CASE FILE #06

The numbers don't lie. But they can tell a completely different story

Imagine opening a news portal in the morning and coming across a dramatic red headline: "New study warns: Eating a favorite food increases the risk of a rare form of cancer by 100%!"

Viktor13 min read
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Jiný Kontext editorial illustrationSurová data jsou jen světlem. To, jaký obraz dopadne na stěnu, závisí na úhlu a brusu optického hranolu.
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The numbers don't lie. But they can tell a completely different story

Imagine opening a news portal in the morning and coming across a dramatic red headline: "New study warns: Eating a favorite food increases the risk of a rare form of cancer by 100%!"

Most readers will feel a pang of dread at that point. The brain automatically translates "one hundred percent" as a disaster: if the risk was high, now it is twice as high, half of the people are at risk.

A look at the laboratory protocol:

In a group of 100,000 people who did not eat the food at all, became ill within ten years 1 person.

In a group of 100,000 people who ate it daily, they got sick 2 people.

Has the number of cases increased from 1 to 2? Yes. Is that a 100% increase mathematically? Absolutely exactly.

But what is your real likelihood of getting the disease? She moved from 0,001 % on 0,002 %. In other words, 99,998 people out of 100,000 will never get the disease.

1. Seven ways to tell the truth and create an illusion

  • Confusion of relative and absolute risk: A 100% increase sounds ominous when you gloss over the microscopic basis.
  • The Average Person That Doesn't Exist (Mean vs. Median): A billionaire enters a pub with ten people - the average salary is suddenly a million, but the median remains 35 thousand.
  • Truncated Axis: A graph axis starting at 38% will create an optical gap from a 3% difference.
  • Cherry-picking: The time series starting in the crisis year tells the opposite story to the series starting at the peak.
  • Simpson's Paradox: The trend valid in each subgroup can be completely reversed after merging.

Numbers can be perfectly objective. However, the choice of numbers is almost never completely neutral.

— Different Context
Sources and literature

Resources for further reading

  1. Huff, D. (1954). How to Lie with Statistics. W. W. Norton & Company.
  2. Spiegelhalter, D. (2019). The Art of Statistics: How to Learn from Data. Basic Books.
  3. Gigerenzer, G. (2002). Calculated Risks: How to Know When Numbers Deceive You. Simon & Schuster.
  4. Bickel, P.J., et al. (1975). Sex Bias in Graduate Admissions: Data from Berkeley. Science, 187(4175).
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