Recently it has become clear that too many findings reported in the scientific literature are irreproducible. We study the causes of this phenomenon from a statistical perspective. Although a certain amount of irreproducible research is unavoidable due to the randomness inherent to scientific observation, two related phenomena conspire to increase the proportion of such findings: publication bias, i.e. the custom that negative findings are usually not published, and confirmation bias, i.e. the human inclination to interpret observations in a way that confirms prior beliefs. Both biases are poorly held in check in the current scientific publication model in which there is no explicit role for the views of a critic, i.e. a scientist with opposing theoretical views. We argue that if researchers are able to play the critic's role imaginatively, they will publish science of higher methodological quality that is not only more reproducible, but also more relevant for theory. To allow for this, we must promote a different view on statistical methodology, seeing statistics not as the gatekeeper of scientific evidence, but as a language scientists may use to discuss uncertainty when they talk about the implications of observations for theory.