The effect of different graphical and numerical likelihood formats on perception of likelihood and choice

Background: Quantitative risk information plays an important role in decision making about health. This study focuses on commonly used numerical and graphical formats and examines their effect on perception of different likelihoods and choice preferences.

Methods: An experimental study was conducted with 192 participants, who evaluated 2 sets of 4 lotteries. Numerical formats to describe likelihood varied systematically between participants (X%, X-in-100, or 1-in-X). The effect of graphic formats (bar charts, icon charts) was assessed as a within-subjects factor. Dependent measures included perceived likelihood, choice preferences about participating in the lottery, and processing times.

Results: Numerical likelihoods presented as 1-in-X were processed fastest and were perceived as conveying larger likelihoods than the X-in-100 and percentages formats (mean response times in seconds: 5.65 v. 7.31 and 6.50; mean rating on a 1-9 scale: 4.38 v. 3.30 and 3.31, respectively). The 1-in-X format also evoked a stronger willingness to participate in a lottery than the 2 other numerical formats. The effect of adding graphs on perceived likelihood was moderated by numerical aptitude. Graphs reduced ratings of perceived likelihood of participants with lower numeracy, while there was no overall effect for participants with higher numeracy.

Conclusion: Perception of likelihood differs significantly depending on the numerical format used. The 1-in-X format yields higher perceived likelihoods and it appears to be the easiest format to interpret. Graphs primarily affect perception of likelihood of people with lower numerical aptitude. These effects should be taken into account when discussing medical risks with patients.