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relative_risk_confusion
This error occurs when relative risk changes (percentages of percentages) are confused with or substituted for absolute risk changes, making effects appear much larger or smaller than they actually are. It is arguably the single most exploited statistical confusion in health journalism, pharmaceutical marketing, and policy debates.
A pharmaceutical company advertises that its drug 'cuts heart attack risk by 36%.' The actual numbers: in the control group 4.5% had heart attacks; in the treatment group 2.9% did. The absolute reduction is 1.6 percentage points — you need to treat about 63 patients for one year to prevent one heart attack. Both numbers are true; only one is featured.
A news headline reads: 'Eating bacon every day doubles your risk of colorectal cancer!' The baseline risk for an average person is about 4.5%. 'Doubled' means roughly 9%. The relative risk increase (100%) sounds catastrophic; the absolute increase (4.5 percentage points) is real but contextualised differently.
A workplace safety intervention is credited with 'reducing accidents by 50%.' Before: 2 accidents per 1,000 worker-years. After: 1 accident per 1,000 worker-years. The relative reduction is genuine, but the absolute reduction (1 fewer accident per 1,000 workers) helps a manager decide whether the cost of the intervention is proportionate.
Binary (yes/no) questions an LLM must answer to identify this aspect: