Icon Arrays

What it is

Numbers such as seven in a hundred or one in ten ask the reader to hold a numerator and a denominator in mind and compare the two. Denominator neglect is the habit of attending to the numerator, the count of events, and giving too little weight to the denominator, the size of the group it sits in. An icon array puts the denominator on the page. A group of a hundred people appears as a hundred symbols, and the affected ones are shaded, so the size of the group cannot be missed while the count of affected people is read.

The display does not change the figures. It changes what is in front of the reader, which is the point of the 2010 paper: its authors conclude that the difficulty lies largely in how the problem is represented and not in the reasoner's mind. That conclusion fits the account of base-rate neglect given by Aron Barbey and Steven Sloman in 2007, in which the effect is smaller when problems are framed so that people can readily represent the nested groups of individuals.

In effect

The 2010 paper, in Medical Decision Making, reports two experiments on how people interpret risk reduction figures when the compared groups differ in size. Participants tended to focus on the numerators, the number of events, and neglected the denominators, the total number of people in each group. Adding icon arrays to the numerical information drew attention to the denominators and improved the accuracy of participants' risk judgments. The benefit was similar for younger and older adults.

The experiments compared groups of different sizes on purpose. When two groups are the same size, the counts alone give the right comparison, so a reader who looks only at the numerators is not misled. When the sizes differ, the counts can point the wrong way, and that is the situation in which attention to the denominators matters.

What it does not say

The finding comes from two experiments on risk reduction figures, and this page reports the authors' conclusion as it stands in the abstract. It does not give effect sizes, and it does not extend the result to every kind of ratio or to every display. An icon array is one way of showing a denominator. The page on denominator neglect covers the effect itself, and the page on base-rate neglect covers the related tendency to underweight how common a category is.

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