## Understanding numbers in the media

Numbers have become the currency of public discourse. It is impossible to pick up a newspaper or watch the news without being bombarded with numbers – the latest opinion poll, a new study linking the use of Facebook to cancer or the size of our national debt. We like to convert the complexity of the world into a handy number. They give credibility to a story or a claim. However quantity is not the same as quality and numbers hold many traps. We fall into them all too easily and we can’t rely on the media to help us out because they are often the worst offenders. Grammar sticklers get het up about people using the word “hopefully” when they really mean “I hope”. On the other hand, we are much more blasé about innumeracy. We need to be aware of the pitfalls of using numbers. What’s more, you can get a kind of subversive thrill in being able to see through dubious government claims or the dodgy data of a newspaper survey. I am no maths geek but it is possible to become savvier consumers of the media. I have recently finished reading The Numbers Game by Michael Blastland and Andrew Dilnot, which gives a lot of handy tips about how to recognise the abuse of numbers in the media. There have been a number of books, articles, programmes and websites aimed at popularising mathematics and I have learnt a lot from reading and listening to them. Here are a few warning signs to look out for when you see numbers in the media.

One particularly egregious mistake that the media make when presenting numbers is to fail to put them into any kind of context. This is important when we are dealing with billions and trillions as well as with tiny numbers. I am totally opposed to Obama’s Detroit bailout, which was supposed to cost around \$15 billion. But it is useful to put this number into perspective that comes out as just one dollar a week for every person in the U.S. for one year. This was not the final cost but this method helps make \$15 billion much easier to understand. When numbers are really miniscule, percentages can be meaningless. Double nothing is still nothing. In his excellent Bad Science column Ben Goldacre analysed the case of Implanon, a contraceptive implant, which women can have inserted for a maximum of three years. A number of newspapers reported the figure of 584 unwanted pregnancies. You can’t make sense of this number without considering how many women used Implanon and for how long. The device came out in 1999, which makes an average of under 60 cases a year. Epidemiologists use “person-years-at-risk” and the figure for Implanon was 4.06m women-years at risk. The 584 unplanned pregnancies represent a failure rate of 0.014 per year; this means, if my maths are right, that only 1 in 2,000 women using Implanon will become pregnant over the course of one year, making it the most reliable form of contraception. You would never have got that impression from the way it was reported.

We are a pattern-seeking species. This ability to identify patterns has been a vital evolutionary tool, enabling us to spot danger early on. This has come at a price we sometimes see patterns where none exist. Chance has a genius for appearing in disguise – numbers often seem to be significant. We like to tell ourselves stories. We think that it couldn’t have happened by chance. One example of this is cancer clusters. Sometimes you will find a lot of cases of cancer in one area. This may mean that something is wrong. However, what people fail to realise is that randomness can produce exactly this kind of result. If a coin is tossed 30 times, chances are you will get at least one sequence of four heads or four tails. You are not going to get an even distribution. The same is true of life events and yet we manage to see significance in randomness.

Sex makes babies. If you plant a seed, a few months later you will have something to eat. Eating a poisonous mushroom can kill you. The human ability to see how one thing leads to another has been vital to our prospering as a species. But like our pattern-seeking disposition, it can play tricks on us. One classic case goes back to the late 1940s, before Johan Salk’s discovery of the polio vaccine. American public health experts believed they had found a relationship between polio and the consumption of ice cream and soft drinks. Consequently, they recommended cutting both of them out of an anti-polio diet. Of course we can now see the relationship was not causal.  Polio outbreaks just happened to be common in the summer months, when people naturally ate more ice cream.

Education is a rich source of examples. Mathematician John Allen Paulos presents his students with data that demonstrates conclusively that children with bigger feet spell better. Before you urge the government to buy a job lot of foot stretchers in order to improve our kids’ spelling, you need to see that this correlation is not causal; the children with bigger feet spell better because they’re older. Blastland and Dilnot look behind the statistics which show that girls at single-sex schools do better than those in mixed schools. This leads many to conclude that single-sex schools are better for girls. This last statement may be correct but you need to prove causation. With a bit of imagination you can provide alternative explanations. What else can we say about girls in single sex schools? A couple of things spring to mind. Firstly, many of them will be going to fee-paying schools and are thus from wealthy families. Money happens to be a strong predictor of academic success.  Secondly these kinds of school tend to be selective about their intake and they may well have more academically gifted students. So we can see that these two factors could well explain differences between the performance of girls in single-sex and mixed schools. The problem then is to know what percentage of the difference is accounted for by these factors.

The final area I want to look at is the proliferation of equations. They may be a boon for PR companies, who are able to get their brand into a paper without paying, but they have absolutely nothing to do with mathematics. All the hard-pressed journalists have to do is copy and paste provided by the PR firms. If the formula is about Britney Spears’s cleavage, you have an excuse to show her in a provocative pose. From pouring gravy, to telling the perfect joke, there seems to be no human activity that cannot be summed up by a bogus formula. Geoff Beattie, who is head of Psychological Sciences at the University of Manchester, was sponsored by Chevrolet, to create the formula for the perfect handshake. Sceptical science writer Jacob Aron, who blogs at justatheory.co.uk, broke the equation down into its component parts:

PH = √ (e² + ve²)(d²) + (cg + dr)² + π{(4<s>2)(4<p>2)}² +(vi + t + te)² + {(4<c>2)(4<du>2)}²

(e) is eye contact (1=none; 5=direct) 5;

(ve) is verbal greeting (1=totally inappropriate; 5=totally appropriate) 5;

(d) is Duchenne smile – smiling in eyes and mouth, plus symmetry on both sides of face, and slower offset (1=totally non-Duchenne smile (false smile); 5=totally Duchenne) 5;

(cg) completeness of grip (1=very incomplete; 5=full) 5;

(dr) is dryness of hand (1=damp; 5=dry) 4;

(s) is strength (1= weak; 5=strong) 3;

(p) is position of hand (1=back towards own body; 5=other person’s bodily zone) 3;

(vi) is vigour (1=too low/too high; 5=mid) 3;

(t) is temperature of hands (1=too cold/too hot; 5=mid) 3;

(te) is texture of hands (5=mid; 1=too rough/too smooth) 3;

(c) is control (1=low; 5=high) 3;

(du) is duration (1= brief; 5=long) 3.

We all love to have a bit of harmless fun at the expense of those mad boffins, but it can have pernicious effects on the public perception of science. When used properly models and equations are such wonderful tools for understanding the world around us.

Does this all mean we should banish numbers from the news? Absolutely not. We just need to be more aware of what they can and can’t do. I think the media could do a much better job. We expect journalists to be literate, but they should also be numerate.  I hope I have shown that maths can be fun. Without any complicated number crunching, you will be able to have  a much better understanding of how numbers work.