so your probability exercise was pretty pointless because you didn’t compare the studies’ opinions about any particular effect size
My probability exercise was not about effect size. It was about the probability of all studies agreeing by chance if there is in fact no link, and so the 95% confidence is what is relevant.
Third, I’d bet a nickel the effect sizes ruled out at 95% in all of these studies are well below the point where it would become concerning (like, say, the effect of the parents being a year older). That is, these studies all likely rule out a concerning effect size with probability much better than 95%.
Not relevant to the main point that you’re making, but relevant to your parenthetical:
(I was, as usual, irked that if a study failed to prove the existence of a link given various assumptions, it was usually cited as having shown that there was no link.)
My probability exercise was not about effect size. It was about the probability of all studies agreeing by chance if there is in fact no link, and so the 95% confidence is what is relevant.
Again, not relevant to the point I’m making here.
Not relevant to the main point that you’re making, but relevant to your parenthetical: