The notion of a severe test has played an important methodological role in the history of science. But it has not until recently been analyzed in any detail. We develop a generally Bayesian analysis of the notion, compare it with Deborah Mayo’s error-statistical approach by way of sample diagnostic tests in the medical sciences, and consider various objections to both. At the core of our analysis is a distinction between evidence and confirmation or belief. These notions must be kept separate if mistakes are to be avoided; combined in the right way, they provide an adequate understanding of severity.