Null hypothesis significance testing (NHST) is linked to several shortcomings that are likely contributing factors behind the widely debated replication crisis in psychology and biomedical sciences. In this article, Denes Szucs and John P. A. Ioannidis review these shortcomings and suggest that NHST should no longer be the default, dominant statistical practice of all biomedical and psychological research. If theoretical predictions are weak, scientists should not rely on all or nothing hypothesis tests. When NHST is used, its use should be justified, and pre-study power calculations and effect sizes, including negative findings should be published. The authors ask for hypothesis-testing studies being pre-registered and, optimally, all raw data being published. Scientists should be focusing on estimating the magnitude of effects and the uncertainty associated with those estimates, rather than testing null hypotheses.