What are the odds of that?

Roulette Wheel 08, by marc e marc

The front page of today’s Times announces a proposal that children should have ‘lessons in gambling’ at school. It’s enough to make the Methodist maiden aunts reach for the smelling salts, but actually it sounds quite a good idea to me.

Understanding risk is one of the toughest lessons we learn. Mostly, we make decisions based on our experience of what’s happened before, and our knowledge of what happens to other people we know. We take risk-based decisions every day on how long to give ourselves to walk to the train station, whether to eat that dodgy-looking hamburger, whether to cross the road on a day that Jeremy Clarkson might be driving through London.

Then there are the more complicated decisions. Should I take out a fixed-rate mortgage, or gamble on interest rates staying low? Should we book the expensive holiday we want to take next year, or wait to see whether we’re both still in a job come next summer? Is it best for Dad to have a hip replacement now, or to try physiotherapy and medication first?

These are the sort of decisions where it really helps to understand risk. What are the chances of interest rates going up over the next 5 years?  How safe are our jobs? What are the chances of a good or bad outcome from hip replacement surgery?

Even if we can get reliable figures, we need to be able to interpret what they mean to us. Is a 10% risk of losing my job in the next year too high, or is that manageable? If the odds of an interest rate rise are 2:1, should I go for that fixed rate?

The trouble is, many of us struggle with understanding risk. I realised how tenuous my grasp of risk was when I noticed that 1 in 20 sounded a bigger risk to me, than 5 percent (yes, they’re exactly the same). Representing risk so that people can get a true understanding of it is an art as well as a science.

One man who knows more about this than most people is David Spiegelhalter, Cambridge Professor for the Understanding of Risk. I met David when he gave a terrific presentation at the Evidence 2011 conference last month, organised by BMJ Group and the Oxford Centre for Evidence-Based Medicine. This week I took a trip to Cambridge to meet him and his colleague Mike Pearson.

Writing about medicine for the general public (as I do with colleagues on the BMJ site BestHealth), I feel a responsibility to get it right when we’re talking about risk. If a paper says that heading a football may cause brain damage, or coffee might lower your cancer risk, it’s important we talk about how big the risk or benefit is, and how likely it is that the research stands up. We’re also writing patient decision aids, to help people decide whether or not to have that hip replacement (see one we did earlier, on the NHS Direct site). We know the importance of using absolute risks rather than relative risks, and not framing information to influence people one way or another, but we’re keen to do better.

So it was immensely helpful to get David’s take on how best to use statistics to help people understand risk. Use of graphics is a great way to do this – see David’s website Understanding Uncertainty for more on this. But it was a quick, throwaway comment that made an immediate difference to the way we work.

When we give figures from papers to several decimal points, we think we’re being accurate – but actually, the figures aren’t that certain. The figure we’re giving is a point estimate, a ‘best guess’ based on the data in the study, but different trials are likely to give slightly (sometimes more than slightly) different results, because of the play of chance. So rounding figures from 8.7 or 23.4% to 9 or 23%, is not being sloppy – it’s actually better practice. The more precise the number we give, the more accurate the number sounds to the general public. This means we may be over-emphasising the reliability of the figures.

So, no more decimal points. And as for the gambling lessons – anything that teaches children how to understand the play of chance and to know when the odds are stacked against you are a good thing. By the way, David Spiegelhalter has calculated that your best bet to win enough to buy a sports car is roulette. Put mine on black.

Image: from marc e marc photostream on Flickr, with CCL.

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