Numerical Illiteracy

In which Quinton becomes a crime hotspot, or not

January 30, 2011
numeracy press

Note: This is an older article from the blog I ran while being an academic. Most of the posts on there are about teaching and learning, but this one is of more general relevance, see also this one.

Quinton had very little burglaries, “averaging just one or two burglaries a month” over the last nine years. But now, crime has “shot up by 29%", more than the rest of Birmingham where crime only rose by 21%.

I find this rather misleading, and I worked through an example with the kids at the dinner table, which illustrates the problem:

  • Suburb A had 10 burglaries in 2009, and 12 in 2010. That is an increase of 20%.
  • Suburb B had 4 burglaries in 2009, and 5 in 2010. Increase of 25%.
  • Suburb C had 1 burglary in 2009, and 2 in 2010. A whopping 100% increase.

First lesson: percentage increase is meaningless unless everybody started in the same place. Why do developing economies have higher growth rates than Europe and the US? Because the percentage looks bigger. If you double your output from 100 cars to 200 cars you increase by 100%, but to maintain that rate you will have to produce an additional 200 cars the year after, and then 400, 800 etc.

Second lesson: without a fixed reference point (such as burglaries per 1000 inhabitants) you have no idea whether the risk of your house being burgled is high or low. Everything is relative, but you still need a fixed point to evaluate things.

Third lesson: this is not mentioned, but is that difference between 29% and 21% statistically significant? With “one or two burglaries a month”, the variation seems rather high, given those small numbers. So if there was one extra or one fewer burglaries, how would the 29% change?

Final lesson: be careful with calling places “crime hotspot” when your statistics are that shaky.

Now I don’t expect a staff reporter at the Birmingham Mail to apply the same rigour as a scientist (or any other, non-science researcher), but the way the article is presented is simply misleading. To me this sounds like a scare story being created out of some random statistics. I don’t know whether that is the case, and maybe Quinton is really a crime-ridden area, but I cannot tell from the few facts given to me in the article. The reason for this development given in the paper is that there are now 5 fewer policemen covering Quinton. Is there really such a cast-iron correlation between policemen and crime rate? How about the influence of the recession on crime? And how many policemen were there before the cut? 50? 500? 5000?

I now have more questions and know less than I did before reading that article!