Medical research makes intensive use of statistics in order to support its claims. In this paper we make explicit an epistemological tension between the conduct of clinical trials and their interpretation: statistical evidence is sometimes discarded on the basis of an (often) underlined Bayesian reasoning. We suggest that acknowledging the potentiality of Bayesian statistics might contribute to clarify and improve comprehension of medical research. Nevertheless, despite Bayesianism may provide a better account for scientific inference with respect to the standard frequentist approach, Bayesian statistics is rarely adopted in clinical research. The main reason lies in the supposed subjective elements characterizing this perspective. Hence, we discuss this objection presenting the so-called Reference analysis, a formal method which has been developed in the context of objective Bayesian statistics in order to define priors which have a minimal or null impact on posterior probabilities. Furthermore, according to this method only available data are relevant sources of information, so that it resists the most common criticisms against Bayesianism.