The objections which have been made to testing statistical null hypotheses as the means of analysing the results of psychological research are assembled. None of these criticisms is by itself new, and none is controversial. Together, however, these criticisms demand a fundamental change in the way we analyse the results of psychological research and the way in which we teach students to analyse data. In order to cumulate a reliable body of knowledge, psychologists should dispense with statistical hypothesis testing and instead use empirical replication as the test of reliability, and should report effect size measures together with an indication of their likely error.