Decisive Evidence on a Smaller-Than-YouThink Phenomenon: Revisiting the "1-in-X'' Effect on Subjective Medical Probabilities

Miroslav Sirota*, Marie Juanchich, Olga Kostopoulou, Robert Hanak

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

25 Citations (Scopus)

Abstract

Accurate perception of medical probabilities communicated to patients is a cornerstone of informed decision making. People, however, are prone to biases in probability perception. Recently, Pighin and others extended the list of such biases with evidence that 1-in-X ratios (e.g., 1 in 12) led to greater perceived probability and worry about health outcomes than N-in-X*N ratios (e.g., 10 in 120). Subsequently, the recommendation was to avoid using 1-in-X ratios when communicating probabilistic information to patients. To warrant such a recommendation, we conducted 5 well-powered replications and synthesized the available data. We found that 3 out of the 5 replications yielded statistically nonsignificant findings. In addition, our results showed that the 1-in-X effect was not moderated by numeracy, cognitive reflection, age, or gender. To quantify the evidence for the effect, we conducted a Bayes factor meta-analysis and a traditional meta-analysis of our 5 studies and those of Pighin and others (11 comparisons, N = 1131). The meta-analytical Bayes factor, which allowed assessment of the evidence for the null hypothesis, was very low, providing decisive evidence to support the existence of the 1-in-X effect. The traditional meta-analysis showed that the overall effect was significant (Hedges' g = 0.42, 95% CI 0.29-0.54). Overall, we provide decisive evidence for the existence of the 1-in-X effect but suggest that it is smaller than previously estimated. Theoretical and practical implications are discussed.

Original languageEnglish
Pages (from-to)419-429
Number of pages11
JournalMedical Decision Making
Volume34
Issue number4
DOIs
Publication statusPublished - May 2014

Keywords

  • "1-in-X" effect
  • subjective probability
  • probability perception
  • meta-analysis
  • Bayes factor meta-analysis
  • COGNITIVE REFLECTION
  • RISK COMMUNICATION
  • RATIO BIAS
  • EXPERIMENTAL-PSYCHOLOGY
  • BAYES FACTOR
  • T TESTS
  • NUMERACY
  • JUDGMENTS
  • COMPREHENSION
  • DENOMINATOR

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