Medical Decision Making (MDM)
May 2014; 34 (4)
http://mdm.sagepub.com/content/current

Decisive Evidence on a Smaller-Than-You-Think Phenomenon
Revisiting the “1-in-X” Effect on Subjective Medical Probabilities
Miroslav Sirota, PhD, Marie Juanchich, PhD, Olga Kostopoulou, PhD, Robert Hanak, PhD
School of Medicine, King’s College London, UK (MS, OK)
Kingston Business School, Kingston University London, UK (MJ)
Faculty of Business Management, University of Economics in Bratislava, Bratislava, Slovakia (RH)
Miroslav Sirota, Medical Decision Making and Informatics Research Group, Department of Primary Care & Public Health Sciences, School of Medicine, King’s College London
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.