False precision
Stating a figure with more exactness than the underlying evidence supports, so that the precision of the number is mistaken for the reliability of the claim.
A number with a decimal point looks measured. "About half" invites a question; "51.3%" ends one. The device borrows the authority of measurement for claims that were estimated, guessed, or invented, and it works because most people cannot see how a figure was made and assume that a precise one was made carefully. The more digits, the more trust, and the digits are free.
Darrell Huff's How to Lie with Statistics gave the device its popular treatment in 1954, and Joel Best's later work on "mutant statistics" traced how a rough estimate becomes, through repetition, a hard number nobody can source. Advertising discovered it earlier: Ivory soap was "99 and 44/100 percent pure" from 1882. Exploits Anchoring and Authority Bias.
Historical examples
Huff's How to Lie with Statistics, still the best-selling statistics book ever published, devoted a chapter to "the semi-attached figure" and another to spurious accuracy, showing how a survey of a few hundred people becomes a national percentage to one decimal place. The book's examples were drawn from advertising and journalism of the day.
Huff, Darrell. How to Lie with Statistics. New York: W. W. Norton, 1954.
Joel Best traced how the claim that the number of children killed by gunfire had "doubled every year since 1950" appeared in a dissertation prospectus, having mutated from a statement that the number had doubled over the whole period: a rough figure, garbled once, then repeated with full precision because no one checked the arithmetic, which would have implied more deaths than people.
Best, Joel. Damned Lies and Statistics: Untangling Numbers from the Media, Politicians, and Activists. Berkeley: University of California Press, 2001.
In advertising and commerce
Procter & Gamble advertised Ivory soap as "99 and 44/100 percent pure" from 1882, a figure derived from a chemist's analysis of impurities and chosen, the company's own history suggests, because the fraction sounded more scientific than "pure." The slogan became one of the longest-running in American advertising, and the number was the reason.
Sivulka, Juliann. Soap, Sex, and Cigarettes: A Cultural History of American Advertising. 2nd ed. Boston: Wadsworth, 2012.
Find a statistic with a decimal point in an advertisement or a news story. Try to find where it came from. If you can't, what does that tell you about the decimal point?
In the wild
Short examples of the technique at work, each with what to notice. The same examples are questions in the quiz, where the answer is not given away.
"Our customers report 43.7% more energy after two weeks." No survey is described.
What to notice. A decimal place on an unmeasurable claim, with no method; the precision is doing the persuading.
"The scheme will cost every household exactly £1,212 a year." The estimate depends on a dozen assumptions.
What to notice. "Exactly" and the four digits present a rough projection as a measurement.
"Kills 99.9% of germs." The claim is tested on a surface in a laboratory, not in a home.
What to notice. The number is precise about a condition that doesn't apply where the product is used.
Sources
- Huff, Darrell. How to Lie with Statistics. New York: W. W. Norton, 1954. ISBN 978-0393310726
- Best, Joel. Damned Lies and Statistics. Berkeley: University of California Press, 2001. ISBN 978-0520219786
- Sivulka, Juliann. Soap, Sex, and Cigarettes. 2nd ed. Boston: Wadsworth, 2012. ISBN 978-1133311133