Background: Patient representatives are increasingly engaged in quality in health care, and even though quality data are publicly available, correct interpretation may be challenging. We designed a randomized study with the primary aim to examine the association between preferred data presentation format and the interpretation of quality data among cancer patients and relatives.Material and methods: Surveys were distributed to the Danish Cancer Society Citizens' Panel between 31 March and 14 April 2019 and 55% completed the survey (N = 464) including six storyboards that presented authentic quality data in table format, league table and point estimates. The storyboards were randomized to expose participants to the data in the three different formats and in varying presentation order. Logistic regression models were used to calculate Odds Ratios (ORs) and 95% confidence intervals (CIs) for the association between preferred presentation format, health literacy, education and cohabitation status as exposures and interpretation of quality data as outcome.Results: The majority of participants (97%) had high literacy and 57% had a medium or long higher education. A total of 60% found the questions difficult or very difficult and 33% were not able to correctly interpret at least one format. Correct interpretation was associated with preferred league table (OR = 1.62; 95% CI = 1.04-5.52) and if the data was presented in the preferred format. Medium and long education were associated with correct interpretation of at least one format (OR = 1.93; 95% CI = 1.16-3.21 and OR = 3.89; 95% CI = 1.90-7.95, respectively) while health literacy and cohabitation status were not.Conclusions: More than one third of the participants were not able to correctly interpret the data and the understanding of quality data improved with longer education and if the data was presented in the preferred format. Decision-makers should carefully consider displaying quality data according to preferred presentation format and to guide interpretation for individuals with short education.