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Sir David Spiegelhalter: How we’re manipulated by numbers in the news

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Surprisingly for a statistician, the University of Cambridge’s Prof Sir David Spiegelhalter is urging people to think about how numbers make us feel when we read about them in the news.

Covid-19 has brought daily reports of statistics and numbers that can seem overwhelming. It’s hard to know what they all mean or which statistics we should pay attention to if you’re not an expert.

But rather than focusing first on the statistical details, our emotional response to a number can be useful, explains Sir David, as it may show whether that number is being used to manipulate us.

“I am a complete convert to this idea that you have to look inside yourself and think, what is my emotional reaction to this number?” says Sir David.

“I think this is a powerful idea because it shows that numbers are not cold, objective, hard facts about the world. When we hear them they are always part of the story and quite often somebody is trying to manipulate us with that story. Very often they’re trying to make something look reassuring or frightening, so they’re telling the story and using a number that is part of their argument.

Prof Sir David Spiegelhalter. Picture: Ilan Goodman
Prof Sir David Spiegelhalter. Picture: Ilan Goodman

“To be able to stop that and start thinking about what I feel when I see that number or hear that and whether I am reassured or more anxious or whatever is incredibly important; because it is through that you start to get an understanding of how essentially you come to manipulate people with numbers.”

As part of the upcoming Cambridge Festival, Sir David, who is chair of the Winton Centre for Risk and Evidence Communication at the University of Cambridge, will be talking to broadcaster Tim Harford from the BBC Radio 4 show More or Less, which examines statistics seen in the news. Harford will be there to discuss his book, How to make the world add up: Ten rules for thinking differently about numbers. He describes the book as “my effort to help you think clearly about the numbers that swirl all around us”.

As a regular guest on More or Less, Sir David has learnt the value of checking whether a number is being used to influence your feelings.

He says: “I’ve gained a lot of experience of just hearing a number being discussed and thinking, do I trust it?

“Tim has come up with some simple rules of thumb about what questions we should ask when we see a number and I think they are very interesting because, as a statistician I might start immediately looking at sample size and some slightly technical issues whereas Tim would say, ‘How does that make me feel’ and reflect back on the emotional impact of hearing this number. When I first heard this I thought, ‘what a ridiculous idea’, but now I agree.”

Politicians may talk about huge sums of money being spent to impress on the public the importance of their version of events. One example Sir David uses is the claim on the Vote Leave bus that by leaving the EU there would be an extra £350million per week to spend on the NHS.

He says: “This is a classic. It’s very clever framing of that number to make it look big but not too big. If we reframe the number into a different context so we can say £350m pounds a week equates to £50 million pounds a day, and that seems like quite a lot.

A Covid-19 vaccine
A Covid-19 vaccine

“But if say there are around 70 million people in this country and you divide that into the number that works out about 80 pence a day per person, and it seems not quite so much. That’s just the price of a packet of cheese and onion crisps. If they had put on the side of the bus that you could save the price of a packet of cheese and onion crisps every day, people might decide that’s not enough to change their mind about whether to vote for Brexit.”

The last 12 months have seen numbers playing a huge role in our daily lives on news and briefings about the coronavirus, and many of them have been confusing. How do we know, for example, how much risk you are at if you are one of the people being asked to shield this time around?

“I was involved in the algorithm that was used to decide who should shield and this was an algorithmic decision,” he says.

“It is based on the statistical analysis of all deaths among around 12 million people in the UK in the first wave. This analysis looked at what are the risk factors that increase your risk of dying or hospitalisation in the first wave. That analysis determined that age was the overwhelming strongest factor and that is what has led to the vaccine prioritisation being overwhelmingly based on age.

“Of course there are other factors. Sex makes a difference. Males do have a high risk and also some medical conditions have greatly increased people’s risk. The initial shielding list was developed really just by judgment, without data, at the beginning of a pandemic. So, I think it’s very reasonable to revise that on the basis of the data that we have now got from the first wave about what the real risks were to people. That work has led groups of people who would not be considered at such high risk to now being put on the shielded list.”

So was there a cut-off point for a person’s individual risk above which they would be asked to shield?

“Yes, and I can tell you exactly what it was. You would be asked to shield if more than one in 200 people like you with your age and sex and medical conditions died in the first wave. That is quite a reasonably high risk as those deaths took place over a 16-week period. You went on the list if you were in a high-risk group but also if you’re high risk relative to your healthy peers.

“If, relative to someone your age and sex who was healthy you have more than 10 times that baseline risk of dying from Covid-19, you also went on the list.”

The vaccine prioritisation has been worked out in a similar way. And although there has been lots of talk about whether Pfizer/BioNTech or Oxford University/AstraZeneca have created the best vaccine, Sir David explains that the research shows there is little difference between them.

“The best evidence for that is from a huge study in Scotland where they had a mix of people having both vaccines. They did a study which in fact involved every single adult in Scotland looking at whether they have been vaccinated or not and then whether they have been hospitalised with Covid-19. They found there’s no real difference between the two in the effectiveness of preventing hospitalisation, which is very encouraging.”

The effectiveness of the vaccines is about 80 to 90 per cent, he says.

David Spiegelhalter, centre, professor of public understanding of risk at Cambridge University, at RAND Europe's 2018 annual reception at Trinity College. Picture: Jo Anthony
David Spiegelhalter, centre, professor of public understanding of risk at Cambridge University, at RAND Europe's 2018 annual reception at Trinity College. Picture: Jo Anthony

“That’s just a huge number. I’m just happy to have anything like that – it’s far better than the flu vaccine. These are big numbers and what they do is take a pretty low risk already of being hospitalised or dying and make it much lower.

“The risk of getting an infection might be reduced by 60 to 70 per cent; the risk of getting symptoms might be reduced by 70 to 80 per cent; the risk of going to hospital might be reduced by 80 to 90 per cent and the risk of dying will be reduced by more than 90 per cent.”

Given these exceptional results, he is astonished by France’s President Macron’s “absolutely idiotic remark that the AstraZeneca vaccine has been quasi effective” in the over-65s.

He adds: “The European concern about AstraZeneca is extraordinary and I predict it is going to lead to loss of lives.”

There were only a small number of over-65s in the AstraZeneca vaccine trial, he says, but the UK’s JCVI committee “absolutely correctly” considered evidence showing there was no reason to believe it would not work in that age group.

He warns any delays to the vaccination programme in France “will mean people dying so I think that’s certainly Macron’s comments were grossly irresponsible”.

Sir David has already received his first dose.

“I have had my first jab and I found the whole experience to be very moving,” he says.

“And most people have been moved. I turned up and found such a positive atmosphere and the whole business has seen such extraordinary credit to so many people. I had the Pfizer vaccine and that’s fine. I wouldn’t mind which one it was. I’m just lucky to have it.”

He also praises the UK government’s “bold decision to delay the vaccine second dose for a 12-week interval” rather than the three weeks tested in the clinical trials.

Administering the coronavirus vaccine (45548645)
Administering the coronavirus vaccine (45548645)

“This has been shown to be the right decision as well and everyone involved deserves enormous credit,” he says.

Now he believes that with our vaccine programme steaming ahead, “it may very well happen that in the summer the British will be able to travel to a much greater extent than other European nations, but in the end we of course want as many people in the whole world to be protected as possible in order to regain some element of freedom of movement.”

With schools returning next week, what are his thoughts on the ‘fast result’ lateral flow tests – which do not have the same accuracy as laboratory tests – to check whether children have the virus before they go into the classroom?

“It’s lovely the idea that rapid tests could free us up from various constraints. But lateral flow tests were originally intended to be ‘red lights’ rather than ‘green lights,’ he says.

“They are ways of identifying people with the virus that might otherwise be missed. They are not really designed to say now you are free to do things, so I think it is something that has to be very carefully rolled out and its impact evaluated.

David Spiegelhalter. Pic: "EXP-editions" (45548640)
David Spiegelhalter. Pic: "EXP-editions" (45548640)

“Also the communication must be very clear that if you take a lateral flow test and it is negative it does not mean you haven’t got the virus and if it’s positive it doesn’t necessarily mean you have got it.

“If there isn’t much circulating, then even with a very good test you can have a situation where many of the positives are false positives so it doesn’t categorically tell you what is the case. It is useful but it’s not the last word.”

He told the Cambridge Independent that it would make sense to give only half of schools the tests and then evaluate whether they had an impact on the number of cases compared to those who did not have them.

“We have to look at the situations where lateral flow tests are being used to open things up – such as schools – and to track the outbreaks. It’s as simple as that. You can build all sorts of (statistical) models but in the end we have to look at our experience and to see whether it is controlling outbreaks or not.”

The Easter holidays coming three weeks after the reopening of schools will be “a natural circuit breaker,” suggests Sir David.

“By three weeks that will give a good window to find out what is happening to increasing cases and what is happening to R [the reproduction number that tracks how many people an individual with the virus is infecting].

“Opening schools would be almost the only thing that has changed. It’s an extraordinary experiment when most of the younger population isn’t vaccinated yet. It will be extremely interesting.”

Whatever the impact of the school reopening, Sir David argues that politicians should never just “follow the data”.

“I have never liked the phrase following the science or following the data which is just as bad. Data does not tell you what to do – it is not the whole story. It would be awful if it wasn’t being considered but this is only one element in the decisions that the government has to make. There are some really difficult decisions and I’m glad I don’t have to make them.”

Sir David and Tim’s talk will take place at 3pm on Saturday, march 27. Visit https://www.festival.cam.ac.uk/events/how-make-world-add. The Cambridge Independent is proud to support the festival.

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