Keep denominators consistent in numerical risk comparisons

Use the same denominator for each group when presenting a numerical risk comparison. For example, rewrite treated-versus-untreated outcomes so both groups are shown as x out of 100 or x out of 800, rather than mixing one numerator over 100 with another over 800.

Matched denominators make the two groups directly comparable in a numbers-only display. Readers do not have to normalize mentally before comparing the event counts, so they are less likely to rely on raw numerators.

Mechanism: Keeping the same denominator across groups reduces the chance that readers will compare absolute event counts as if they were proportions.

Evidence: When the study presented equally effective treatments with different denominators in the treated and untreated groups, many participants misestimated risk reduction; errors were much lower when the denominators were equal. This pattern was strongest among low-numeracy participants, showing that consistent denominators improve numerical comparisons (Garcia-Retamero & Galesic, 2009).

• User Goal: Understand how much one option changes risk relative to another.
• Task: Compare two group risks from numbers alone.
• Data: Two-group outcome counts that can be expressed on a common base.
• Chart Setting: Text-heavy or numbers-only risk communication without paired icon arrays.
• Audience: Mixed public audiences, especially readers with low numeracy.
• Success Criterion: Readers estimate the same treatment effect regardless of which raw group size was larger.

Break it when: You can add icon arrays that show the full denominator for each group. Why: The source found that icon arrays eliminated the denominator-size effect even when the group totals remained unequal.

Sacrifice: You may need to restate the comparison on a common base instead of presenting only the original raw counts.
Risk: Leaving mixed raw denominators prominent beside the common-base rewrite can keep attention on the raw numerators.
Mitigation: If the original unequal totals must remain visible, pair the standardized numbers with icon arrays.

Mistake: Mix denominators across groups in a numbers-only comparison. Why it fails: Readers compare raw event counts instead of proportions and overestimate or underestimate the treatment effect.

Failure Sign: Reader judgments change when only the group denominators change, even though the true relative risk reduction stays the same.
Quick Check: Rewrite the same comparison once with matched denominators and once with unmatched denominators; if answers differ, standardize the denominators.
Stronger Test: Ask readers to estimate deaths per 1000 after reading the comparison; if the implied relative risk reduction is too high when the treated group is smaller or too low when it is larger, change the denominators.

• Convert each group’s outcome to the same denominator before presenting the comparison.
• Replace mixed forms such as x out of N versus y out of M with matched forms such as x out of 100 versus y out of 100.
• Keep the comparison on that common base wherever readers are expected to judge treatment effect from the numbers.
• If unequal raw totals must remain visible, add paired icon arrays that show each full denominator.