Research articles in the clinical and translational science literature commonly use quantitative data to inform evaluation of interventions, learn about the etiology of disease, or develop methods for diagnostic testing or risk prediction of future events. The peer review process must evaluate the methodology used therein, including use of quantitative statistical methods. In this manuscript, we provide guidance for peer reviewers tasked with assessing quantitative methodology, intended to complement guidelines and recommendations that exist for manuscript authors. We describe components of clinical and translational science research manuscripts that require assessment including study design and hypothesis evaluation, sampling and data acquisition, interventions (for studies that include an intervention), measurement of data, statistical analysis methods, presentation of the study results, and interpretation of the study results. For each component, we describe what reviewers should look for and assess; how reviewers should provide helpful comments for fixable errors or omissions; and how reviewers should communicate uncorrectable and irreparable errors. We then discuss the critical concepts of transparency and acceptance/revision guidelines when communicating with responsible journal editors.