Is £300m really a lot of money?

September 7, 2007

Not if it's spent on a million children over five years. But journalists and politicians don't do the sums and swallow such absurdities. Andrew Dilnot pleads for more numeracy

The numbers nerd sped across London on his bicycle, almost late for his train. Hot and bothered, he slumped into a seat seconds before the train was due to leave. Twenty minutes later, the train was still in the station, and tempers among passengers began to fray.

Sitting opposite the nerd was a poet and lecturer in English literature, who was particularly cross about the state of the railways, the roads, indeed the whole transport infrastructure. "Why doesn't anything work any more? What on earth has gone wrong?" is a polite summary of what he had to say.

The nerd had a ready response. "As it happens, I have some very interesting figures about that here in my bag: numbers and graphs." And it was true; the numbers were relevant, surprising and persuasive. The poet's reply, given the vehemence of his views, was lamentable.

"I don't do numbers," he said. "I'm not interested."

He'd heard quite enough figures, thank you. He didn't understand them and didn't see why he should try. His objection was final. There was no piece of evidence that would talk him out of his opinion as he held fast to what he thought he already knew.

But how can one make sense of what has happened to public transport unless one knows about the real level of investment over the years? The poet's stance seemed to mask fear, but it also expressed a belief that it was intellectually acceptable to ignore all that is quantifiable.

However, it should be just as unpardonable to say "I don't do numbers" as "I don't see the point in fiction".

This isn't a struggle for intellectual supremacy but a recognition that numbers are a vital part of our shared language and need to be understood as much as any other part. It is also an argument, as Michael Blastland and I demonstrate in detail in our book The Tiger That Isn't , that this is often a good deal simpler than it looks.

Of course, those who love numbers have been guilty of failing to take care to make what they say comprehensible and of allowing too much numerical nonsense to pass uncorrected. But forming an opinion in wilful ignorance of the numbers is only likely to lead to a row. You can sound off all you like if you never have to be reconciled to evidence. It is also an attitude - whenever it infects decision-making, as it often does - that we all pay for in bad policy and damaged lives.

Numbers matter. Some people find them bamboozling, and those who seem fluent in this language sometimes use it to deceive. But we can also be optimistic about the possibility of seeing through the nonsense, hopeful that anyone can feel less intimidated and even empowered. There are ways for our lecturer on the train (or at the lectern) to wield less bombast and more authority, and - what's most surprising - it is often easy to do.

That's just as well, because the failure to treat numbers seriously can be laughable.

Joel Best, an American sociologist, is fond of quoting from a dissertation prospectus that landed on his desk from a graduate student. It was about gun rime. The student wrote: "Every year since 1950 the number of American children gunned down has doubled." Best assumed a mistake in copying the claim from its source. In fact, the line had been lifted accurately from a scholarly journal. This quotation, he says, wins his nomination for the worst social statistic ever.

What makes the statistic so bad, as Best points out, is that even if we assume the number of children "gunned down in America" in 1950 was 1, by 1965 it would have been 32,768, in 1970 it would have passed 1 million and reached 1 billion in 1980. By 1995, when the article was published, the number of child victims "gunned down" each year would have surpassed 35 trillion, or 35,000,000,000,000.

Does it matter that the general thought - gun crime is going up - is let down by a calculating error? Yes, because it gives the impression of carelessness towards evidence in favour of a loose prejudice about what the truth will probably be like.

Here is an extraordinarily simple principle: doubling a number repeatedly will increase its size extremely quickly. It isn't hard to get right. You look a fool if you don't.

For those besieged by performance measures and targets, where the accountants seem to have taken over the academy, the case for numbers is often unwelcome.

What's more, some feel that numbers have become a false god and that to be guided by them is often delusional. Close to home, they cite as a recent example publication within the research assessment exercise, which seems to have created a transfer market between universities for those academics whose numbers look good, but with debatable effects on performance.

And while it is a powerful notion that the world is, in some essentialist, Platonic fashion, mathematical, there are plenty of academics who would rather side with the romantic claims of poets such as Blake, Shelley, Coleridge and Wordsworth. That tradition asserted, and still asserts, that what they would regard as artificial and analytical modes of reasoning are inadequate: knowing and understanding are achieved through life, inspiration and sympathy.

Numbers have their limitations. But this simple fact seems often to give way to a ludicrous polarity of expectations, sometimes in the same head at the same time. On the one hand, they are derided; on the other, they are used with an absurd degree of certainty, as if they are a shortcut to absolute truth. The unsurprising fact is that neither caricature is accurate, and the less certain middle course is more realistic. Numbers can be powerfully useful, if not definitive; they can help us towards an answer, if not always give it; they are instructive evidence, if not judgment. We are fools to ignore them.

The difficulty is that, without certainty one way or another, whether damning or fawning, we require a bit of thinking and a bit of judgment. But it really is often only a bit: the effort required is frequently trivial. For example, try this absurdly simple question as a means of challenging numerical claims: "Is that a big number?"

Do not be fooled by its apparent naivety. Silliness over size is one of the most persistent and underrated problems in the way we produce and consume numbers. Take the claim by the Labour Government in the late 1990s that it would provide an extra million childcare places for five years with £300 million of new spending. Three hundred million? Is that a big number? No one at the time seemed in any doubt of its immensity. But £300 million divided by a million places is £300 per place. Over five years, that's £60 a year, or a bit more than £1 per place per week. Could you buy childcare for a bit more than £1 a week? Britain's entire media and political classes discussed the policy as if you could. Does political debate often really not know what "big" is? Apparently not, nor does it seem to care that it does not know. When Michael and I asked the head of one of Britain's largest news organisations why journalists had not spotted the absurdity, he acknowledged that there was an absurdity to spot, but said he wasn't sure that was their job.

Treating a number like a Colossus on the basis that it has some zeros at the end of it will strike many readers as risible, but it happens, often. What's odd is that this mistake was only possible because no one took the trouble to think about these numbers on a human scale. Yet the human scale is one with which we all ought to be familiar. There is nothing the least bit intimidating or difficult about this calculation; it is simply a case of having the imagination to do it and remembering how big we are. Can a question such as "Is that a big number?" really be key to unlocking numbers and the policies that depend on them? Often, it can.

Statistics is not a trainspotter collection of facts. It is about making what subtle sense we can of whatever evidence we can gather. That is the objective of all research and intellectual endeavour. Those who do it with numbers are often detectives of quiet ingenuity who know the perils of trying to capture life this way far better than some of those who ridicule them, and they work tirelessly to try to spot the complexities and improve.

Is lack of appreciation of this getting worse in higher education? Without proper statistical evidence, how could we possibly say? But we are aware of some instances where there are grounds for concern. The Economic and Social Research Council recently questioned the quality of numeracy in sociology as an older generation of quantitative sociologists moves on. That's not a criticism of qualitative work, which can be excellent, yet profound observations about what is going on within, say, a set of relationships or an organisation are of unknown value unless you know whether they are unique or widespread - unless, in other words, you know their statistical relevance. It seems, according to the ESRC, that statistical options are less attractive to today's students, and so the mathematical content of courses has sometimes been reduced in terms of quantity or difficulty.

Even the reputation of higher education itself might depend on treating the numbers with care. The White Paper on The Future of Higher Education says this (on page 17) about fair access: "Higher education entrants by social class groups (1960 2000): Those from the top three social classes are almost three times as likely to enter higher education as those from the bottom three. (The) figure below is even more disturbing, because it shows that the gap has widened."

"More disturbing"? Imagine that these two lines represent heights of people at different times. Are the heights more glaringly different in 1960 or in 2000? Are these people really becoming less alike? This is not a hard principle. We are simply turning an absolute comparison into a relative one, more like the kind of comparison you would instinctively make if you could find a way of visualising the problem. Using that insight, we might now want to say that if the class difference is "almost" three times in 2000, as the White Paper likes to put it, it was seven times in 1960. Is that trend, measured in its own preferred terms, "disturbing"?

In relative terms, the gap between your chances of going to university if you are poor, compared to the chance of going if you are from the top three classes, has not widened, it has narrowed substantially. And while the intake from the top half has gone up by 70 per cent, lower-class intake has gone up by 600 per cent.

The aim is not to show that anything can be proved with statistics. It is to show that "the gap has widened" is a crude and limited reading of the numbers, based perhaps on a pre-existing belief. The more subtle truth is that in some ways it has widened, in others it has narrowed. None of these numbers tells us what to do next or whether this is something that ought to worry us. Those judgments come partly from elsewhere. Numbers are best understood not as a political plaything, nor as giving absolute answers effortlessly, but as information.

And information is not knowledge, as the old saying goes; we need to apply some intelligence to it and take the trouble to understand how it can be interpreted. We could make a start by learning the principles on which numbers work, which are often less abstract or alien to ordinary life than people suspect. It can often help to think about numbers in terms of such everyday notions as relative height, or to convert apparently big numbers on to a more familiar human scale. Often, all this takes is an application of what is known already, from life. And there is no alternative, because knowledge without information is a fraud.

Do not dismiss numbers as rubbish, or we will be supremely ignorant, however assertive on the train. Take a very few pains to become acquainted with the way they work, and they will reward you.

Andrew Dilnot is principal of St Hugh's College, Oxford, and co-author (with Michael Blastland) of The Tiger That Isn't: Seeing through a World of Numbers , published by Profile Books, £12.99.

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