Peer review is widely considered fundamental to maintaining the rigour of science, but it often fails to ensure transparency and reduce bias in published papers, and this systematically weakens the quality of published inferences. In part, this is because many reviewers are unaware of important questions to ask with respect to the soundness of the design and analyses, and the presentation of the methods and results; also some reviewers may expect others to be responsible for these tasks. We therefore present a reviewers' checklist of ten questions that address these critical components. Checklists are commonly used by practitioners of other complex tasks, and we see great potential for the wider adoption of checklists for peer review, especially to reduce bias and facilitate transparency in published papers. We expect that such checklists will be well received by many reviewers.