When More Is Less: Pitfalls of significance testing

Abstract: The controversy about statistical significance vs. scientific relevance is more than 100 years old. But still nowadays null hypothesis significance testing is considered as gold standard in many empirical fields from economics and social sciences over psychology to medicine, and small $p$-values are often the key to publish in journals of high scientific reputation. I highlight, illustrate and discuss potential pitfalls of statistical significance testing on three occasions.