Null hypothesis significance testing (NHST) has several shortcomings that are likely contributing factors behind the widely debated replication crisis of psychology, cognitive neuroscience and biomedical science in general. We review these shortcomings and suggest that, after about 60 years of negative experience, NHST should no longer be the default, dominant statistical practice of all biomedical and psychological research. Different inferential methods (NHST, likelihood estimation, Bayesian methods, false-discovery rate control) may be most suitable for different types of research questions. Whenever researchers use NHST they should justify its use, and publish pre-study power calculations and effect sizes, including negative findings. Studies should optimally be pre-registered and raw data published. The current statistics lite educational approach for students that has sustained the widespread, spurious use of NHST should be phased out. Instead, we should encourage either more in-depth statistical training of more researchers and/or more widespread involvement of professional statisticians in all research.