(This is getting into the weeds enough that I can’t address the points very quickly anymore, they’d require longer responses, but I’m leaving a minor note about this part:
Suppose every 4th of July, you go camping at one particular spot that does not have a lake. Then we observe that July 4th correlates with camping but does not correlate with swimming (or even negatively correlates with swimming).
For purposes of causality, negative correlation is the same as positive. The only distinction we care about, there, is zero or nonzero correlation.)
For purposes of causality, negative correlation is the same as positive. The only distinction we care about, there, is zero or nonzero correlation.)
That makes sense. I was wrong to emphasize the “even negatively”, and should instead stick to something like “slightly negatively”. You have to care about large vs. small correlations or else you’ll never get started doing any inference (no correlations are ever exactly 0).
(This is getting into the weeds enough that I can’t address the points very quickly anymore, they’d require longer responses, but I’m leaving a minor note about this part:
For purposes of causality, negative correlation is the same as positive. The only distinction we care about, there, is zero or nonzero correlation.)
That makes sense. I was wrong to emphasize the “even negatively”, and should instead stick to something like “slightly negatively”. You have to care about large vs. small correlations or else you’ll never get started doing any inference (no correlations are ever exactly 0).