Sneeky numbers

Book Review: The Tiger that Isn't by Michael Blastland and Andrew Dilnot

On 12 November 2002, BBC news reported that "for every alcoholic drink a woman consumes, her risk of breast cancer rises by 6 per cent". Many readers will instantly see that this is obviously arrant nonsense. You don't need to reach for the calculator to see that if such a statistic were true, very few women who enjoyed a cocktail from time to time would escape cancer. So how did this travesty make it to the air?

The broadcasters, clearly, had misinterpreted some numbers. Sadly, this is not an uncommon scenario, even among educated journalists, and the results can be misleading and potentially dangerous. Improving this situation is the task that Michael Blastland and Andrew Dilnot, a former director of the UK Institute for Fiscal Studies, regularly set themselves in their BBC radio programme More or Less. Their crusade continues in their new book, The Tiger that Isn't. (The title alludes to humans' primitive propensity to see patterns, and the likelihood that those best equipped to envisage a possible tiger attack in the rustling of leaves were best placed to become our ancestors.) The authors succeed engagingly, even providing some very accessible critiques of quite advanced statistics.

So what went wrong in reporting the breast cancer study? Cancer Research UK had published a study concluding that a woman's risk of breast cancer "rises 6 per cent for every drink consumed on a daily basis". Two drinks per day, the study said, raised the risk by 12 per cent. Roughly 9 per cent of women suffer breast cancer, so a 6 per cent increase in risk means an additional absolute risk of about 0.5 per cent.

So, out of 1000 teetotal women, about 90 will suffer breast cancer; but of every 1000 women who have one drink per day, every day, according to that study, about 95 will do so.

Unfortunately, all that makes for a really boring headline, and this is a major problem in reporting number-based news. Blastland and Dilnot acknowledge this and do their bit to help fix the problem. They do not, however, address the underlying cause. Their colleagues at the BBC did not understand how to do multiplication or division of percentages. Even if they did, their reports would still leave one-third of the population cold, as surveys show that 1 in 3 people do not understand percentages at all. They have no idea that "6 per cent" means "6 out of every 100". (Hang on: one-third of which population?)

These people cannot be blamed for not knowing, especially as growing pressure on teachers to deliver high exam results means "teaching to the test" is promoted as a replacement for actual education. I have lost count of the number of friends who say they gave up on school mathematics in frustration because teachers would not or could not answer their "but why?" questions.

Would these friends have done better if teachers had started with the axioms of number theory: "There exists an entity 'zero', such that..."? Perhaps some would. Teaching someone to understand numbers is like giving directions to a stranger: some need landmarks to find, some a trail of street shapes to follow, some make do with the Cartesian coordinates of "Ninth street and Vine" - and you have to try them all until something works.

Someone, somehow, needs to find a way of conveying to everyone that the whole point of numbers is that they must not just sit there on the page, signifying. And when it comes to statistics, journalists should never quote any number until they have played with it, twisted it around, multiplied it by the population of Scotland or of the world to detect what exactly it is counting - or, if it occurs in a press release, how it is misdirecting them.

“Journalists should never quote any number until they have played with it”

Those who spin numbers for a living don't need this book, but every journalist should get paid leave to read and reread The Tiger that Isn't until they've understood how they are being spun.

Mike Holderness is a science writer in London
From issue 2621 of New Scientist magazine, 15 September 2007, page 57