))
Do note that the correlation is, IIUC, between the mean Canadian rating for a given age and the mean reproductive value of female !Kung of a given age, meaning that “if the correlations were tested, the degrees of freedom would be (the number of ages) − 2 = 8, not (the number of subjects − 2) as is usually the case when testing correlations for significance”, so IIUC, we expect a large influence of random variation in the sample. (The authors don’t actually provide p-values for the correlations.) That’s not surprising, really; if the highest! correlation! ever! came from an experiment that did not allow for significant influence of random effects (because of really large sample size, say), that should make us suspicious, right? (Because if there were real effects that large, there should be other people investigating similarly large effects with statistically weaker methods, and thus occasionally getting even more extreme results?)