A prominent example of people’s difficulties with ratio concepts is denominator neglect [15�C17]. That is, people often pay too much attention to the number of times a target event has happened (numerators) and insufficient attention to the overall number of opportunities for it to happen (denominators; [16]). Denominator neglect has been studied both in medical sellectchem and nonmedical contexts [18�C21]. To illustrate, in an experiment by Yamagishi [22], participants were presented with estimates of the number of deaths in the population due to eleven causes (e.g., cancer) and had to assess the risk of dying of such causes. These estimates were presented both as numbers of deaths out of 10,000 and of 100. Participants rated the likelihood of a cancer killing 1,286 out of 10,000 people (i.e., 12.

86%) as higher than 24.14 out of 100 people (i.e., 24.14%). The degree of perceived riskiness, therefore, varied according to the number of deaths presented (numerators), irrespective of the total possible number of deaths (denominators).Denominator neglect can have important consequences when making decisions about health. In medical practice, for example, the overall number of patients who receive a certain treatment is often smaller than the number of those who do not [23, 24]. Therefore, patients and their doctors might be able to think of more people who did not have a particular screening or take a novel drug than those who did. If individuals disregard the overall number of treated and nontreated patients (e.g., 100 and 800, resp.), they might perceive the treatment to be more effective than it actually is.

That is, they might compare the absolute numbers of treated and nontreated patients who die (e.g., 5 and 80, resp.) rather than the proportion of treated and nontreated patients who die (e.g., 5 of 100 and 80 of 800 for a treatment risk reduction of 50%; see Figure 1). Notably, most of the past research examining people’s perceptions of treatment risk reduction has employed samples Entinostat of treated and nontreated patients of the same size (see [7, 25]), and even experts in medical decision making recommend doing so [26�C28]. As an exception, Garcia-Retamero et al. [29] conducted a study with unequal samples of (hypothetical) treated and nontreated patients and showed that participants overestimated risk reduction when the overall number of treated patients was lower than the overall number of patients who did not receive the treatment.Figure 1Numerical information about relative risk reduction and additional visual information (icon array). A new drug for reducing cholesterol, Estatin, decreases the risk of dying from a heart attack for people with high cholesterol. Here are the results of …