For this blog post I want to make two points, and tell an old story involving a zebra.
Firstly, our knowledge is incomplete. This is a common problem with social statistics: this is the reason why the news doesn't report the number of unemployed people, but always gives the number of those out of work and claiming benefits. Just as nobody knows precisely how many people are not working, nobody knows precisely how many crimes are committed. We do know precisely how many crimes are recorded by the police, but we also know that lots of crimes aren't - which is why we use figures from the Crime Survey for England and Wales. But the CSEW is a sample-based survey - they ask roughly 50,000 people about their experiences of crime, then multiply out to give an estimate of the number of crimes in the country as a whole. So there is no precisely accurate, "God's eye view" figure for the number of crimes that are committed. What's more, because it's a residential survey completed by adults, we know that the BCS is highly unlikely to record crimes against some groups of people: for example, children, dependent elderly people, students living in halls, people of no fixed abode...
Every statement about crime levels should be followed by "as far as we know".
Secondly, crime is highly patterned (as far as we know). And the ways in which it's patterned aren't entirely surprising, if you think about deprivation and social injustice generally. Living in a neighbourhood with "high levels of disorder" is associated with a higher risk of crime. Black and minority ethnic people are statistically at a higher risk of crime than Whites, even if we're only talking about "colour-blind" crimes like burglary. Almost half of all victims of domestic violence are repeat victims, suggesting very strongly that domestic violence is - as feminists say - part of a continuing relationship of unequal power. There are also some interesting and very significant findings about age: sorry to bring bad news, but if you're under 25, your statistical risk of crime is much higher than average, particularly if you're living alone or with other young people.
Thirdly, the zebra story. A man was so terrified of being in a railway accident that he avoided travelling by train at all. Eventually he decided to approach the problem rationally and spent a long time trying to work out ways of making train travel safer. He concluded that his best option was to travel everywhere with a horse, because there were far fewer train crashes when the train had a horse on board than when it didn't. When someone asked if he was happy like that - presumably meeting him coming out of a railway station leading his horse - he said he couldn't help feeling he should have held out for a zebra. The statistics did record one or two train crashes when there had been a horse on board, but none at all involving a zebra.
If this was true, would taking a zebra with you on a train makes you safer? Obviously not - but why not? Similarly, if (according to police figures) 20% of domestic burglaries involve the burglar getting in through an open window, does this mean that leaving a window open is actually safer - since, after all, 80% of burglaries didn't involve an open window? Again, this conclusion seems wrong, but why?
The zebra example is fairly easy. Let's say that 1 in every 1,000 train journeys ends in a crash (the real figure is much lower, of course). Then let's say that there are a million train journeys in a year, and 2,000 of them involve somebody transporting a horse. Then there will be 1,000 train crashes, out of which 2 involve a horse and 998 don't. But that doesn't mean that travelling with a horse is safer, just that it's rarer: the rate of crashes is the same (2 out of 2,000, 998 out of 998,000).
As for the open windows, we need a couple more pieces of information to work that one out. According to official figures, the annual risk of burglary is 2.5% - unless you've got "no home security measures" (which we'll translate as "windows left open"), in which case it's 25%. So 20% of burglaries are from the "open windows" group of properties, but if you are in that group you have a 25% chance of becoming one of those burglary victims. If you're in the "closed windows" group, you have a less-than-2.5% chance of becoming one of the other 80%. (It's less than 2.5% because the 2.5% risk is averaged out over all households, including the ones with their windows open.)
Now, say you're looking at a city of 4,000,000 households (imaginary figure). In any one year, 2.5% of them will be burgled: there will be 100,000 burglaries (ignoring repeat burglaries for the time being). 20,000 of those burglaries will be of households with open windows (20% of 100,000 = 20,000). But we also know that households with open windows had a 25% risk of being burgled - and that tells us that, overall, there are only 80,000 households in the city which leave their windows open. (There's a joke here about how many of those are in Fallowfield, but I won't stoop to it.) This is the crucial missing piece of information: 20% of burglaries are of households with an open window even though there are very few of them. 20% of burglaries occur in 2% of households (80,000 / 4,000,000 = 0.02 = 2%). The other 98% have a risk of burglary which is even lower than 2.5%; in fact it's just slightly over 2% (80,000 / 3,920,000 = 0.204 = 2.04%).
In the horse/zebra example, the numbers look so different because a single rate (of train crashes) is applied to two very different populations (the number of train journeys on one hand, the much smaller number of journeys involving a horse on the other). The 'open window' example is more complex because there are two different rates: a low rate for a very large population, a much higher rate for a very small one.
Why does all this matter? It matters because we need to know the underlying numbers in order to make sense of the statistics - and making sense of the statistics is vital if we're going to get an accurate picture of questions of power, injustice and social exclusion in our society. Suppose you hear that 5,000 Romanians have entered Britain in the past year: what does that mean? Is it a lot? Is it ten times as much as the previous year, or half as much? ten times as many Romanians as Poles, or half as many? Or suppose you hear that 100 Manchester residents of Asian origin were arrested for shoplifting in the past year, but only 20 Chinese - does this tell you that the Chinese population of Manchester is five times as law-abiding as the Asian population? If not, why not?
PS According to Manchester City Council, the main ethnic groups in Manchester are as follows:
| White | 66.7% | 347,000 |
| Asian | 14.4% | 75,000 |
| Black | 8.6% | 45,000 |
| Mixed | 4.7% | 24,000 |
| Chinese | 2.7% | 14,000 |
| Arab | 1.9% | 10,000 |
| Other | 1.2% | 6,000 |
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