The economist John Maynard Keynes said that when the facts changed, he changed his mind. Politicians at loose with statistics are tempted to a different tack: changing the facts. "Lies, damned lies and statistics" expresses a cynical truth that citizens all understand.

And yet, despite sharing the scorn for statistical sleights of hand, we believe that this saying is one of the worst to infect public argument.

Its fault is to encourage disengagement. If we have nothing better to show than cynicism, we resign ourselves to powerlessness, and turn away, understanding nothing, griping about everything.

Andrew Dilnot is principal of St Hugh's College, Oxford and former director of the Institute of Fiscal Studies

Michael Blastland is a journalist and radio producer who makes programmes for BBC Radio 4. He is the author of Joe: The Only Boy in the World (Profile, 2007)

Andrew Dilnot & Michael Blastland are the co-authors of The Tiger That Isn't: Seeing Through a World of Numbers (Profile, 2007), available from Amazon here

The wiser alternative, the engaged response, is to find the means of seeing through what the politicians are up to, some way of challenging and understanding the numbers. If we fail, the debate on the big political issues becomes meaningless - on everything from health risks, foreign aid, government spending, social change, to targets, league-tables, comparisons, surveys and samples, about hospitals, schools, migrants, crime, and climate change. To dismiss numbers, whether through fear or loathing, is to give up the game on almost every cause you love or hate. For numbers are now, whether we like it or not, for good or ill, the dominant language of public argument.

So what can citizens do? The first task is to begin understand the tricks played on us. Fortunately, this is often easier than it looks, and acquiring a more accurate measure of a political statement can sometimes be preposterously easy. Here are three such examples of how politicians' rhetoric can deceive, and recommendations for a way of responding to it.

The scale of words

The first such ploy is over size. Faced with a few zeros on the end of a number, many of us are quickly confused, and even readily impressed. Politicians enjoy playing to that tendency, and throw large numbers about with bravado.

So pause a moment. Then offer a challenge that appears naïve, a question of banal simplicity, but one that touches the most underrated problem with the way numbers are produced and consumed: "is that a big number?"

Though it will strike some as painfully obvious, the problem is persistent, and the media frequently taken in.

Take the agreement reached by the G8 on developing-country debt at its Gleneagles summit in July 2005. At a face-value of $50 billion, it initially appeared a gesture of startling magnitude, and was indeed helpful to some countries. But ask the question: was it a big number?

$50 billion was the total stock of debt, not the annual cost to the G8, so a better measure would be to say that the G8 wrote off annual repayments of about $1.5 billion a year, divided between eight of the richest countries of the world. Put that into pounds sterling and it equals about £750 million. Conveniently, the population of the G8 is also about 750 million, making Gleneagles equivalent to £1 per person, per year... or 2p a week. Though since at least some of the money came from existing planned aid budgets, it was probably less than that.

The principle here is that numbers relating to the developing world, the G8, or even a single country, will all, most likely, be in the millions, billions, or even trillions. They trail zeros simply because there are an awful lot of people about in such huge economies or large sweeps of the globe. The simple, sensible way to get a number into proportion, indeed the only way to begin to know if it is genuinely big or small, is to divide it by the whole population it affects or represents. On a global or national scale, it's hard to make sense of the numbers. Convert them to a personal one, and it's easier.

The reality gap

A second signal to watch for is how well politicians' grand rhetorical promises are supported by the data. This simple check should not be the kind to escape media attention, but it often does. The question, "does the data match the promise?", may seem in one sense trivial, but it can be surprisingly powerful.

So when Gordon Brown, as Britain's chancellor of the exchequer, said in March 2006 that the government's intention was to raise annual education spending on state-school pupils (about £5,000 per head) to the average level of spending for private-school pupils (about £8,000 per head), it was greeted as an act of bold significance as he announced the first stage in that process - an additional £600 per head of already planned and genuinely new spending.

Also in openDemocracy on statistics, media and politics:

* Jean Seaton, "The numbers game: death, media, and the public" (6 October 2005)

* Mary Dejevsky, "Russia: what demographic crisis?" (27 September 2006)

* Michel Thieren, "Deaths in Iraq: how many, and why it matters" (18 October 2006)

* Phil Gunson, "Bolivarian myths and legends" (1 December 2006)

* Gunnar Heinsohn, "Islamism and war: the demographics of rage" (16 July 2007)

Check the ambition against the declared long-term spending plans, however, and it turns out the government is beginning to slow rapidly from the high rates of public-spending growth of the last few years. At a rate implied by current plans, it would take until about 2018 for the government's aim to be realised, assuming - and this is the nub - that private-school spending per head stayed still. Unsurprisingly, it doesn't. Even at the rapid rates of rising state- education spending since 2001 in Britain, the gap between state and private schools has not closed. Yet in future, this rate of increase on the state side is likely to slow down. The words do not match the numbers.

To compare rhetoric with data is a task we should be able to expect of any self-respecting newspaper or broadcaster. If they don't do it, then we must withhold judgment on the politics, however great the promises.

A respect agenda

The third trick to look for is one of comparison. The question to ask is: "are politicians comparing like with like?" This is a question for whenever we are offered a league table or international comparison. And we are offered a growing multitude of them. Being top, or bottom, is a boast for any government and ammunition for every opposition. But it is seldom what it seems. A quick example makes the point

Christopher Pollitt of Erasmus University, on a visit to Finland, was surprised to discover a category of prison - open prisons - with no escapes, ever. "You never have anyone escape from an open prison?" he asked an official. "Oh no, but because they are open prisons we don't call it an escape, we classify them as absent without leave."

Imagine such differences of definition or value when we are offered, as we are, rankings of countries' whole healthcare systems, and where what constitutes a good system is in many ways a political judgment, not at all a simple metric.

A recent home secretary in Britain was responsible for another example of bogus comparison: he managed to compare released former prisoners with those currently electronically tagged, to claim that since the tagged commit fewer crimes, measured over a shorter period, tagging is better at preventing reoffending.

But either you are let out early wearing a tag or you are not let out until later. So the alternative to tagging is jail, not liberty. That means the proper comparison group for the tagged is the incarcerated, either when both are serving sentence, or when both are fully free, not when one is still serving sentence and monitored, while the other is out and about. Like with like?

Often, such maneouvres are accompanied by a huffing-and-puffing insistence from politicians about their right to interpret the figures as they see them.

But this is more serious than the expression of a point of view. It is about having respect for data over wishful thinking, respect for the public, and for themselves. If you'd prefer to be flattered by bogus numbers, to believe that the world changes when you play statistical games, or at least to act as if it does, you are, let's be blunt, delusional and dangerous.

The citizen trying to come to terms with the blizzard of numbers that often now passes for political argument can easily feel daunted. But the principles we need in order to begin to see through the tricks politicians and others play are often relatively straightforward, if we can bear to apply them.

The great advantage of a more engaged reaction to numbers is that it raises the political cost of abusing them. So the first improvement to public argument with statistics is most likely to come from us, citizens and voters. Let's ask these three questions, consistently and more often.