title: Risk estimates from an online risk calculator are more believable and recalled better when expressed as integers.
abstract: BACKGROUND
  Online risk calculators offer different levels of precision in their risk estimates. People interpret numbers in varying ways depending on how they are presented, and we do not know how the number of decimal places displayed might influence perceptions of risk estimates.
  
  
  OBJECTIVE
  The objective of our study was to determine whether precision (ie, number of decimals) in risk estimates offered by an online risk calculator influences users' ratings of (1) how believable the estimate is, (2) risk magnitude (ie, how large or small the risk feels to them), and (3) how well they can recall the risk estimate after a brief delay.
  
  
  METHODS
  We developed two mock risk calculator websites that offered hypothetical percentage estimates of participants' lifetime risk of kidney cancer. Participants were randomly assigned to a condition where the risk estimate value rose with increasing precision (2, 2.1, 2.13, 2.133) or the risk estimate value fell with increasing precision (2, 1.9, 1.87, 1.867). Within each group, participants were randomly assigned one of the four numbers as their first risk estimate, and later received one of the remaining three as a comparison.
  
  
  RESULTS
  Participants who completed the experiment (N = 3422) were a demographically diverse online sample, approximately representative of the US adult population on age, gender, and race. Participants whose risk estimates had no decimal places gave the highest ratings of believability (F(3,3384) = 2.94, P = .03) and the lowest ratings of risk magnitude (F(3,3384) = 4.70, P = .003). Compared to estimates with decimal places, integer estimates were judged as highly believable by 7%-10% more participants (χ(2) (3) =17.8, P < .001). When comparing two risk estimates with different levels of precision, large majorities of participants reported that the numbers seemed equivalent across all measures. Both exact and approximate recall were highest for estimates with zero decimals. Odds ratios (OR) for correct approximate recall (defined as being within 50% of the original estimate) were, for one decimal place, OR = 0.65 (95% CI 0.49-0.86), for two decimal places, OR = 0.70 (95% CI 0.53-0.94), and for three decimal places, 0.61 (95% CI 0.45-0.81). Exact recall showed a similar pattern, with larger effects.
  
  
  CONCLUSIONS
  There are subtle but measurable differences in how people interpret risk estimates of varying precision. Adding decimal places in risk calculators offers little to no benefit and some cost. Rounding to the nearest integer is likely preferable for communicating risk estimates via risk calculators so that they might be remembered correctly and judged as believable.
authors: Program in Health Communication and Decision Making, Center for Bioethics and Social Sciences in Medicine, University of Michigan, Ann Arbor, MI, United States. hollywit@med.umich.edu
authors: Holly O
authors: HO
authors: Witteman
authors: Brian J
authors: BJ
authors: Zikmund-Fisher
authors: Erika A
authors: EA
authors: Waters
authors: Teresa
authors: T
authors: Gavaruzzi
authors: Angela
authors: A
authors: Fagerlin
mesh_terms: D000328:Adult; D054626:Consumer Health Information; D003626:Data Display; D003627:Data Interpretation, Statistical; D004812:Epidemiologic Methods; D005260:Female; D006801:Humans; D020407:Internet; D008297:Male; D008403:Mass Screening; D008875:Middle Aged; D012107:Research Design; D018570:Risk Assessment / Q000706:statistics & numerical data*; D012307:Risk Factors; D016008:Statistical Distributions; D014481:United States; D055815:Young Adult