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Meta-analysis, the statistical analysis of results from separate studies, is a fundamental building block of science. But the assumptions of classical meta-analysis models are not satisfied whenever publication bias is present, which causes inconsistent parameter estimates. Hedges' selection function model takes publication bias into account, but estimating and inferring with this model is tough for some datasets. Using a generalized Gleser-Hwang theorem, we show there is no confidence set of guaranteed finite diameter for the parameters of Hedges' selection model. This result provides a partial explanation for why inference with Hedges' selection model is fraught with difficulties., Comment: 12 pages

Publication bias and p-hacking are two well-known phenomena that strongly affect the scientific literature and cause severe problems in meta-analyses. Due to these phenomena, the assumptions of meta-analyses are seriously violated and the results of the studies cannot be trusted. While publication bias is almost perfectly captured by the weighting function selection model, p-hacking is much harder to model and no definitive solution has been found yet. In this paper we propose to model both publication bias and p-hacking with selection models. We derive some properties for these models, and we compare them formally and through simulations. Finally, two real data examples are used to show how the models work in practice., Comment: 21 pager, 6 figures

I present a frequentist method for quantifying uncertainty when correcting correlations for attenuation due to measurement error. The method is conservative but has far better coverage properties than the methods currently used when sample sizes are small. I recommend the use of confidence curves in favor of confidence intervals when this method is used. I introduce the R package "attenuation" which can be used to calculate and visualize the methods described in this paper., Comment: 9 pages, 2 figures