What to do when your estimate is 1 standard error away from 0?

We provide a new answer to this simple yet very important question. Thinking clearly about this problem leads us to bring in many ideas in statistical analysis and computing, including causal identification, meta-analysis, Mister P, expectation propagation, decision analysis, experimental design, and the fundamental unity of Bayesian and frequentist statistics. We demonstrate our approach in examples from many applications, including medicine, social science, business, sports, and public policy.

This work is joint with Witold Więcek and Erik van Zwet.