Show both affected and unaffected counts when accuracy is the goal
For part-whole risk communication in quantitative displays, use both numerator and denominator on the same graphic to improve fidelity and mitigate inflated risk impressions for readers making accuracy-focused judgments.
- purpose:refine
- basis:empirical
- quality:fidelity
- lever:layout-structure
- operator:part-whole
- communication:framing
advice
Show numerator and denominator together
Display the affected count together with the total at-risk count when the goal is accurate risk judgment. For example, use a stacked bar that shows affected and unaffected people out of the full population instead of a bar that shows only the affected count.
reason
Why full part-whole context changes risk judgments
Foreground-only graphics make the affected cases dominate attention. Adding the unaffected remainder restores the full part-to-whole context and reduces inflated reactions to the risk.
Mechanism: When viewers see both the affected cases and the full population, they judge the size of the risk against its denominator instead of reacting mainly to the numerator.
Evidence: The paper reports that graphs emphasizing only the foreground, such as the number affected, increase perceived risk and risk-avoidant behavior, while displays that show both foreground and background decrease risk-avoidant behavior; it also recommends proportional part-to-whole graphics when accurate magnitude judgment is the goal (Lipkus, 2007).
context
Use when the goal is accurate risk magnitude, not persuasion
- User Goal: Understand how large a risk is without exaggeration.
- Task: Judge an affected count in relation to the full population at risk.
- Data: A numerator and a denominator that form a part-whole relationship.
- Chart Setting: A risk graphic where affected cases could be shown alone or against the full population.
- Audience: Readers making judgments or decisions from the display.
- Success Criterion: The denominator is visible and the risk is not inflated by foreground-only emphasis.
exceptions
Do not use when heightened concern is the main goal
Break it when: The communication goal is to heighten concern or encourage risk-avoidant behavior. Why: The source reports that foreground-only displays are more persuasive and increase risk-avoidant responses.
costs
Tradeoffs of adding the denominator visually
Sacrifice: You give up some persuasive force.
Risk: The display can reduce the felt urgency of the risk.
Mitigation: If urgency is the goal, use foreground emphasis deliberately rather than by accident.
mistakes
Common failure mode in risk graphics
Mistake: Showing only the affected cases when the goal is accurate risk magnitude. Why it fails: Foreground-only emphasis increases the perceived size of the risk.
check
How to test whether denominator context is missing
Failure Sign: The graphic shows harmed or benefited cases but no visible total population.
Quick Check: Ask whether a reviewer can answer both “how many are affected” and “out of how many total” from the graphic alone.
Stronger Test: Compare reactions to a foreground-only version and a version that shows both affected and unaffected counts.
fix
What to change
- Add the unaffected remainder or total population to the graphic.
- Convert an affected-only bar into a stacked bar or equivalent part-whole display.
- Keep the displayed parts visually proportional to the underlying counts.