Add icon arrays when compared groups have unequal denominators

Add icon arrays to numeric risk comparisons when the groups being compared have different total sizes. For example, place one array for each group beside the numbers and show the full at-risk population in each array with the affected cases marked within it.

Icon arrays make the full group size visible at the same time as the affected cases. Readers then inspect the event count against the whole population instead of treating the numerator as the main signal.

Mechanism: Showing all individuals in each group creates an immediate part-to-whole display, which draws attention to the denominator and reduces numerator-driven judgments.

Evidence: When icon arrays were added to numerical risk information, accuracy improved substantially for unequal-denominator comparisons in both a within-subject laboratory study and a between-subject web study, and the benefit held for both younger and older adults (Garcia-Retamero et al., 2010).

• User Goal: Judge treatment effectiveness from displayed outcome counts.
• Task: Compare two risks when one group is larger or smaller than the other.
• Data: Two groups with affected and unaffected individuals, with unequal totals.
• Chart Setting: A numeric risk statement supplemented by one icon array per group.
• Audience: Younger and older adults reading health-risk information.
• Success Criterion: Readers estimate relative risk reduction accurately despite unequal denominators.

Break it when: The compared groups already use the same denominator in the numeric presentation. Why: Numeric presentations were already fairly accurate in the equal-denominator conditions, so the specific denominator-neglect problem is much smaller there.

Sacrifice: Icon arrays take more physical space than a numeric-only presentation. Risk: Large arrays can become bulky in space-constrained layouts. Mitigation: Use them where unequal denominators are central to the comparison and accuracy matters.

Mistake: Present unequal-denominator risks with numbers alone and leave the full group sizes visible only as denominators in text. Why it fails: Readers over-rely on the raw event counts and misjudge the treatment effect.

Failure Sign: One group’s event count looks smaller or larger mainly because its total population is also smaller or larger. Quick Check: Verify that each group has a complete icon array showing the whole population, not just the affected cases. Stronger Test: Compare a numeric-only mockup with the icon-array version; if the unequal totals are only immediately visible in the icon-array version, keep the icon arrays.

• Add one icon array for each comparison group beside the numeric statement.
• Show the full population size in each array.
• Mark the affected cases within each array so the count is read against the whole group.
• Keep the arrays paired with the numbers so readers can cross-check the comparison.