The Tiger That Isn't

by Andrew Dilnot

  Whatever use these middles have as a description of values, they are hopeless as a classification of where people stand within the rainbow variety of incomes or economic circumstances.

  In the United States, the household truly in the middle of the income distribution (known as the median) has income of about $48,000 (£24,000) before taxes (in 2006). (If two people in a household have incomes, statisticians add them together, and call it household income.) The middle 20 per cent of house-holds are between about $38,000 (£19,000) and about $60,000 (£30,000). The middle 60 per cent – to stretch the membership – are between about $20,000 (£10,000) and $97,000 (£48,500).

  Should all these households belong in the same economic and social bracket? How much in common does one family have with another when its income is nearly five times higher? The Democratic Presidential contender John Edwards said in 2007 that even $200,000 (£100,000) was middle class. Hilary Clinton topped that, saying the middle class went up to $250,000 (£125,000). $250,000 a year would take a household into the top 3 per cent, more than four times the income of the household truly in the middle and twelve times the income of some households in the middle 60 per cent. When concepts become this elastic, they belong to comic-book superheroes.

  Our sense of the middle, of what's average, depends on who is around us, on our neighbours or colleagues. We slip into thinking that what is typical here is typical everywhere, even if we live in a mews house in Kensington.

  Our sense of where we fit is also heavily weighted, in the case of incomes, by the feeling that our own is nothing special, even when, by comparison, it is extremely high. Both influences mean we are poor judges of the income rainbow, and have a generally hopeless sense of what is typical. Most media comment about the middle, economically speaking, hasn't the faintest idea where it is.

  In the 2005 general election, Charles Kennedy, then leader of the Liberal Democrats, found himself ducking the notion of the average income like a sword of truth, swung in defence of the ordinary citizen.

  His party had said we should get rid of council tax, replacing it with a local income tax. Some – the richest – would pay more, most would pay less. Then came the inevitable question: how much did you have to earn before local income tax raised your bill? As Charles Kennedy stumbled, at a loss for the accurate figure, the journalists at the press conference sniffed their story. The answer, when it came in a scribbled note from an adviser, gave the Liberal Democrats their roughest ride of the campaign: A little over £40,000 per household.

  The problem was that this figure turned out to be about twice average earnings. To take the example every news outlet seized, a firefighter on average earnings living with a teacher on average earnings would pay more under the Liberal Democrats' proposed new system.

  The campaign trail was suddenly hazardous for Charles Kennedy, the questions and coverage indignant: what was fair about a system that hit people on average earnings? If it is going to be more expensive for the average, how can you possibly say most people will be better off? So, the Lib Dems are hitting Middle England? And so on.

  There might be other good reasons for opposing the policy, but there is also such a ragbag of misconceptions about the idea that lay at the root of the criticism – the average earner – that it is hard to know where to start.

  As with pregnancy, or American tax cuts and tax rises, so with income: the average is not in the middle, and more people are on one side than the other. A household with two individuals each on average individual earnings is not in the middle of the household income distribution, it is, in fact, in the top quarter; it is, if you are wise to the rainbow distribution of incomes and not cocooned by the even larger salary of a national newspaper commentator, to be relatively rich. This is for two reasons: first, because in this case the average is pulled well beyond the middle by a relatively small number of enormously high incomes; second, because it is relatively unusual for both members of a couple to have average earnings. In most cases where one half of a couple has average earnings, the other will earn significantly less. It might surprise us to find that a teacher and a firefighter living together are relatively rich, but only if we do not know how they compare with everyone else, don't know where they are in the distribution, and have ignored the colours of the income rainbow.

  The next chart shows the distribution of income in the UK for childless couples – two people living together, their incomes combined. Half have net incomes (after tax and benefits) of less than £18,800 (marked as the median), but the average for the group is around £23,000, pulled up by the relatively small numbers of very high incomes. That is, most are more than 18 per cent below average. The highest incomes are far too high to fit on the chart, which would need to stretch many feet to the right of the edge of the page to accommodate them. The most common income is around £14,000, about 40 per cent below average. More people in this category have incomes at this level than any other. If that is a shock, it is probably due to the familiarity of the much higher and more widely quoted average. Middle Britain seems to exist wherever politicians or media want it to, conjured up to give a respectable home to their prejudices, regardless of the economic facts, or what is truly typical.

  Figure 7 Who earns what?

  A Dutch economist, Jan Pen, famously imagined a procession of the world's population where people were as tall as they were rich, everyone's height proportional to their wealth, this time, rather than income. A person of average wealth would be of average height. The procession starts with the poorest (and shortest) person first and ends, one hour later, with the richest (and tallest).

  Not until twenty minutes into the procession do we see anyone. So far, they've had either negative net worth (owing more than they own) or no wealth at all, and so have no height. It's a full thirty minutes before we begin to see dwarfs about six inches tall.

  And the dwarfs keep coming. It is not until forty-eight minutes have passed that we see the first person of average height and average wealth, when more than three quarters of the world's population has already gone by.

  So what delays the average so long after the majority have passed? The answer lies in the effect of the people who come next. 'In the last few minutes,' wrote Pen, 'giants loom up … a lawyer, not exceptionally successful, eighteen feet tall.' As the hour approaches, the very last people in the procession are so tall we can't see their heads. Last of all, said Pen (at a time before the fully formed fortunes of Bill Gates and Warren Buffett), we see John Paul Getty. His height is breathtaking, perhaps ten miles, perhaps twice as much.

  One millionaire can shift the average more than many hundreds of poor people, one billionaire a thousand times more. They have this effect to the extent that 80 per cent of the world's population has less than average.

  In everyday speech, 'average' is a word meaning low or disdained. With incomes, however, the average is relatively high. The colloquial use, being blunt, thoughtless and bordering on a term of abuse, distorts the statistical one, which might, according to the distribution, be high, or low, or in the middle, or altogether irrelevant. If only one thought survives about averages, let it be that they are not necessarily anywhere near the middle, nor representative of what's typical, and that places often called 'the middle' by politicians or the media may be far removed. These ideas have been lazily hitched together for too long. It is time for divorce. We must have a little background before we know the real relationship.

  The writer and palaeontologist Stephen Jay Gould had special reason to find out. Diagnosed with abdominal mesothelioma in 1982, a rare and highly dangerous cancer, at the height of a brilliant career and with two young children, he quickly learned that it was incurable and that the median survival time after discovery was eight months. He gulped, he wrote later, and sat stunned for fifteen minutes.

  Then, he says, he started thinking. He describes the ensuing story – a statistical one – as profoundly nurturing and life-giving.

  The median is another variety
of average: it means the point in a distribution where half are above and half below, what Gould and others call a central tendency. In this case it meant that half of all people diagnosed with abdominal mesothelioma were dead within eight months.

  A number like that hits hard. But it is worth recalling that other numerical characteristic which applies particularly to averages of all kinds, namely, that they are not hard and precise, do not capture some Platonic essence, are not, as Stephen Jay Gould understood to his advantage, immutable entities. Rather, averages are the classic abstraction, and the true reality is in the distribution, or as Gould says: '… in our actual world of shadings, variation and continua'.

  In short, wrote Gould, 'we view means and medians as the hard “realities” and the variation that permits their calculation as a set of transient and imperfect measurements.' In truth, so far as there are any hard realities at all, they are in the variation, in the vibrant individual colours of the rainbow, not in the abstracted average that would declare the rainbow white.

  Once again, to make sense of this average, we must ask what is in the distribution. The first part of the answer is straightforward: half will live no more than eight months, that much is true, but half will also live longer, and Gould, being diagnosed early, reckoned his chances of being in the latter half were good.

  The second part of the answer is that the eight-month median tells us nothing about the maximum for the half who last longer than eight months. Is eight months half-way, even for the luckiest? Or is the upper limit, unlike the lower one, unconstrained? In fact, the distribution had a tail that stretched out to the right of the graph for several years beyond the median, being what statisticians call right-skewed. If you lived longer than eight months, there was no knowing how much longer you might live beyond that.

  Understanding the distribution behind the average allowed Gould to breathe a long sigh of relief: 'I didn't have to stop and immediately follow Isaiah's injunction to set thine house in order for thou shalt die, and not live,' he wrote. 'I would have time to think, to plan, and to fight.' He lived, not eight months, but another 20 years, and when he did die, in 2002, it was of an unrelated cancer.

  The same skewed distribution lies behind the average life span for people in Swaziland, the lowest in the world according to the 2007 CIA Fact-book and United Nations social indicators, at 32 years for men and 33 for women. It is a frighteningly low figure. But 32 is not a common age of death – most who make it that far survive longer – it is simply that in order to calculate the average their fates are bundled together with the shocking number who die in infancy. The average is pulled down by Swaziland's high rates of infant mortality. And so the figure for average life expectancy stands like a signpost between two destinations, pointing at neither. It fails to convey either of what we might call the two most typical life spans, but is an unsatisfactory blend of something truly awful and something more hopeful, a statistical compromise that describes very few. A better way of understanding life expectancy in Swaziland would be to say that it is either only a few years, or that it is not very far from our own. Prospects there are largely polarised; the average yokes the poles together.

  Should averages simply be avoided? No, because for all their hazards, sometimes we want a figure to speak for a group as a whole. And averages can be revelatory. Making them useful is mainly a question of working out which group we are interested in. What we most often want to know when we find ourselves reaching for an average about some social, economic or political fact of life, is what is true for most people or most often, what is typical, what, to some extent, is normal for a particular group. Some of the many reasons an average might not tell us any of these things are found above, to do with the awkward failure of life to behave with regularity. But say we are pig-headed and still want to know. Then there is nothing for it: with all those caveats about what might be going on in the misty reaches of the distribution, we still need to find words for a summary. And sometimes that summary of the typical will be what we most want to know about the success or failure of a policy.

  A good current example is hospital waiting lists. The government has set a target – currently that no one should wait more than six months (twenty-six weeks) for an operation. This is about to change to the much more demanding target of a maximum of thirteen weeks from GP referral to treatment, continuing the deliberate focus on one end of the distribution, the long-waiting end. Once there was a long tail to the waiting list, and you could wait years for treatment, but it is now an abrupt cut-off with a maximum waiting time for all. It reminds us how certain parts of the distribution rather than the whole can acquire political importance.

  As a result of this policy, the government has been fond of saying that waiting times are coming down (Department of Health press release, Wednesday 7 June 2006: 'Waiting times for operations … shorter than ever'), and it is quite true that the longest waits have been reduced dramatically. But the longest waits, though a real problem, are a small proportion of the total number of waits. Not very many were ever kept waiting more than two years compared with the millions who were seen within a few months. So this is a case where we might also want to know, in order to say with authority what is happening generally to waiting times, what is happening to everyone else, not only to the long waits, but also to the more typical waits, those who always were inside the maximum.

  The government has taken one part of the distribution and talked about it as if it spoke for the whole. How do we find a more satisfactory measure?

  The best answer in this case is to ask what happens to a patient whose wait is somewhere in the middle of all waits, the point where half of all patients wait less and half more, and which is an average called, as in the Stephen Gould case, the median. These figures are decidedly mixed, and in some cases startling. Even so, this example will not take the median for every patient in the country, but will identify the median for various large groups.

  Before we look at them, we will also do one other thing to the calculation of waiting times. We will strip out a practice that seems to have increased significantly in recent years of resetting the waiting-time clock for what are sometimes opportunistic reasons (see Chapters 3 and 6 on counting and targets). This is permitted but easily abused – the hospital rings you to offer an appointment with one day's notice, you can't go, they reset your waiting time. Once you strip out this behaviour to compare like with like waits, five years ago with now, and look at the typical patient, not just the very longest waits, the effects are illuminating.

  In one primary care trust (PCT) area we looked at (in late 2006), for example, waiting times for trauma and orthopaedics had gone up for the typical patient from 42 days to 102 days. In another there was an increase from 57 days to 141 days. A third saw a rise from 63 days to 127 days. Waiting times for ear, nose and throat (ENT) told a similar story, where the typical patient in about 60 per cent of primary care trusts was waiting as long or longer than five years ago.

  In general surgery, figures for more than half of all PCTs showed that the typical patient was waiting longer than five years ago. In a number of cases, though not a majority in the areas we looked at, even the waits for the 75th percentile (how long before 75 per cent of patients are treated) had gone up. Finally, in March 2008, the UK media were shocked when it was officially admitted that median waiting times had gone up across the board, from 41 days to 49 days.

  The key point of our analysis is that it makes little sense to say waiting times are going one way or another unless you say 'for whom?' and identify the group that interests you. The figures are not moving the same way for everyone, and in some large categories of treatment, though not for all, most patients, as typified by the median, are waiting as long or longer than five years ago.

  It is important to know what has happened to the longest waits and it is quite reasonable to say that shortening them is a success for those patients, but it makes no sense to say that these alone tell you whether 'waiting ti
mes have come down'. They do not. For this, there is no option but to use some kind of average, and the most appropriate average is the median.

  Incidentally, we found that most hospitals we asked could not tell us what was happening to the typical (median) patient, and the data came from another source – the Dr Foster organisation – which had access to the raw hospital episode statistics and the in-house capacity to crunch the data.

  Always ask about an average: which group are we really interested in? Maybe when we ask about the average income, we don't want to know about the stratospheric earners, we want to know about what's more typical. And maybe there are other strange colours in other averages that we don't want in the mix, as well as some that we do. What matters is that you know what's in and what's out, and that you are sure you have achieved the mix you want. Averages are an abstraction, a useful one, but an abstraction all the same. If we look at them without knowing what it is that we have abstracted from, we will be misled. It is an average, but an average of what? Remember the vibrancy and variety of real life. Remember the rainbow.

  6

  Targets: The Whole Elephant

  Pick a number to tell your story, a single measure to summarise your life's worth. What's it to be? Height? Weight? How about your salary? For some, that would do nicely. Most would feel cheapened. How about your personal tally of wives or husbands? Or maybe longevity captures it? Up to a point, perhaps, until someone asks what you did with all those years. Whatever the measurement, if one part is taken for the whole, it can become comical. One number, because it implies one definition, is almost never enough.