How do you figure? The word 'correlated' means that a relationship has been shown to be statistically _unlikely_ to have happened purely by chance. It can never be shown to be impossible however. And there can (and often are) subtle mistakes in the calculations that mean even the correlation isn't what one first thought.

And obviously statistics alone can never prove (or rule out)_ a causation, I think we agree there.

I haven't examined the research under discussion in detail enough to know if they controlled for all the things you suggest would be good to control for, etc., I have no idea.

But yeah, in the end we use our judgement as to what statistical correlations actually mean (such as a causation, and what sort through what mechanism). We can also do experiments or analysis to try and rule out (or confirm) other plausible alternate explanations. That's science, yep.

I think we mostly agree. I still object to what I think was an overly facile implication on your part that a few minutes of thinking of alternate explanations and deciding they are implausible -- on your own without seeing what other people's responses to the study in the literature have been, without an in depth analysis and consideration of the original research -- is sufficient to determine that there's "quite strong evidence" for correlation. That's not science.