Also, it's extremely hard to account for all kinds of biases and systematic errors in a meta-analysis. I'd take most meta-analyses, even by renowned statiticians, very, very skeptically. Teasing out small effects from samples that need corrections for lots of confounding factors, and then trying do combine many such results is next to impossible.

If your effect is small enough that you need a meta-analysis in the first place, that's a warning sign.

Some background: https://journals.plos.org/plosone/article?id=10.1371/journal... (with perhaps more approachable explanation here https://www.talyarkoni.org/blog/2016/06/11/the-great-minds-j... )

Obviously it's sometimes possible to do this right, but the reproducibiility crisis didn't appear out of nowhere; it's best to be wary of overly clever statistics; hard to know what you don't know.