Tom Chivers - How to Read Numbers: A Guide to Stats in the News (and Knowing When to Trust Them)

Dedicated to our grandparents, Jean and Peter Chivers

Numbers do not feel. Do not bleed or weep or hope. They do not know bravery or sacrifice. Love and allegiance. At the very apex of callousness, you will find only ones and zeros.

Amie Kaufman, Illuminae

Numbers are cold and unfeeling. People often dislike them for that reason, and its easy to understand why. At the time of writing, newspapers still report on daily death tolls from Covid-19, the pandemic which began to sweep around the world in the first half of 2020. When, in Britain, those daily tolls dropped down to the mere hundreds, where before they had been in their thousands, it felt like a light at the end of the tunnel.

Every one of those people, though, was an individual; they were unique. We can talk about the number of people who died during the pandemic 41,369 in Britain by August, or 28,646 in Spain; or however many will have died around the world once the disease has eventually run its course, if it ever does. But that stark number tells us nothing about those individuals. They all had stories who they were, what they did, who they loved and who loved them back. They will have been mourned.

Representing all those lost lives with a simple number today X people died seems both harsh and stark; it ignores all the grief and heartbreak. It elides all that individuality, all those stories.

But if we hadnt recorded daily death rates, and therefore kept track of the spread of the disease, it is very likely that many more people would have died. Many more unique, individual stories would have been brought to premature ends. We just wouldnt have known how many.

In this book, were going to talk a lot about numbers: about how theyre used in the media, and about how they can go wrong and give misleading impressions. But along the way we will need to remind ourselves that those numbers stand for something. Often they will represent people, or if not people, then things that matter to people.

This is, sort of, a book about maths. You may think that you are bad at maths and you may be worried you wont understand it. You are not alone. Almost everyone seems to think they are bad at maths.

David teaches economics at the University of Durham. His students need to get an A in A-level maths to be admitted to the course, but quite a lot of them still say theyre bad at maths. Tom thinks he is pretty bad at maths, but he has won two awards from the Royal Statistical Society for statistical excellence in journalism (he likes to drop that into conversation from time to time). David, too, sometimes thinks hes bad at maths, and he literally teaches maths to people who are, themselves, good at maths.

You are probably better at maths than you think too. What you might not be particularly good at is mental arithmetic. When we think of people who are good at maths, we tend to think of people like Carol Vorderman or Rachel Riley off Countdown, people who can quickly do sums in their heads. They are good at maths, of course; but if you cant do those sums in your head, it doesnt mean that youre not good at it.

Most of the time, we think of maths as having a right answer and a wrong answer. Again, thats not really the case a lot of the time, at least in the sort of maths were talking about. For instance, take an apparently simple, if horrifying, number: the total death count from Covid-19. What number should we use? Should we talk about confirmed deaths, where the diagnosis was established with a test? Or should we talk about excess deaths, comparing the number of people who have died this year to the statistical average from the last few years? The two will give you very different answers, and which one we should use depends on what question were trying to answer. Neither is wrong; but neither is the correct answer either.

Whats important is understanding why these numbers arent clear-cut, and why sometimes what sounds straightforward is in fact more complicated especially since it is easy to use numbers to mislead or obfuscate, as people (notably but not exclusively politicians) have a tendency to do. These debates affect our lives, and our ability to participate in democracy. By analogy, its hard to have a functioning democratic state without a literate population; we need to be able to understand the policies our leaders are putting in place, in order to vote knowledgeably for or against those leaders when it comes to election time.

But its not enough to only be able to understand words. You also need to have some grasp of numbers. Our news increasingly comes in number form: police-reported crimes go up and down; a nations economy shrinks or grows; the latest figures on deaths and cases from Covid-19 are released. In order to understand the world around us, we may not need to be good at maths, but we do need to understand how numbers are made, how theyre used and how they can go wrong, because otherwise well make bad decisions, as individuals and as a society.

Sometimes, its fairly clear how misunderstanding the statistics could lead to bad decisions: if we dont know how many people have Covid-19, for instance, then we cant judge the appropriate response. In others such as those well discuss elsewhere in this book, cases like whether or not bacon causes cancer, or whether or not drinking fizzy drinks makes you violent it might not be so obvious. But we all use these numbers, consciously or otherwise, to help us navigate the world. Drinking red wine, taking exercise, investing money we do these things on the basis that we think their benefits (to pleasure, health or wealth) outweigh their risks. We need to know what those benefits and risks are, and how big they are, if were going to make those decisions wisely. Often, were getting our understanding of those benefits and risks from the news.

You cant rely on news organisations to give you those numbers straight, without exaggeration or cherry-picking. Thats not necessarily because theyre trying to deceive you; its just because they are trying to report exciting, interesting or shocking things, so that you buy their papers or watch their shows. Its also because they and we crave narrative: stories in which problems have identifiable causes and solutions. And if youre selecting numbers by how exciting, interesting or shocking they are, youre likely to pick quite a lot that are wrong or misleading.

Also, while journalists are usually clever and (despite the stereotype) well intentioned, theyre not traditionally very good with numbers. That means the numbers you read in the news tend to be wrong. Not always, but often enough that it is wise to be wary.

Fortunately, the ways numbers get misrepresented are often predictable: for instance, they can be cherry-picked, by taking an outlier or using a particular starting point, or by chopping up the data repeatedly until you find something; they can be exaggerated, by using a percentage increase rather than the absolute change; they can be used to suggest causation, when really its just a correlation; and many other ways. This book will arm you with the tools you need to spot a few of them.

We dont want to suggest that you cant ever trust any number you read. We just want to help you make better decisions about which ones to trust, and when.

Weve tried to keep the maths to a minimum. Almost everything that looks like an equation has been cut out and put into boxes outside the main text; you can read them if you like, but if you dont it wont limit your understanding.