The “New Statistics” emphasizes effect sizes, confidence intervals, meta-analysis, and the use of Open Science practices. We present three specific ways in which a New Statistics approach can help improve scientific practice: by reducing overconfidence in small samples, by reducing confirmation bias, and by fostering more cautious judgments of consistency. We illustrate these points through consideration of the literature on oxytocin and human trust, a research area that typifies some of the endemic problems that arise with poor statistical practice.