'Every journalist should get paid leave to read and reread The Tiger That Isn't until they've understood how they are being spun' – New Scientist
'Personal and practical … might even cause a social revolution' – Independent
'This very elegant book constantly sparks “Aha!” moments as it interrogates the way numbers are handled and mishandled by politicians and the media' – Steven Poole, Guardian
'A very funny book … this is one of those maths books that claims to be self-help, and on the evidence presented here, we are in dire need of it' – Daily Telegraph
'This delightful book should be compulsory reading for everyone responsible for presenting data and for everyone who consumes it' – Sunday Telegraph
'Clear-eyed and concise' – The Times
'A book about numbers and how to interpret them doesn't sound like interesting bedtime reading. Yet in the hands of Michael Blastland and Andrew Dilnot, that is what it becomes … a reliable guide to a treacherous subject, giving its readers the mental ammunition to make sense of official claims. That it manages to make them laugh at the same time is a rare and welcome feat' – Economist
'I have sat with Andrew Dilnot in many television studios and watched with awe as he eviscerates politicians who are trying to distort the figures to suit themselves. He is ruthless in exposing the lies that statistics can seem to support. This witty and fascinating book explains to us laymen how to make sense of numbers and how we can avoid having the wool pulled over our eyes. Invaluable' – David Dimbleby
'A very fine book' – Rod Liddle, Spectator
'With an appealing combination of dry wit and numerate common sense, the authors succeed in seeing off many “tigers”' – Financial Times
'An eye-opening lightning tour through the daily use and abuse of “killer facts”: the way that statistics can beguile, distort and mislead … This is essential reading for anyone interested in politics, economics or current affairs' – Scotland on Sunday
'Brilliant excursion into the way we misuse and misunderstand numbers and statistics, and how to see around it … A great experience. Very readable, always informative and often entertaining, this is a book that every politician, civil servant and, well, everyone should read' – popularscience.co.uk
'A book that is both illuminating and highly entertaining' – Geoff Barton, Times Educational Supplement
'The arguments are fascinating and the examples accessible and relevant. Not only for mathematicians, but for everyone who reads the newspaper or watches the news. Journalists would be advised to read it closely and maths or stats teachers will find a wealth of real-life examples for direct use in the classroom' – Plus, online maths magazine
'The Tiger That Isn't is that rarest of things: a compelling book about statistics. The book does a superb job at reminding us that numbers can only go so far in describing our very messy, very complicated, very human world' – readysteadybook.com
'This book is a valiant attempt to encourage healthy scepticism about statistics, against a culture in which both news producers and consumers like extreme possibilities more than likely ones' – New Statesman
'How to use the knowledge we already possess to understand numbers and make sense of the world around us' – Mervyn King, Governor of the Bank of England
'If every politician and journalist were required to read this engaging and eye-opening book before embarking on their career, we would live in a wiser, better-governed world' – Matthew Taylor, Chief Executive of the Royal Society of Arts, former chief advisor to the Prime Minister
'Illuminating and comprehensible to even the mathematically challenged' – thefirstpost.co.uk
'Should be compulsory reading. It teaches critical thinking about numbers and what they mean in a hugely entertaining way' – enlightenmenteconomics.com
MICHAEL BLASTLAND is a writer and broadcaster, and was the creator of More or Less and the author of Joe: The Only Boy in the World, also published by Profile.
ANDREW DILNOT presented More or Less on BBC Radio 4. He is Principal of St Hugh's College, Oxford, and formerly the Director of the Institute for Fiscal Studies.
The Tiger That Isn't
Seeing Through a World of Numbers
MICHAEL BLASTLAND
&
ANDREW DILNOT
This expanded edition published in 2008
First published in Great Britain in 2007 by
PROFILE BOOKS LTD
3A Exmouth House
Pine Street
Exmouth Market
London EC1R 0JH
www.Profilebooks.com
Copyright © Michael Blastland and Andrew Dilnot, 2007, 2008
10 9 8 7 6 5 4 3 2 1
Typeset in Palatino by MacGuru Ltd
[email protected]
Printed and bound in Great Britain by
Bookmarque Ltd, Croydon, Surrey
The moral right of the authors has been asserted.
All rights reserved. Without limiting the rights under copyright reserved above, no part of this publication may be reproduced, stored or introduced into a retrieval system, or transmitted, in any form or by any means (electronic, mechanical, photocopying, recording or otherwise), without the prior written permission of both the copyright owner and the publisher of this book.
A CIP catalogue record for this book is available from the British Library.
eISBN 978-1-84668-111-0
Contents
Note on the New Edition
Introduction
1 Counting: Use Mushy Peas
2 Size: It's Personal
3 Chance: The Tiger That Isn't
4 Up and Down: A Man and his Dog
5 Averages: The White Rainbow
6 Targets: The Whole Elephant
7 Risk: Bring Home the Bacon
8 Sampling: Drinking from a Fire Hose
9 Data: Know the Unknowns
10 Shock Figures: Wayward Tee Shots
11 Comparison: Mind the Gap
12 Correlation: Think Twice
Finally …
Acknowledgements
Further Reading
To Catherine, Katey, Rosie,
Cait, Julia and Joe
Note on the New Edition
This expanded and updated edition includes almost all the material from the original, together with a new chapter, numerous new examples (including a few to show that it is not only the UK that enjoys a culture rich in the murderous use of numbers), some new tricks, new arguments and old ones sharpened (we hope) by experience, and, finally, a quick checklist at the end. It also allows us an opportunity to make one new claim: that though the book is all about the way numbers are used, it is best thought of as being not about numbers at all, certainly not about numbers for their own sake. The kind of numbers we come across every day, the kind examined here, are always a means to an end; that end being a better understanding of life.
Michael B and Andrew D
April 2008
Introduction
Numbers saturate the news, politics, life. For good or ill, they are today's pre-eminent public language – and those who speak it rule. Quick and cool, numbers often seem to have conquered fact.
But they are also hated, often for the same reasons. They can bamboozle not enlighten, terrorise not guide, and all too easily end up abused and distrusted.
Potent but shifty, the role of numbers is frighteningly ambiguous. How can we see our way through them?
First, relax …
We all know more than we think we do. We have been beautifully conditioned to make sense of numbers, believe it or not, by our own experience. This is the radical premise of this book – that readers have no need to throw up their hands in fea
r or contempt, if only they see how much they know already.
Numbers can make sense of a world otherwise too vast and intricate to get into proportion. They have their limitations, no doubt, but are sometimes, for some tasks, unbeatable. That is, if used properly.
So although there is a rich store of mischief and scandal here, it is not to discredit numbers themselves. There are lies and damned lies in statistics, for sure, but scorning numbers is no answer. For that is to give up the game on every political, economic or social argument you follow, every cause you love or hate.
Our aim is rather to bring numbers back to earth, not only by uncovering the tricks of the trade – the multiple counting, dodgy graphs, sneaky start dates and funny scales – there have been exposés of that kind of duplicity before, though there are gems in the stories that follow; nor by relying on arcane statistical techniques, brilliant though those often are. Instead, wherever possible, we offer images from life – self, experience, prompts to the imagination – to show how to cut through to what matters. It is all there; all of us possess most of it already, this basic mastery of the principles that govern the way numbers work. It can be shared, we think, even by those who once found maths a cobwebbed mystery.
But simple does not mean trivial; simple numbers help answer imperative questions. Do we know what people earn and owe, who is rich and who poor? Is that government spending promise worth a dime? Who lives and who dies by government targets? Are those league tables honest? Do speed cameras save lives? What about that survey of teenage offending, the 1 in 4 who do this, the 6 per cent increase in risk for women who do that, inflation, Iraqi war dead, HIV/Aids cases, how one country compares with another, the decline of fish stocks, the threat of cancer, the pension time bomb, NHS budgets, waste and waiting times, Third World debt, UK debt, predictions of global warming? Hardly a subject is mentioned these days without measurements, quantifications, forecasts, rankings, statistics, targets, numbers of every variety; they are ubiquitous, and often disputed. If we are the least bit serious about any of them, we should attempt to get the numbers straight.
This means taking on lofty critics. Too many find it is easier to distrust numbers wholesale, affecting disdain, than get to grips with them. When a well-known writer explained to us that he had heard quite enough numbers, thank you – he didn't understand them and didn't see why he should – his objection seemed to us to mask fear. Jealous of his prejudices or the few scraps of numerical litter he already possessed, he turned up his nose at evidence in case it proved inconvenient. Everyone pays for this attitude in bad policy, bad government, gobblede-gook news, and it ends in lost chances and screwed-up lives.
Another dragon better slain is the attitude that, if numbers cannot deliver the whole truth straight off, they are all just opinion. That damns them with unreasonable expectation. One of the few things we say with certainty is that some of the numbers in this book are wrong. Those who expect certainty might as well leave real life behind. Everyone is making their way precariously through the world of numbers, no single number offers instant enlightenment, life is not like that and numbers won't be either.
Still others blame statistical bean-counters for a kind of crass reductionism, and think they, with subtlety and sensitivity, know better. There is sometimes something in this, but just as often it is the other way round. Most statisticians know the limits of any human attempt to capture life in data – they have tried, after all. Statistics is far from the dry collection of facts; it is the science of making what subtle sense of the facts we can. No science could be more necessary, and those who do it are often detectives of quiet ingenuity. It is others, snatching at numbers, brash or over-confident, who are more naively out of touch.
So we should shun the extremes of cynicism or fear, on the one hand, and number idolatry on the other, and get on with doing what we can. And we can do a great deal.
Most of what is here is already used and understood in some part of their lives by almost everyone; we all apply the principles, we already understand the ideas. Everyone recognises, for example, the folly of mistaking one big wave for a rising tide and, since we can do that, perhaps to our surprise, we can unravel arguments about whether speed cameras really save lives or cut accidents. In life, we would see – of course we would see – the way that falling rice scatters and, because we can see it, we can also make simple sense of the numbers behind cancer clusters. We know the vibrancy of the colours of the rainbow and we know what we would lack if we combined them to form a bland white band in the sky. Knowing this can, as we will see, show us what an average can conceal and what it can illuminate – average income, for example. Many know from ready experience what it costs to buy childcare, and so they can know whether government spending on childcare is big or small. We are, each one of us, the obvious and ideal measure of the policies aimed at us. These things we know. And each can be a model for the way numbers work. All we seek to do is reconnect what anyone can know with what now seems mysterious, reconnect numbers with images and experience from life, such that, if we have done our job, what once was baffling or intimidating will become transparent.
What follows will not be found in a textbook: even the choice and arrangement of subjects would look odd to a specialist, let alone the way they are presented. Good. This is a book from the point of view of the consumer of numbers. It is short and to the point. Each chapter starts with what we see as the nub of the matter: a principle, or a vivid image. Wipe the mental slate clean of anxiety or fuzziness and inscribe instead these ideas, keep each motif in mind while reading, see how they work in practice from the stories we tell. In this way we hope to light the path towards clarity and confidence.
The alignment of power and abuse is not unique to numbers, but it is just possible that it could be uniquely challenged, and the powerless become powerful. Here's how.
1
Counting: Use Mushy Peas
Counting is easy when you don't have to count anything with it: 1 , 2 , 3 … it could go on for ever, precise, regular and blissfully abstract. This is how children learn to count in the nursery, at teacher's knee.
But for grown-ups putting counting to use in the wider world, it has to lose that innocence. The difference is between counting, which is easy, and counting something, which is anything but. Some find this confusing, and struggle to put the childhood ideal behind them.
But life is more complicated than a number. The first is a melée, the other a box. That is why, when counting something, we have to squash it into a shape that fits the numbers. (In an ideal world, the process would be the other way round, so that numbers described life, not bullied it). Worst of all, the fact that all this was a struggle is forgotten. To avoid this mistake, and master counting in real life, renounce the memory of the classroom and follow a better guide: mushy peas.
'Yob Britain! 1 in 4 teen boys is a criminal!' said headlines in January 2005. '1 in 4 teen boys claims they have done a robbery, burglary, assault or sold drugs.' As another newspaper put it: 'Welcome to Yob UK!'
A survey of teenage boys suggested Britain had nurtured a breed of thugs, thieves and pushers. Newspapers mourned parenting or civilisation, politicians held their heads in their hands in woe and the survey itself really did say that 1 in 4 teenage boys was a 'prolific or serious offender'.
A competent survey, which this was, asking boys what they'd been up to and then counting the answers, ought to be straightforward (assuming the boys told the truth). Counting, after all, is simple enough for the nursery, where one number follows another, each distinct and all units consistent: 1, 2, 3 …
The common, unconscious assumption is that this child's-play model of counting still applies, that it is a model with iron clarity in which numbers tick over like clockwork to reach their total. But when counting anything that matters in our social or political world, although we act as if the simple rules apply, they do not, they cannot, and to behave otherwise is to indulge a childish fantasy of orderliness in a wo
rld of windblown adult jumble.
It is, for a start, a fundamental of almost any statistic that, in order to produce it, something somewhere has been defined and identified. Never underestimate how much nuisance that small practical detail can cause.
First, it has to be agreed what to count. What is so hard about that? Take the laughably simple example of three sheep in a field:
What do we want to count?
Sheep.
How many are there?
Three.
Counting is seldom straightforward. How many centenarians are there in the United States, for example? You don't know? Neither do we. But someone does, don't they? They just go out and count 'em, surely?
'How old are you?'
'101'
'Thank you.' And they tick the box.
We often talk of social statistics, especially those that seem as straightforward as age, as if there were a bureaucrat poised with a clipboard, peering through every window, counting; or, better still, some kind of machine to do it for them. The unsurprising truth is that for many of the statistics we take for granted there is no such bureaucrat, no machine, no easy count, we do not all clock in, or out, in order to be recorded, there is no roll call for each of our daily activities, no nursery 1, 2, 3.
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