Lies, Damned Lies and Statistics

How numbers persuade

Numbers carry an aura of objectivity that words lack, and for that reason they are among the most persuasive tools available to a writer. Yet the same data can support strikingly different conclusions, depending on how it is selected and presented.
A medicine that reduces the risk of a condition from 2 in 1,000 to 1 in 1,000 can honestly be described as “halving the risk” — a relative reduction of 50%. It can equally honestly be described as reducing the risk by 0.1 percentage points — an absolute reduction. The first sounds dramatic; the second sounds negligible. Both are true, and neither, on its own, is the whole story.
Correlation offers further temptation. Towns with more ice-cream shops record more drownings; it would be absurd to conclude that ice cream causes drowning, since both rise with hot weather. Less absurd examples are easily overlooked, and the confusion of correlation with causation remains one of the commonest flaws in persuasive writing.
The responsible use of statistics, therefore, involves more than accuracy. It requires that the writer present the figures a reader needs to interpret the claim — the base rate, the absolute number, the sample size, the comparison — rather than only the figure that best supports the argument.