Absolute vs. relative risk: what a 25% reduction means

Start with people, not the headline

“Twenty-five percent fewer” sounds like a complete result. It is missing a starting point. Twenty-five percent fewer than what, over how long, and among how many people? A relative change can be calculated correctly while giving you very little sense of how common the event was. The original counts are often the most useful place to begin.

NIH’s risk explainer distinguishes absolute risk, the chance of an event in a defined setting, from relative risk, a comparison between risks. It also stresses that the population and time period affect what a number means. A population estimate does not calculate one individual’s future. NIH: understanding health risks

Consider a wholly fictional comparison. In one group of 200 people, 12 report an unwanted event during a four-week follow-up. In another group of 200, 9 report it. These numbers are invented to explain the arithmetic; they do not describe a supplement or cannabis study. Writing down all four numbers already tells you more than the shortest percentage would.

Ask how many people the percentage represents.

Do both calculations

Twelve out of 200 is 6%; nine out of 200 is 4.5%. The absolute difference is 1.5 percentage points. For the relative reduction, divide the difference between 12 and 9 by the first group’s 12 events: three divided by 12 is 25%. The relative percentage and the absolute difference describe the same fictional comparison in different ways.

A reduction of 25% is not a reduction of 25 percentage points. Subtracting 25 percentage points from 6% would be a different calculation and would not describe this example. “Percent” and “percentage points” are small pieces of wording with a substantial effect on the meaning.

Now consider how an advert could frame the fictional result. “Twenty-five percent fewer events” foregrounds the relative change. “Three fewer people out of 200 over four weeks” makes the counts and time period visible. Neither phrasing, on its own, tells you whether the study design supports a causal explanation or whether the difference is statistically persuasive.

Find the denominator

Before doing arithmetic, check what the denominator counts. People, study visits, days with a symptom and individual test results are not interchangeable. A person could contribute several measurements. If a paper reports the proportion of positive tests, you cannot automatically rewrite that as the proportion of people affected.

Follow the groups through the methods and results. Were 200 people enrolled, or did 200 complete the follow-up? Were any results excluded? The number in a study’s headline summary can refer to recruitment while the reported outcome uses a smaller analysis group. Our guide to reading a research abstract helps locate these differences before you interpret the most memorable sentence.

Also check the outcome itself. “Any reported symptom” is broader than one specified event. A questionnaire score changing is a different measure from fewer people crossing a defined threshold. Both may be legitimate outcomes, but translating one into the other invents information the result did not supply. NCCIH: abstracts and main sections

The comparison needs a design

The two imaginary groups could come from a randomized trial, an observational study or a customer survey. Those designs do not answer the same causal question. People choosing different products may differ in other ways, and a before-and-after comparison can change over time for reasons beyond the product being discussed. NCCIH: types of research

Look for the comparator the researchers actually used. Was it placebo, another preparation or the participants’ own earlier measurements? A result against one comparator is not automatically a result against every competing product. The general distinction between laboratory and human research is a useful first filter, but human studies still need this closer reading.

Uncertainty belongs beside the estimate. Check confidence intervals, the sample size and what the authors say about the analysis. A difference between two observed percentages does not by itself establish a reliable benefit. A small trial can produce an interesting estimate that later research changes; a precise-looking decimal does not remove that possibility.

Some percentages describe a change in an average score rather than an event’s frequency. A percentage improvement on a questionnaire is not automatically a percentage fewer people experiencing a problem. Find the original scale and outcome definition before treating a change in score as a change in risk. The arithmetic may use similar symbols while answering a different question.

Write the result in an ordinary sentence

For the fictional example, a complete first sentence could be: “Over four weeks, 9 of 200 people in group B reported the event, compared with 12 of 200 in group A.” You could then add the 1.5-percentage-point difference and 25% relative reduction. The order helps a reader understand the size of the observation before encountering its most striking framing.

The same habit works when you are reading a product claim: identify the event, the groups, the counts and the time period, then consider the study’s limits. If those details are unavailable, the percentage remains incomplete. It cannot tell you which product to use or predict how you will respond, however confidently it appears in a headline.