The following numbers are not the result of a particular medical study. They are a deliberately simple illustration of the difference between relative and absolute risk.
Imagine the headline: “Eating food X raises the risk of a rare disease by 100 per cent.”
In two equally sized model groups of 100,000 people, one unexposed person and two exposed people developed the disease during the ten-year observation period.
The case count rose from one to two: a relative increase of 100 per cent. Absolute risk changed from 0.001 per cent to 0.002 per cent — one additional case per 100,000 people over ten years.
In the exposed group, 99,998 of 100,000 people did not develop the disease during those observed ten years. The observation does not justify saying that they will “never” develop it.
1. Five ways a correct number can create the wrong impression
- Confusing relative and absolute risk: a 100 per cent increase sounds dramatic if the change from one case to two is omitted.
- A mean without the distribution: ten people each earn 35,000 Czech crowns per month. One person earning 10,000,000 crowns per month joins them. The median remains 35,000 crowns, while the mean rises to about 940,909 crowns.
- A truncated Y-axis: starting just below the measured values can make a small difference look large. Truncation is not automatically wrong, but it must be visible and justified.
- Selecting the starting year: a time series beginning in an exceptional trough may create a different impression from a longer series that includes the preceding period.
- Simpson’s paradox: a relationship seen within subgroups may weaken or reverse when the groups are combined because their composition differs.
2. What a statistic must show
The reader needs the base, unit, period, population and selection method. For health risks, the reader also needs to know whether the evidence came from an experiment, an observational study or a model, and whether the result is statistically and practically important.
Mean and median answer different questions. Relative and absolute change describe the same result on different scales. Selecting one correct value may therefore still leave out information needed for a decision.
3. What the model claims — and what it does not
The same change can truthfully be described as a doubling and as one extra case per 100,000 people. Decisions often require both figures.
Invented numbers prove nothing about a particular food, disease or causal relationship. They only demonstrate the calculation and the wording.
A calculation may be mathematically correct. The choice of number, base and time frame still determines which story the reader sees.
— Jiný Kontext