Reading a percentage

A headline reports that a treatment cuts the risk of a disease by fifty per cent. That sounds decisive. Whether it is depends entirely on a number the headline has left out.

Suppose the risk of the disease was two in a thousand. Cutting it by half makes it one in a thousand. The relative reduction is fifty per cent; the absolute reduction is one person in a thousand. Both numbers are true. They describe the same result and they create completely different impressions, and the larger-sounding one is the one that reaches print.

The pattern repeats everywhere. A shop advertises that sales are up two hundred per cent without saying that three items became nine. A report finds that a rare side effect has doubled, which may mean it rose from one case in a million to two. Journalists are not always being dishonest. Relative change is genuinely easier to say and often genuinely what matters. But without the starting number, a reader cannot tell the difference between a discovery and a rounding error.

The habit worth building is a single question: per cent of what? Fifty per cent of a large base is a large number. Fifty per cent of almost nothing is almost nothing. The question takes two seconds and it is the difference between understanding a figure and being impressed by one.

The same applies in the other direction. When a number sounds trivially small — a two per cent failure rate, say — multiply it by the population it applies to before deciding it does not matter.