It may have come to your attention that the UK is experiencing some difficulties over an issue called Brexit. During the referendum in June 2016, an iconic image of the Leave campaign was a big red bus plastered with the message “We send the EU £350 million each week – let’s give it to the NHS”. It is plausible that this brilliant use of numbers may have tipped the narrow balance of 52% to 48% in favour of Leave.
The UK Statistics Authority has ruled that this number was not reliable, being based on gross rather than net contributions, and ignoring EU contributions to public funds. But it had a strong emotional appeal, showing that statistics are not cold hard facts – as Nate Silver says in The Signal and the Noise, “The numbers have no way of speaking for themselves. We speak for them. We imbue them with meaning.” Even if we assume this number is accurate, then its impact can be altered simply by reframing: as there are 66 million people in the UK, £350 million a week is equivalent to around 75p a day – say about the cost of a small packet of crisps. If the bus had said “We each send the EU the price of a packet of cheese and onion crisps each day”, the campaign might not have been so successful. And just to show my lack of bias, the Remain claim that leaving the EU would cost every family £4,300 is equally flimsy.
Such examples have led to claims that we live in a post-truth society, abounding in misinformation and exaggeration, in which numbers are used as tools to persuade rather than inform, and emotional responses trump balanced consideration of evidence. These issues are deeply concerned with trust in expertise, but the philosopher Onora O’Neill has claimed that it is inappropriate to try to be trusted: instead we should attempt to demonstrate trustworthiness, which requires honesty, humility and transparency. This idea has been very influential: the revised Code of Practice for official statistics puts Trustworthiness as its first ‘pillar’.
We should aim to improve both the trustworthiness of statistical evidence being communicated, and the ability of audiences to ‘call out’ bad practice and exaggerated claims, say about the ‘risks’ of burnt toast, coffee, and a single daily drink. For example, the clickbait headline below refers to evidence that 25g of bacon a day (equivalent to a large bacon sandwich every other day) increases bowel cancer risk by 19%. Should you care?
It has been established through formal psychological experiments that such calculations are better expressed using the idea of expected frequencies – eg what does it mean for 100 people? So out of 100 non-bacon eaters, we would expect 6 to get bowel cancer during their lifetime. Whereas out of 100 people who ate 25g of bacon a day, say a large bacon sandwich every other day, then we would expect an extra 19% to get bowel cancer, that’s 19% of 6, which is around 1 extra. That means 100 people would need to eat around 180 a year for their whole life, which is around 10,000 each, or a total of million great greasy bacon sandwiches to expect one extra case of bowel cancer. To which your response might be – pass the tomato ketchup.
As scientific evidence is inevitably limited, the challenge then becomes: how can we communicate numbers, risks and unavoidable scientific uncertainty in a transparent and trustworthy way? This is an empirically researchable issue, and we have been carrying out randomised experiments on the impact on audiences of alternative verbal, numerical and graphical means of communicating uncertainty. Of course, available evidence may often not permit a quantitative assessment of uncertainty, and we are also examining scales being used to summarise degrees of ‘confidence’ in conclusions, in terms of the quality of the research underlying the whole assessment.
Statistics has played a leading role in our scientific understanding of the world for centuries, yet we are all familiar with the way numbers can be used to support sensationalised claims, whether political or scientific. As data becomes more influential in our society, data literacy becomes an increasingly essential skill. This means a new approach to statistics education is necessary, in which real problems provide motivation for ideas, and technicalities are delayed as long as possible. My latest book, The Art of Statistics, demonstrates this approach, and may help to counter some of the dubious numbers in the news. But I would not count on it.
Sir David Spiegelhalter is Winton Professor for the Public Understanding of Risk, and Professor of Biostatistics, at the University of Cambridge. He also hosted the BBC Documentary “Tails You Win: The Science of Chance”. To book him (or any other speaker) for your event please contact JLA here.