Annotated Bibliography of Some Papers on Combining Significances or p-values

TL;DR

This paper reviews key literature on combining significance levels or p-values from multiple experiments, highlighting how different assumptions influence the preferred methods.

Contribution

It provides a curated list of influential papers on combining significances, with comments and excerpts, clarifying the impact of assumptions on method choice.

Findings

Different assumptions lead to different combining methods

The paper summarizes prominent approaches in the literature

It clarifies the importance of context in combining p-values

Abstract

A question that comes up repeatedly is how to combine the results of two experiments if all that is known is that one experiment had a n-sigma effect and another experiment had a m-sigma effect. This question is not well-posed: depending on what additional assumptions are made, the preferred answer is different. The note lists some of the more prominent papers on the topic, with some brief comments and excerpts.