A crash course in understanding numbers

A Field Guide to Lies and Statistics. By Daniel Levitin. Dutton; 292 pages; $28. Viking; £14.99.

PEOPLE take in five times as much information each day as they did in the mid-1980s. With all these data sloshing around it is easy to feel lost. One politician uses a statistic to back up her argument; a newspaper uses another fact to refute it; an economist uses a third to prove them both wrong. In “A Field Guide to Lies and Statistics” Daniel Levitin, an American neuroscientist, shows the reader how to find a way through all this numerical confusion.

A book about statistics can easily be boring. Fortunately, Mr Levitin is the perfect guide. Before becoming an academic he used to work as a stand-up comedian. Drawing on those skills Mr Levitin peppers his book with wisecracks. He uses the phrase “on average, humans have one testicle” to make the point that the mean can be a misleading description of a population. He goes off on interesting tangents, granting the reader some light relief from detailed analysis of sampling and probabilities. Only occasionally is his hokey style annoying.

Using plenty of examples, Mr Levitin shows how easily statistics can lead people astray. Take the following assertion, which on a quick skim might seem perfectly reasonable: “In the 35 years since marijuana laws stopped being enforced in California, the number of marijuana smokers has doubled every year.” One will soon realise that this must be nonsense; even with only one smoker to begin with, after doubling every year for 35 years there would be more than 17bn of them. Mr Levitin repeatedly throws these statistical curveballs at his readers, training them to adopt a take-nobody’s-word-for-it attitude. It is an effective pedagogical technique.

Some statistics turn out to be plain wrong, but more commonly they mislead. Yet this is hard to spot: numbers appear objective and apolitical. A favourite of academics and journalists, when analysing trends, is to “rebase” their figures to 100 so as to back up the argument that they wish to make. For instance, starting a chart of American GDP growth in 2009, when the country was in recession, tricks the reader into thinking that over the long term the economy is stronger than it really is. “[K]eep in mind that experts can be biased without even realising it,” Mr Levitin reminds people.

A basic understanding of statistical theory helps the reader cope with the onslaught of information. Mr Levitin patiently explains the difference between a percentage change and a percentage-point change, a common source of confusion. When a journalist describes a statistical result as “significant”, this rarely carries the same meaning as when a statistician says it. The journalist may mean that the fact is interesting. The statistician usually means that there is a 95% probability that the result has not occurred by chance. (Whether it is interesting or not is another matter.)

Some readers may find Mr Levitin’s book worthy but naive. The problem with certain populist politicians is not that they mislabel an x-axis here or fail to specify a control group there. Rather they deliberately promulgate blatant lies which play to voters’ irrationalities and insecurities. Yet if everyone could adopt the level of healthy statistical scepticism that Mr Levitin would like, political debate would be in much better shape. This book is an indispensable trainer.