The mandated public availability of individual hospital’s audit data for children’s heart surgery in the UK creates a challenging scenario for communicating these complex and sensitive data to diverse audiences. Based on this scenario, we conducted three experiments with the aim of understanding how best to help lay people understand these data, and the practical goal of improving the public presentation of these data. The experiments compared different outcome measures for displaying the survival rate (percentage scale vs. the ratio of the predicted/observed rates) and presentation formats (individual hospital vs. all hospitals shown) for outcomes data presented relative to prediction intervals generated by a risk model that adjusts for case mix. Our data highlight how easily inappropriate comparisons can influence evaluations of complex data: for instance, both a survival ratio of 1 and the presence of other hospitals seemingly provided reference points that resulted in inappropriately harsh evaluations of some hospitals. By drawing on evaluability theory, we demonstrate how to enhance people’s understanding of these complex data while also discouraging inappropriate comparisons, which has implications for communicating risk and uncertainty, and for choice architecture design in a range of contexts.