When someone quotes a relative change ("cuts your risk by 50 percent", "doubles the danger"), ask what the risk was before and after in plain counts out of the same number of people, because the same fact sounds enormous as a ratio and modest as a difference.

How to do it

1. 1Notice the tell: a percentage change with no starting point. "Reduces risk by a third", "40 percent more likely", "twice as effective" are all relative figures.
2. 2Ask the two-number question: out of 1,000 people like me, how many have this happen without the treatment (or product, or policy), and how many with it?
3. 3Subtract. A drop from 2 in 1,000 to 1 in 1,000 is a 50 percent relative reduction and a 0.1 percentage-point absolute reduction. Both are true; only the second tells you how much you gain.
4. 4Turn the difference into a number needed to treat: 1 divided by the absolute difference. One in a thousand means a thousand people have to take the thing for one to benefit.
5. 5Check that benefits and harms are in the same format. A common move is to give the benefit as a relative figure (big) and the side effects as an absolute figure (small).
6. 6Ask over what period. "Out of 1,000 people over ten years" and "per year" differ by a factor of ten.

When to use it

• •Deciding about a screening test, drug, supplement, or procedure on the strength of a percentage benefit.
• •Reading a health or crime headline that says a risk "doubled" or "soared".
• •Evaluating a sales or investment claim built on percentage improvement ("300 percent more effective").
• •Hearing a policy defended or attacked with a percentage change and no baseline.

Counters

Evidence and how strong it is

Gigerenzer (2002) documents how relative-risk formats mislead patients, physicians, and journalists, using cases such as the 1995 UK contraceptive-pill scare, in which a "twofold" increase in thrombosis meant a change from about 1 to about 2 in 7,000 women and was followed by a rise in unwanted pregnancies and abortions. Malenka et al. (1993) showed patients choose a treatment far more often when its benefit is given in relative terms than when the identical benefit is given in absolute terms. Gigerenzer et al. (2007) review the literature and recommend absolute risks and natural frequencies as the transparent formats; a Cochrane review (Akl et al. 2011) confirms that relative risk reductions are perceived as larger and more persuasive than the same effect expressed as absolute reduction or number needed to treat. Evidence strength: strong (randomized format experiments and a systematic review) that the format changes perception and choice; evidence that asking the question improves real-world decisions is indirect.

1. Gigerenzer, G. (2002). Calculated Risks: How to Know When Numbers Deceive You. Simon & Schuster
   The case for absolute risks and natural frequencies, including the contraceptive-pill scare example.
2. Gigerenzer, G., Gaissmaier, W., Kurz-Milcke, E., Schwartz, L. M., & Woloshin, S. (2007). Helping Doctors and Patients Make Sense of Health Statistics. Psychological Science in the Public Interest, 8(2), 53-96
   Review of statistical illiteracy in medicine and the recommendation to use absolute risks, natural frequencies, and mortality rates.
3. Malenka, D. J., Baron, J. A., Johansen, S., Wahrenberger, J. W., & Ross, J. M. (1993). The Framing Effect of Relative and Absolute Risk. Journal of General Internal Medicine, 8(10), 543-548
   Experiment showing patients prefer a treatment described by relative benefit over an equivalent one described by absolute benefit.
4. Akl, E. A., Oxman, A. D., Herrin, J., et al. (2011). Using Alternative Statistical Formats for Presenting Risks and Risk Reductions. Cochrane Database of Systematic Reviews, (3), CD006776
   Systematic review finding relative risk reduction is perceived as larger and is more persuasive than absolute risk reduction or number needed to treat.