Ioannidis 2005 states that, for a study with two groups (one control, one experiment), N = 2000, and true odds ratio of 1.1, the median observed odds ratio will be 1.23 among studies reaching significance ($p \leq .05$).
I'm trying to reproduce this result. I think I want to do something like:
Where $p(t)$ expresses the probability of an odds ratio of $t$. Then I would solve for $x$ and find that it's 1.23.
But I worry that this is overly simplistic, and even if it's not I'm not certain what to put in for $p(t)$. I could assume $\sim N(0,1)$, but I'm not sure if that's correct.