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Prior research found that "1-in-X" ratios led to higher and less accurate subjective probability than "N-in-X*N" ratios or other formats, even though they featured the same mathematical information. It is unclear, however, whether the effect transfers into health decisions, and the practical significance of the effect is undetermined. Based on previous findings and risk communication theories, we hypothesized that the 1-in-X effect would occur and transfer into relevant decisions. We also tested whether age, gender, and education differences would moderate the 1-in-X effect on decision making. We conducted 3 well-powered experiments ( n = 1912) using a sample from the general adult UK population to test our hypotheses, estimated the effect, and excluded a possible methodological explanation for such a transfer. In hypothetical scenarios, participants decided whether to travel to Kenya given the chance of contracting malaria (experiment 1) and whether to take recommended steroids given the side effects (experiments 2 and 3). Across the experiments, we replicated a small to medium 1-in-X effect on the perceived probability (Hedge's g = -0.36; 95% confidence interval [CI], -0.47 to -0.24; z = -6.18; P < 0.001) and found a small effect on subsequent decisions (odds ratio = 1.32; 95% CI, 1.10-1.59; z = 2.99; P = 0.003). The perceived probability fully mediated the effect of the ratio format on decision. Age, gender, and education did not moderate the 1-in-X effect on decision. We argue that a high prevalence of 1-in-X ratios in medical communication makes these small changes clinically relevant. Therefore, to communicate information accurately, 1-in-X ratios should not be used or at least used cautiously in medical communication.

Background: Previous research has shown that format effects, such as the "1-in-X" effect-whereby "1-in-X" ratios lead to a higher perceived probability than "N-in-N*X" ratios-alter perceptions of medical probabilities. We do not know, however, how prevalent this effect is in practice; i.e., how often health professionals use the "1-in-X" ratio., Methods: We assembled 4 different sources of evidence, involving experimental work and corpus studies, to examine the use of "1-in-X" and other numerical formats quantifying probability., Results: Our results revealed that the use of the "1-in-X" ratio is prevalent and that health professionals prefer this format compared with other numerical formats (i.e., the "N-in-N*X", %, and decimal formats). In Study 1, UK family physicians preferred to communicate prenatal risk using a "1-in-X" ratio (80.4%, n = 131) across different risk levels and regardless of patients' numeracy levels. In Study 2, a sample from the UK adult population ( n = 203) reported that most GPs (60.6%) preferred to use "1-in-X" ratios compared with other formats. In Study 3, "1-in-X" ratios were the most commonly used format in a set of randomly sampled drug leaflets describing the risk of side effects (100%, n = 94). In Study 4, the "1-in-X" format was the most commonly used numerical expression of medical probabilities or frequencies on the UK's NHS website (45.7%, n = 2,469 sentences)., Conclusions: The prevalent use of "1-in-X" ratios magnifies the chances of increased subjective probability. Further research should establish clinical significance of the "1-in-X" effect.

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.