Report compared risks on a shared denominator

Report both groups on the same denominator when presenting numeric risk reduction. For example, restate treated and untreated outcomes as rates out of a shared base such as 100 or 1000 instead of comparing values like 2/100 against 50/500 or 30/500 against 10/100.

Using the same denominator removes the need to mentally reconcile different group sizes. Readers can compare like with like instead of judging the effect from raw event counts alone.

Mechanism: A shared denominator makes the part-to-whole relation directly comparable across groups, so the numerator is read in relation to the same total in both groups.

Evidence: In both studies, numeric-only judgments of treatment risk reduction were fairly accurate when treated and untreated groups used equal denominators, but accuracy dropped when denominators differed and participants relied too much on numerators (Garcia-Retamero et al., 2010).

• User Goal: Judge how much a treatment changes risk.
• Task: Compare two group risks and infer relative risk reduction.
• Data: Two event counts out of two group totals, where the original group sizes may differ.
• Chart Setting: Numeric-only risk communication in which the comparison is carried by the reported ratios.
• Audience: Younger or older adults interpreting health-risk information.
• Success Criterion: Readers can estimate the treatment effect accurately without over- or under-weighting raw event counts.

Break it when: The main display must preserve the original unequal group sizes and cannot restate both risks on a common base. Why: The paper treats matched denominators as the preferred convention, but recommends visual displays when that convention is not feasible.

Sacrifice: The main ratio statement no longer shows the original sample-size imbalance directly. Risk: Readers may miss that one group was actually much larger or smaller in the underlying study or recall set. Mitigation: If the unequal group sizes must remain visible, keep them visible with a visual display such as icon arrays instead of relying on numeric ratios alone.

Mistake: Keep unequal denominators in a numeric-only comparison and assume readers will mentally normalize them. Why it fails: Many readers judge the comparison from the absolute event counts and misread how large the effect really is.

Failure Sign: The two compared risks are written with different totals. Quick Check: Rewrite both ratios to the same base and see whether the perceived strength of the effect changes. Stronger Test: If the comparison becomes directly readable only after normalization, the original formatting is inviting denominator neglect.

• Rewrite each compared risk to the same denominator.
• Use the normalized values as the main comparison when you report risk reduction.
• If you cannot normalize the main comparison, add icon arrays rather than leaving the comparison numeric-only.