In a blog post, I have found the claim that
"I believe WG Cochrane the first point out (roughly 1970′s) that with confidence intervals in an observational setting, small sample sizes result in better coverage with large enough samples providing near zero coverage!"
Now I assume that the CI width should approach 0 with increasing sample size, but the idea that coverage would concurrently worsen is not convincing to me. Is this claim true, and under which circumstances? Or am I misreading it?
I've run a simulation using random normally distributed data with sample sizes from 10000 to 1000000 (one-sample t-test, 95% CI), 1000 runs at every sample size, and coverage did not get any worse for the higher sample sizes (instead, I found the expected near-constant ~5% error rate).