Beyond Bonferroni: Hierarchical Multiple Testing in Empirical Research

This paper offers a general, practical review of methods for dealing with multiple hypothesis testing, aimed at applied researchers who must draw inference on multiple outcomes, subgroups, or model specifications but often lack clear guidance on how to proceed. We distill key lessons from the methodological literature, explain why several common practices are flawed, and clarify the guarantees provided by alternative approaches. Beyond standard corrections such as Bonferroni, Holm, and false discovery rate controls, we emphasize the value of hierarchical procedures that exploit causal or logical structure to deliver more powerful and interpretable results. By linking these tools to real applications, we translate methodological advances into accessible guidance and provide researchers with a clear roadmap for producing credible, transparent, and policy-relevant empirical work.