title: Decisive evidence on a smaller-than-you-think phenomenon: revisiting the "1-in-X" effect on subjective medical probabilities.
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.
authors: School of Medicine, King's College London, UK (MS, OK).
authors: Miroslav
authors: M
authors: Sirota
authors: Kingston Business School, Kingston University London, UK (MJ)
authors: Marie
authors: M
authors: Juanchich
authors: School of Medicine, King's College London, UK (MS, OK).
authors: Olga
authors: O
authors: Kostopoulou
authors: Faculty of Business Management, University of Economics in Bratislava, Bratislava, Slovakia (RH)
authors: Robert
authors: R
authors: Hanak
mesh_terms: D001499:Bayes Theorem; D003142:Communication; D003657:Decision Making; D006801:Humans; D010358:Patient Participation; D011336:Probability; D018570:Risk Assessment
keywords: Bayes factor meta-analysis; meta-analysis; probability perception; subjective probability; “1-in-X” effect