Top journals in psychology routinely publish ridiculous, scientifically implausible claims, justified based on “p < 0.05.” And this in turn calls into question all sorts of more plausible, but not necessarily true, claims, that are supported by this same sort of evidence. To put it another way: we can all laugh at studies of ESP, or ovulation and voting, but what about MRI studies of political attitudes, or embodied cognition, or stereotype threat, or, for that matter, the latest potential cancer cure? If we can’t trust p-values, does experimental science involving human variation just have to start over? And what do we do in fields such as political science and economics, where preregistered replication can be difficult or impossible? Can Bayesian inference supply a solution? Maybe. These are not easy problems, but they’re important problems.