# Vital statistics

### The Art of Statistics: Learning from Data

David Spiegelhalter

Pelican, pp. 425, £

Scientists, it turns out, are really bad at statistics. Numerous studies show that a startling proportion of academics consistently misunderstand the statistics they’re using, and the conclusions that can be drawn from them. A computer algorithm that highlights basic statistical errors was recently set loose on a huge sample of published research papers in psychology  and found that almost half contained a mathematical mistake; 13 per cent had a serious screw-up that meant their reported results might have been completely wrong. If scientists — who use statistics all day to analyse their experiments — are so innumerate, what hope is there for everyone else?

Enter Sir David Spiegelhalter, Winton professor for the public understanding of risk at Cambridge University. His new volume, The Art of Statistics, is in the great educational tradition of its publishing imprint, Pelican Books: an attempt to get everyone up to speed with the practical uses of statistics, without pages of terrifying equations or Greek letters. In a series of spry, airy chapters introducing the reader to probability, regression, causation, machine-learning and what’s nowadays called ‘data visualisation’ (also known as ‘making pretty graphs’), he succeeds fabulously.

Although it wouldn’t be a statistics book without a few dice-rolling analogies (thankfully it avoids references to poker, a common but never intuitive explanatory tool), the examples used are generally lively and well chosen. Does going to university really increase your risk of getting a brain tumour, as an already infamous scientific press release claimed in 2016? Unlikely. What was the probability that the skeleton dug up in a Leicester car park in 2012 was really that of Richard III? 0.999994, once you take carbon-dating and DNA evidence into account. Spiegelhalter provides all the statistical reasoning required to reach these conclusions, often circling back later to give another perspective on each problem. In the process, he demonstrates that statistics is far from a settled field and is still subject to intense — if somewhat nerdy — debate.

Most strikingly, Spiegelhalter describes his experience designing a statistical model that, had it been implemented before the murders began, would have flagged up the alarmingly high mortality rate among Harold Shipman’s patients. He concludes that using his model would have stopped Shipman’s spree by 1984, saving 175 lives. There could hardly be a stronger reason for sharpening up our statistical skills. I was reminded of an opposite example, the case of the Manchester ‘Pusher’, a fabled serial killer believed by many to be the cause of a recent spate of drowning deaths in the city’s canals. A BBC analysis cast severe doubt on the idea of a murderer, though: it revealed that the number of fatalities, though tragic, was around what we’d expect purely by accident — especially on stretches of canal that are poorly lit, poorly fenced-off and close to many pubs and bars.

Statistical reasoning can help us resolve these kinds of cases, but it brings with it the potential for false positives. Spiegelhalter mentions a different GP who had an unusually high patient mortality rate, but this time for completely innocent reasons (he happened to work in an area with a preponderance of retirement homes), who mistakenly had his collar felt by the Shipman-hunting statistical model. As models and algorithms become more common in daily life, we’ll see many more such blind, potentially harmful, uses of statistics. This makes efforts like Spiegelhalter’s, to teach us what the models do and don’t mean, all the more crucial.

Things get more complex in the latter half of the book. If you’re completely new to statistics, you may need a strong cup of coffee before digging into the details of ‘Bayesian multi-level regression and post-stratification’, an advanced statistical model that has pollsters excited because of its accurate election predictions. But this complexity is inherent to statistics, and is hardly a failing of Spiegelhalter, who keeps things admirably clear and engaging. He ends with a section on scientists’ and journalists’ misuse of statistics in their research and stories, and gives useful practical advice on how we might avoid further statistical blunders.

Some parts were too brief for my liking. For instance, Spiegelhalter hints that he’s sceptical of the analyses routinely used by economists that claim to conjure causal conclusions from correlational data, but he doesn’t say why. I’d have liked to see his working. But any quibbles I have are — as a statistician might say — only marginally significant. A book that crams in so much statistical information and nonetheless remains lucid and readable is — sorry, another statistical pun — highly improbable, and yet here it is. In an age of scientific clickbait, ‘big data’ and personalised medicine, this is a book that nearly everyone would benefit from reading. Though perhaps you shouldn’t trust my advice about statistics. After all, I’m a scientist.