For most of us Disraeli was something in 19th-century politics. He was also the guy who said: 'There are three kinds of lies: lies, damned lies, and statistics'. It has stuck in the British imagination ever after. It neatly connects up with the self-deprecating habit the Brits have of saying (with mincing pride) that they're no good with numbers. Or with 'maths' (which ignores the fact that maths is more than numbers).
Knowing as we do a lot more than Disraeli, following the popular idea that anything and anyone modern is certain to know more than and be better than anything long ago, we also know that there are damned statistics. A quartet of popular things to worry, bamboozle and intimidate us – lies, damned lies, statistics, and now damned statistics.
Eyes glaze over when newscasters and commentators refer to immigration figures. What is the magic number, the one that satisfies the voters and reassures us all that the government has at last got things under control? Is it better/lower/different than and from what it was yesterday? Because it's simply a number (rather than 'a direction of travel') does that turn it into a reliable fact? And who says so? Why should we damned well believe it anyway? As Paul Goodwin says, in
Something Doesn't Add Up: Surviving Statistics in a Post-Truth World (Profile Books, 2020), maths seems to offer a tidy distraction to a messy world, confusing objectivity with subjective experience, and implying misleading coincidences.
None of us believe in anything these days. We live in a post-truth era in which opinion counts as truth. Yet, paradoxically, we find we need numbers, for all that we often don't believe them and only some of the time think we understand them. Educationalists stress the importance of teaching young people to budget: it will help them deal with the business of living. Businesses must have financials so as to monitor and account for what they do; government agencies need statistics on family spending, defence and crime, elections and transport, to run the country; scientific testing and medical treatments depend on reliably valid and credible data.
And statistics can be invented, shaped in order to support implausible ideas, presented in ways that deliberately confuse, and draw upon devious or incompetent evidence. Cosmetics adverts cite surveys of x respondents, 95% of whom have found that product Q really did improve their skin. We both believe and disbelieve it – wow! It must be good so I'll give it a try! Yuck! They would say that, wouldn't they! We're presented with surveys of personal spending, or how often people eat takeaway meals, or how much they save for retirement, and they're all so easy to believe.
But who says so, who compiled the data, what is the margin of error, is it a mere coincidence, might it really apply to me? All good questions raised by Anthony Reuben's
Statistical: Ten Easy Ways to Avoid Being Misled by Numbers (Constable, 2019). Could it be, he asks, that the age profile of men in top football teams is correlated to goal scores? And what about ONS forecasts about unemployment?
Being streetwise to the games marketing plays, we accommodate the cognitive dissonance (believe-don't believe) by sliding past the ad and deciding to make up our mind later – if we don't forget all about it. Who is to be believed about the alleged decline in SNP numbers? – down 30% or not? Whether the cure – independence – will save the patient? Are we interested in the cost-benefit crisis over the Scottish bottle bruhaha, or how much it really costs (opportunity costs included) in deciding who is to build ferries to the islands?
Sliding past the claims – and the numbers – is a familiar and useful ploy. It shows we're not suckers, available to scammers and statistical manipulation. But as with tax and insurance, staying safe and keeping on top entails a lot of work. We can only be streetwise if we put in the homework and do the thinking. Being sceptical is not enough, and at worse can be little more than evasion and confusion.
It's a dangerous world out there, as Norm discovered in Michael Blastland and David Spiegelhalter's book
The Norm Chronicles: Stories and Numbers about Danger (Profile, 2013) – fry-ups and the chance of obesity, catching cold, that 12% risk of heart attacks. Did you know, as Norm didn't, that richer nations have more deaths from car accidents? I wonder why.
It was with this in mind that, back in the 1950s in the USA, the writer and statistician Darrell Huff (1913-2001) wrote
How to Lie with Statistics. It was published in 1954, and has become probably the most popular book on statistics ever written. It took off in Britain too, published by Gollancz in 1954, then by Pelican Books in 1973 and by Penguin Books from 1991 onwards.
It's lively, friendly, to the point, short and thoughtful. Some stuff has dated but this is understandable (WW2 was still in readers' thoughts, reference is made to 'Negroes', the workplace is male and the home is for the women, the case studies have period charm). Despite this baggage, it's worth suppressing any thoughts of wokery in order to acknowledge just how useful – and unusual – such a popular work really was.
Statistics as a field of study has always been a domain of specialists – easy with concepts like significance and risk and probability, adept at handling large data sets and extrapolating from them. Darrell Huff's little book offered something to everyman and everywoman, and set in a trend in statistics publishing that continues to this day.
Lively though the book is – and still is today, despite so many style changes and cultural shifts – Huff had a serious intent. He was seriously concerned as an educationalist. He knew that big business like the tobacco industry could invent and manipulate statistics of their sales, and recognised the power of contemporary arguments (being made even by medics at the time) that smoking actually improved your health. Surveys of medical practitioners who said so were regularly produced by the industry. Echoes today persist, as we know from popular studies of 'bad science', 'big pharma' (read Ben Goldacre's fascinating study
Bad Science for more) and post-truth claims (such as Trump's election figures).
The UK edition of
How to Lie with Statistics is decorated with cartoons by Mel Calman (1931-1994), whose sardonic cartoons capture the tone of Huff's argument perfectly. 'Don't be a novelist – be a statistician. Much more scope for the imagination', Calman's introductory cartoon says. Further on in the book, another cartoon shows a man looking in the mirror: 'Every day in every way I get to be more average', capturing that tendency to the mean that every statistician knows and where means-medians-modes are constantly confused.
We have, Paul Goodwin suggests, a rank obsession – that is an obsession to rank things in order (usually of subjective preference, like what has been our best holiday, which cafe does the best bacon buttie) and so are predisposed to believe 'official' stats when they rank, say, healthcare annual figures by QUALYs or imply plausible suggestions like Brexit has succeeded in reducing illegal immigration (it might have done, but then legal immigration really has gone up).
It comes as a shock to most of us who fell in love to imagine that perhaps it's all due to a random distribution. Huff's book went international, often in the US edition illustrated by Irving Geis (1908-1997), the well-known scientific illustrator. The book works because it uncannily picks out just what both confuses and irritates us about statistics. Samples can have built-in biases for instance, and wild claims are often made based on spurious examples. Graphic presentations like bar charts can misrepresent rises and falls of a firm's profitability, costs of a shopping basket for the 'average' family (itself contestable), migration figures, or deaths of salmon from pollution in Scottish rivers, foreshortening time scales, comparing apples with oranges, and over-dramatising pictorials for mere effect.
Huff explores causal relationships too – whether, if there's more of one factor, there is necessarily more of another, and whether there is any causal link between them. We might imagine, for instance, the rise in readership for the crime novels of Stuart MacBride or Val McDermid on the one hand, and the increase in violent crime in Scotland. There is a theory that reading crime fiction actually reduces criminality. Even sampling a survey, assuming the sample is representative, might reveal only that respondents say what they think the samplers want rather than what the real reading patterns.
Post Hoc Rides Again is a revealing chapter of the book. X happens and as a result (so it seems) Y happens – did X cause Y? Coincidence and causation are, rightly, preoccupations of statisticians, and in our everyday life, we constantly wonder whether how and if it really shapes events (eg stats about knife crime could actually increase knife crime, following the logic that the more people who fear it are more likely to arm themselves and overreact when threatened). We stock up on food and more goes off (of course). We worry more about the future and more bad things happen (do they?).
Huff's term for all this statistical mischief is 'statisticulation'. Calculated manipulation by canny players in order to sell things, get you to believe things, persuade you to buy things. He recommends 'talking back to a statistic': ask 'who says so?' (do they have an angle or a bias?); 'how do they know?' (evidence?); 'what's missing?' (for example, reports of cancer are up but that's because more reporting is going on); 'watch for change of subject' (for example, when a false conclusion is made from raw numbers, when AI will replace 50% of the jobs at BT); and finally 'does it make sense?' (for example, the claim that the nurses' strike has increased NHS wait lists for elective surgery by 300%).
How to Lie with Statistics has remained in print ever since 1954. Other books of his can still be found (on Amazon of course) –
How to Figure It and
How to Take a Chance among them. His tone of healthy scepticism and helpful explanation continues in a vigorous literature of current popular statistics. Some of these popular works have been mentioned in this article – like Paul Goodwin's
Something Doesn't Add Up, Anthony Reuben's
Statistical, and
The Norm Chronicles.
Perhaps best known are the books by Tim Harford, like
The Undercover Economist (2005) and the more recent
How to Make the World Add Up! (2020). Tim Harford's Radio 4 programme
More or Less is, like Paul Lewis'
Money Box, essential listening. If only to keep us safe by being streetwise – the message is as much that numbers are central to daily life, even for those of us who take disingenuous pride in being 'mad at maths'. Rob Coulson's
What are the Chances: Probability, Statistics, Ratios and Proportions (2016) is good for younger readers.
All these and many more exist alongside the numerous textbooks on statistics for particular professions (for example, statistics for nurses or for social scientists). Even so, the tradition established by Darrell Huff goes from strength to strength. Confusing and confused though statistics often are, we need them all the time, and need to feel confident that we are being given truthful and reliable statistics.
Writers like Huff help us interpret them and relate them to our own experience and understanding of the world, filtering out the flim-flam, warning us to the marketing tricks, suggesting ways to hit back, but also educating us at the same time. We're always being told that we should be better at numbers, and quite frankly saying you're bad at maths is a cop out.
Brits can take self-deprecation too far, and often do. Believe me – I've carried out a survey on them, and as we know surveys can always be trusted. By the way, did you know that brushing your teeth regularly can delay the onset of dementia, that watching TV for more than five hours will cause blocked arteries in the lungs, and that an obsession with statistics can shorten your life.
Dr Stuart Hannabuss is a writer and reviewer based in Scotland
