Ratio Format Shapes Health Decisions: The Practical Significance of the “1-in-X” Effect

Abstract

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.