Instant Genius - How to understand statistics in the news and when to trust them

Episode Date: April 12, 2021

In this week's episode of the Science Focus Podcast, editor Daniel Bennett speaks to Tom Chivers and David Chivers. Tom is a veteran science journalist and author and David is lecturer in economics at the University of Durham. As well as a surname, they share a passion for statistics, or more precisely for the way that numbers are used and presented in the media. Together they’ve written a new book: How to Read Numbers: A Guide to Statistics in the News and Knowing When to Trust Them. They talk to Daniel about how to understand the sometimes confusing stats surrounding health and risk, how to spot a suspicious claim when you see one, and how to think about the current concerns surrounding the Oxford/AstraZeneca vaccine. Let us know what you think of the episode with a review or a comment wherever you listen to your podcasts. Subscribe to the Science Focus Podcast on these services: Acast, iTunes, Stitcher, RSS, Overcast Read the full transcription of this episode [this will open in a new window] Listen to more episodes of the Science Focus Podcast: Sir David Spiegelhalter: There's no such thing as Blue Monday Matt Parker: What happens when maths goes horribly, horribly wrong? Hannah Fry: How much of our lives is secretly underpinned by maths? Prof Linda Scott: Why is there still economic inequality between men and women? Hannah Fry: What's the deal with algorithms? Robert Elliott Smith: Are algorithms inherently biased? Hosted on Acast. See acast.com/privacy for more information. Learn more about your ad choices. Visit podcastchoices.com/adchoices

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of BBC Science Focus magazine. In this episode, I'm speaking to Tom Jivers and David Chivers. Tom is a veteran science journalist and author, and David is a lecturer in economics at the University of Durham. As well as a surname, they both share a passion for statistics, or more precisely for the way that numbers are used and presented in the media. Together, they've written a new book, How to Read Numbers, A Guide to Statistics in the News, and knowing when to trust them. Over the next hour, we talk about how to understand the confusing stats around health and risk, how to spot a suspicious claim when you see one, and how to think about the current concerns surrounding the Oxford AstraZeneca vaccine.

I speak to Tom first, and I asked him whether it was a sheer coincidence that they had written this book at a time when the public, the government and the media have been obsessing over numbers more than ever before. Well, I tell you what, we were trying to work out the other day what the specific story was that triggered us wanting to write this book. It came from us in our Twitter DMs complaining about some news story or other with terrible numbers in it and just going, well, someone should write a book about how you can do better than this and then realizing that we were probably quite a good sort of pair to do that because, you know, he's an economist,

I'm a journalist with some interest in numbers. But no, it was a coincidence that it happened just before the, just as the pandemic was cracking, it was sort of appearing. I, I remember, remember when I wrote the, or when we wrote the proposal, which I think must have been February last year, or January or February last year, it was, you know, the numbers were just starting to spiral out of control, especially in China, I think it was starting to come across. And the, it just felt, I think our agent suggested before we put the proposal across to the publishers. Look, you really need to mention some stuff about this, you know, this would be the biggest statistical story of the next few weeks, You should probably mention something in a proposal, so we did. But it wasn't what we started out with.

We started out with some story about numbers of deaths from something or other in a university, which we ended up cutting from the book itself altogether. So, yeah, it was, I mean, from a purely sort of self-interested point of view, it was very well-timed, I think it's fair to say. I think they're being a bit unfair there, and I think we could have just said we predicted the crisis it was going back. Yeah, amazing forecasting. As mentioned in chapter,

he has to go through his own chapter list, but he's chapter 17, in fact, yes. And so obviously, as we speak today, this will be going out next week, but as we speak today, there's a big, in fact, it's emblazoned on one of the front pages of one of the newspapers, a big statistic. You know, everyone's talking about the risk of blood clots

in the under 30s in regards to, the Oxford AstraZeneca vaccine. Now, it's, you know, it's understandably quite a scary topic and, you know, quite a sensitive topic. But I'm just wondering, you know, given that you've spent a lot of time thinking about this stuff, if you could give our listeners some advice on how to think about this story and this idea around the risk of vaccinations. Do you want to go first day?

Yeah. So I think there are two. things here. And the first one is it's understanding about what the evidence is surrounding blood clots and vaccines. Because even though the sort of regulators are suggesting there may be some link, how exactly do we know for certain that these vaccines are causing blood clots? And we actually, we don't know that. There is some evidence to suggest that there may be a link between the two, but how confident do we have to be before we inform people that there is some evidence? And that's something that's very difficult to betray.

And something that we talk about in our book as well about what evidence means and how likely this would be. So that's one risk we need to suggest that you need to take into account, which is that we don't know the evidence is there quite, you know, it's not quite for certain. The other thing, and that's the risk of the actual blood clot itself happening when you take the vaccine, will depend quite largely on your age group. But how you actually process that risk is something that Tom and I've been discussing this morning actually. very difficult because these involve incredibly large numbers. And we're not very good at thinking in large numbers. And I often tell people that risk is a feeling. It's something that we interpret in a feeling sort of kind of way. And how exactly me as an individual is meant to process the risk of, say, a one in 100 chance or a 1 in 10,000 chance, or a 1 in million? Because to me,

they just seem zero. Or it's very difficult to comprehend and how that makes you feel is very difficult. But the important thing to remember is that everything we do involve some level of risk and everything we do in society is risky, crossing the road, eating a sandwich, playing football, anything will come with a certain background risk. And it's important to compare. And I think Tom's written about that. So maybe he could come in on that point. Well, coming a bit. One thing, I was speaking recently to David Spiegelhalter, who has just become one of the great celebrities of the pandemic. The Winton Professor of the Public Understanding of Risk at Cambridge University's a very great statistician. And he said one way to look at it was that if you took Wembley Stadium

and filled it with 20-year-olds and gave all of them the AstraZeneca jab, that at the current rate of COVID in the population, you'd expect about one of them to end up. with, end up in the ITU, intensive treatment unit with COVID, and about one of them to end up in the intensive treatment unit with the, um, with the, uh, with the Oxford-Australrogenicazerab. So, you know, because, because, and what he's saying is that actually, COVID is very, very not risky for, uh, these, you know, for young people under 20, under 30, under 20.

But, and so, so actually, the, from an individual point of view, the, um, the risk is low whether you take the vaccine or not. I was talking about this with Dave earlier, though, and he pointed out. that actually, again, like, as he says, we're not very good at thinking in terms of these large numbers. And can you visualize how many people there are in, in Wembley Stadium? Does that mean anything to you? I don't know. I don't know. So, I mean, the numbers, other people I've been trying to get hold of or trying to make sense of it. You know, this is, it's roughly your risk of dying, well, the, given that not most people who have these clocks then go on to survive. It's about, I think, about one in four of them so far who tragically died.

It works out as about your risk of dying, crossing the road in a given six-month period. So these are things that we do, you know, it's very comparable to just like the normal risks of background risks of being alive day-to-day. And so I think you can try and get these sort of contexts of risk across. I think that is a useful thing to do. But, I mean, sort of fundamentally, it is worth remember. that for for young people, COVID isn't very risky. It is actually much, much riskier for our old people. There's the complication of long COVID and, you know, the long term effects of, you know,

like fatigue and some sort of cognitive issues and muscle pain and so on. They are real. But from a point of view of death or acute disease, it is very low risk for individuals. And actually, when you talk about this risk of severe illness from the disease versus severe illness from the vaccine in young people, while they might be balanced, it doesn't take into account the fact that when you get vaccinated as a young person, what you're actually doing is doing it for society, doing it to protect people around you and older people and who are a much higher risk.

And that feels a bit unfair to bring up because so much of this pandemic has been about young people sacrificing large chunks of their life to protect older people who are at greater risk. And I think, you know, and maybe it's unfair to look it by that. But I think this sort of starkly looking at the, on the one hand, you have this risk from the clot. And on the one hand, you have the risk from the disease. That doesn't take into account the wider societal benefits of the vaccine. And I would still be very, very keen if someone does get offered the Oxford Astrosanika jab,

be very, very keen to stress that they should take it both for their own sake and for societies. And while for their own sake calculation gets less obvious at the lower end of the age range for the 2020, 30 somethings. There's still the benefits for society at large are enormous and should be, we shouldn't lose sight of that. I think that's a very good point about, you know, that underlines a lot of this book that life is not without risk. And David's, you know, that's always sort of the point he starts from is thinking about, you know, the broader, the broader dangers at play. So I just want to go back to your book a bit then. And I'm, and pick up on the first sentence, actually,

which I thought was great, by the way. Many writers, you know, probably torture themselves over the first sentences. Numbers are cold and unfeeling. Do you think that's why we're so drawn to them as readers, journalists, politicians, when we try and persuade people or when we try and make points on Twitter?

Is that what you think their power is? I think so I thought a lot about this actually as a line I think when we're suggesting this because one of the things that's very difficult as someone these lot of numbers like Tom and I sort of do is thinking about how someone else would feel if they you know that so don't really like numbers and I know lots of my friends and lots of people say I'm not a numbers person is quite is quite a sort of common feeling and I think there's two reasons that we we sort of think about and one is that people think they can't do the numbers which we talk a bit about as well and introduce And another one is that they just don't like them. There's a sort of, I think it because it really just doesn't capture anything that we think as an individual. You know, if someone to treat me as a number, I think I'd get quite upset because I'm an individual as a person, you know, and we sort of have that sort of feeling. In fact, I often, when I think about that sort of idea of thinking about numbers, I actually

in my mind, I think a lot about sort of World War I and sort of, you know, there's sort of people going over the top and just treating people just as if they're just complete casualties. and it seems to me quite a, I don't know, it evokes something that seems quite wrong in my mind. The thing is, though, is that because numbers are so useful, and this is what we wanted to argue, and because we can then use them in a way that actually helps us treat people as if they weren't numbers, if they, you know, we actually can care about them, that's why we need to sort of, sort of, that's why we need to, I think, have a different sort of view on them. So rather than just thinking about them as treating people as numbers,

we're using numbers to treat people as people as themselves. I think that's sort of what we wanted to get across there. I don't know if Tom had anything. Yeah, I do. So you're also talking about whether or not that's why people like them. And I feel like, I think a lot of people, a lot of the reasons why people do like them. But why they get used a lot is because they have this veneer of truthiness, I think, is the word, isn't it? So if some figure comes out, you know, a politician says child poverty has gone down by X since this time or whatever, you know.

And that sounds like a hard and fast, cold number that you can't really argue with. But the other thing we really wanted to make clear with this book is that so much about the numbers you use and the numbers you hear is about which ones you choose and how you frame them. That example of child poverty is one we mention in a chapter on how you cherry pick numbers. And if you happen to, you know, sometimes numbers go up and down, right? Some years, the economy is better, whatever, you know, things just randomly change. And some years child poverty is higher or lower than it is. And if you say, for example, in 2010, child poverty happened to be really low and in 2011, it happens to be really high. and then you're in 2018 or 2020 looking back you say

oh I want to make it look like my you know I'm the leader of the opposition I want to make it look like the government has done really badly I can choose the year when child poverty was really low as my starting point and now compare it to that child poverty is now and say look it's gone up whereas if I'm the leader of the government I could start from the height the year when it was really high and look at compare it to now and say look it's gone down and which of these is right which is the accurate well neither

is true, neither is there is no right answer there. What you've done is, is chosen, you know, you've chosen this sort of way of looking at it, which makes you look better than you, than you, then, you know, makes you look as good as possible. And what we're trying to do in, in this book is sort of say, look, a lot of this is about how you frame it. There is no, there, a lot of it is not, it's about choosing the angle you look at things from. And actually, sometimes these numbers aren't as sort of, there's not, there's not, there's a right answer. And actually, you need to be better at sort of zooming out, putting it into context and trying to understand how they can go wrong, how they can mislead,

and how you can sort of stumble towards making them tell more truthful stories. And so I just, so before we get on to some of the examples in the book, because there's a lot of them and they're brilliant, that just made me wonder, you know, when I read this book, and this, you know, it's a feeling you get often in a really good science book. you sort of finish it and you think, why aren't they teaching this or they should be teaching this? Is that something that you

sort of feel should be more widely taught in schools or university? Because at the end you even have a little guide for journalists, but this is far beyond journalists and politicians, isn't it? Yes. I think the problem is that when you are enthusiastic about something, it's very easy to say we should do more something in school. So I'm sure if we did in English, Shakespeare, they'll say Shakespeare needs to be taught more than it is at school. And fortunately, I'm an economist. So I actually think statistics, although it's part of economics, should be taught more in schools than economics.

Because it is essentially the foundations of science to a lot of the state. A lot of science we do now involve statistics and numbers. And what we think about truth is scientific. And I do feel that statistics is something that we use every day, even interpreting things like risk. So I would like to see statistics being taught more in school. I mean, it is taught, because I did it at a level as an optional thing, and it is taught in university. But I think it's something that we probably need to have a better handle on in society. When we're hearing them all in the news, and it's not something we really, I think as a society, we're very good at.

Whereas I think with other things that we do concentrate on, things in English, like grammar and all that sort of stuff, we actually do probably quite a lot of it. And I think we can actually understand words quite well in comparison to numbers. And I think we should be able to have the same level of understanding or at least a higher level of understanding that we do now in numbers as we do in words. And I think that's something we sort of argued in the book is that if we think sort of literacy is important for democracy, I mean, we can't imagine a society that couldn't read participating in democracy, even though it did. It literally would exist a few hundred years ago, you know, it was a thing. then we have now a society that isn't very good at reading numbers, and that's where lots of information is given to us.

And if we can't participate in that, it just seems sort of fundamentally wrong to me. But I do think then this probably gets to the fact that it's sort of slightly acceptable to not be very good at numbers. People would say, oh, you know, I'm not a numbers person, that's okay. But I'm sure if I made a spelling mistake, you know, people would absolutely, people really get angry if I'm making selling mistakes. But, you know, if you make a math state, oh, that's okay, because math is hard. And it's, yeah.

A whole load of people telling me off for saying, for plugging the book by saying Dave and me have written a book. And they're like, oh, actually, it's Dave and I. It's colloquial use. Yeah, it's quite funny because the meaning is very clear. And this is very strange. Dave and me or Dave and I, it's completely obvious what you meant. No one's going to go, hmm, I really wonder if that's the case.

But if we just had a probability like, you know, like we say in the book, like, oh, there's a 20% increase in something. it's perfectly, you know, you'd be perfectly grammatically correct, but it gives you absolutely no information. It's entirely unclear what we're talking about, but that is acceptable, whereas Dave and me is not acceptable. To me, I think I know my priorities lie really in that. Yes, no, I agree.

And on the subject of should this stuff be taught, if you're saying, should every school child in Britain have to buy a copy of our book, then I say yes. But I have had a couple of messages from university teachers, lectures and from school teachers saying has anyone else, but I've been started using this to teach in core maths, and I was just thrilled about that,

because I think that's really, you know, that's, firstly, that's a great endorsement of our book. Secondly, I do think, first thing, you know, also I do think it's like, this is, this shows how numbers are relevant to our everyday life, right? Because we will read these things. It is not just about, you know,

it's so easy. I remember math thinking, when will I ever use quadratic equations or whatever, But actually, if you read a news story saying red wine, we'll make you, you know, give you, make you healthy, or give you cancer, prevent cancer, or if you read any of these things about the risks of crime and everything like that, we use these news stories to navigate the world. We sort of, we make decisions about the risks we face in the world every day,

you know, literally down to crossing the road, buying what we eat, what we drink, whether, you know, whether we leave the house and whether we feel safe. And I think it's really important to be able to just put the, hopefully this book gives you the tools to be able to put those sort of numbers in context and not just hear this scary. If you have a child over the age of X, then your risk of something goes up by 33%. What does that mean if you don't know what the risk was? So, yes, I would love it if this stuff was taught. I would love it even more if we sold millions and millions of copies to school libraries, but that's probably a separate thing.

I think what's important, though, is that people who maybe haven't read the book probably think it's a lot about, you know, actual adding up or taking away of numbers or some kind of multiplication, you know, usually doing it in your head. It is not about that. And that is really important because I think when we think about mathematics, a lot of the time we are thinking about adding up, taking away in the head, these type of complicated scenarios. Honestly, I can't remember the last time I've actually added something up in my head. I'm using a computer program all time statistics. These are more conceptual debates. If you're interested in debating or philosophy or arguments or anything about this, this is what we're talking about. And so how to read numbers and understand them is a lot of the time I'm spending on what is the right variable to choose. What is the right kind of thing we're doing? And these are arguments. These are sort of debates that we can have. And it's a real thing. It's not sort of like, okay, can you do 27 times 34 in your head?

A computer can do that. I mean, it's great if you can do that in your head. But it's not the most important thing when we're talking about. you know, how to read numbers. So, you know, don't worry about how fast or how, you know, how fast you are calculating stuff in your head. It's more important to sort of, you know, look at the actual arguments that these sort of numbers are making and whether you can do that. Yeah, this is, this is exactly, this is really relevant to the thing we were talking about earlier on, about the Oxford Astrodenica vaccine and blood plots, because, I mean, I, the first thing I wrote

about it a few weeks ago, I was talking about, I looked at the background, the background rate of blood clots in the society and really you know just in a if you give 18 million people whatever if you just take 18 million people what number of them will have these sort of clots in a given period anyway and I think well that's is that the right base rate that I should be comparing it to or should I be comparing it to as I've decided would have as we now realize later on as a better comparison we'd be comparing it to the right rate of oh god cerebral venous venous sinus or and then actually as it turns out that thank you very much And then as it turns out, there is, it's actually a more complicated thing than that.

Still, it is a particular and rather rare combination of that and something called from thromocytopenia or low plate accounts. So what is the correct, you know, if we're comparing the risk, what's our base rate that we should comparing it to? And that is not a question of being able to add up numbers. It is a question of wisely choosing the correct base rate to be comparing it to, how to put it into context. And yes, you can do any multiplication or a number.

addition problem you want in the search bar of your browser, it takes five seconds and it's not difficult. And you don't need, you don't even need a calculator. You don't need any sort of skill. What you need is sort of the mindset of thinking, oh, right, that sounds like a big number, but is it a big number? How do we find out? What context do we put it into to make it to establish how seriously I should take it? And yes, it's a philosophical or sort of, well, yeah, a philosophical discussion as much as it is a numbers one. Yeah, it certainly struck me that You know, especially for us as journalists, the tools for sort of critical thinking in the world and the many problems we face and how much data there is that we can pull up on any given problem, just could be immensely valuable. So throughout the book, you sort of outline, you know, different, effectively, in a sense, red flags, things to spot or ways of thinking about problems.

when it comes to statistics and claims or, you know, even reports made of studies. And I was curious, you know, I was a little bit worried. You know, I'll be honest, I was nervous. I'm going to see science focus in it. But, you know, because it is so tricky and it is so treacherous. But I wondered how hard did you find it to find these examples? Was it worryingly easy? Or did you have to do some digging?

it's not hard to find examples I mean that I suppose it's not it's partly it's not hard to find examples because I can just go through my back you know my my my back catalogue of times I've complained about people getting the numbers wrong in the past

it felt a bit like doing the greatest hits album to be honest but the but the yeah I mean the thing is right I I actually I'm a journalist now I've been a journalist for oh god I don't want to think about it 13 14 years

whatever and I am And I genuinely have a high opinion of journalists as people. I think we are generally well-intentioned. We're generally clever, generally sort of trying to do best, trying to do good in the world. But generally speaking, we are better with words than we are with numbers. And that is, you know, we are not, as a profession,

journalists are not especially numerous. And I don't, that's not a huge criticism. It's, you know, any more than it would be a criticism of mathematicians to say that they're not especially literate. you know, that's the skill set that gets trained. And I, um, so I think that has led to, means that journalists are susceptible to falling into these sort of pitfalls. When you see, when you see a thing saying,

um, uh, something puts your risk, you know, your, your, your risk of, uh, baking, so eating bacon every day raises, raises your risk of a particular kind of cancer by 20%. That sounds really bad. And, and you, oh, that's your headline. percent risk, go. But then, and it doesn't occur to journalists because they haven't had this sort of way of thinking drilled into them, just say, wait, wait, wait, actually, that's a red flag. I should tell 20% more than what? You know, what's my, what's my starting point? Where do I go from there? And I think that is something that I would love journalists to get better at, but at the moment, I think it is a, it is a common problem. And there's also, there's another issue which we will,

which we discuss in book, is that there's an incentive problem. for journalists, which is that we do want to improve the world and help everyone, help everyone understand the world and generally, you know, we see journalism in the public service but it is also a business and you are trying to sell papers or get people

to watch your news story or listen to your podcast, whatever. And if you go around constantly saying no one died of a plane crash in a plane crash today, then you won't sell any papers. You are incentivized to find the exciting things, the dramatic things, the shocking, startling, surprising things. and if that is, you know, and the thing is that quite often the surprising things will be

that will not always be the ones that are best for navigating the world. I mean, like that, a 20% raise in cancer risk sounds much more dangerous than, I think, I can't remember the exact numbers, but it works out there's about a one in 90 chance that will actually affect you when you look at the, you know, it's not nothing, but it's not, it's not a big deal. It's not as big a deal as it sounds like. So, so when you, so you are incentivized as a journalist to make it sound as dramatic as you can so that you sell more papers. And journalists try not, do sometimes try not do that, but there is, as well as this sort of not, the sort of, not naturally not being brilliant at numbers, there is also a sort of enemy action problem that you are pushed into

doing the most dramatic and, uh, sometimes misleading versions of stories or versions of numbers that you can find. And I think, I think that incentive, so it's not always a journalist's fault, other things. It can also be speaking in an academic. In academics, while we have our own incentivization problems with trying to, you know, this whole publish or perish idea, the fact that we are, if anything, and academia is, it's all about trying to publish things that are, you know, usually sort of startling, just like you were in news. Oh, this is an interesting event. And the problem with that is that you can lead to publication bias. So we can, and that's something we talk about in our book, this sort of idea that, you know, we have certain effects that may be more

prominent, whereas actually we wouldn't see, we wouldn't see more of sort of balancing out of some negative and positive effects. I'm not sure we did a good job of explaining publication bias there, but the idea, though, is that I think it is a problem. And I think that, you know, and there's also even incentivizing to really talk to the media is not massive. You know, I think in some countries, it's slightly different. But, you know, there's not huge incentives, at least for promotional things in academia, to, you know, talk about the work compared to, say,

just publishing in a journal that, you know, say, two or three people read, it would be seen as quite a big accomplishment compared to, say, you know, sort of talking to the nation or explaining, it's quite tricky. There's a thing we talk about in the book is the replication crisis. I'm sure you've discussed out on this podcast before,

but, you know, that's exactly it. a lot of scientists who themselves, as it turned out, weren't, were either not very good at statistics or deliberately using statistics as dark arts, almost. And they found that they could, you could get essentially a noisy data set that doesn't say anything in particular and chop it up in lots of different ways until you find something that looks like it's real. And then you can say, look, I found this, I found that if you eat,

that men eat twice as much pizza when they're in front of women to impress them or something like that, then you get that published in a journal and everyone goes, ooh, very exciting. And then when someone goes back more carefully and checks, so no, that doesn't stand up. The data isn't there. But you've got your, you know, you've got your citation, you've got your publication, you've got your citator,

you've got to get cited, you get tenure as a professor, you know, you're incentivized to do these things. And then so, and then, so that's exactly what we're talking about here. So you're incentivized as a scientist to push these dramatic findings, even if they're not real. And then as a journalist, you're incentivized to cherry pick the most exciting of them and put them in a newspaper. So by the time a statistic makes it into the newspapers or into the news, it has already gone through two filters of excitingness, which may well mean

that it is not actually true by the time it gets to you. And I think that's a real problem. And it's a lot to ask journalists to say you should be able to check the work of scientists to make sure it's, you know, because the scientists can't do it. And the one I just mentioned about the pizza thing, that turned, that was uncovered. by some really sophisticated data sleuthing, also one really badly judged blog post by the guy who did it, and then also some proper investigative journalism by BuzzFeed Stephanie Lee,

who got leaked emails and good old fashioned investigative journalism to uncover those as bad statistical practice going on. The idea that you could do it as a science correspondent of, I don't know, the independent or the Times or something like that, and who's writing two or three science stories in a day, you haven't just haven't got the time or the bandwidth, with to go and go through the stats like that. So it's a lot to ask journalists to be better at that sort of thing.

I mean, I did have a colleague once upon a time who was a sort of their degree. I'm probably going to purchase this now. I think it was in mathematical physics. And even, you know, when they were starting out, they did not hurt. They didn't know what a P value was, which is, you know, essentially we're talking about what is the statistical significance? which is probably best left for another time, but of this result. And so it is very hard for both, you know, journalists and the public to sort of often navigate this.

But I guess that's what the book's for, right? Yeah. I will say about statistical significance. It is that one of the things we go on about a lot in the book, it would be lovely to have time to explain it. You may be right. No, go. I would love people to take away from this in the book that the word statistical significance does not in any way imply actually.

significance and just means that it might not, that it probably is, whether it may not be not real or something like that. I'll let Dave, you probably do explain. I think the idea with statistical significance is people, when they think of significance, is affect size, right? That's a significant binding you've got there, like a really important big thing, right? But actually, when we, it's probably better to think of it as detectable. So bacon is a really good example, bacon and cancer. Statistically significant result that is a, a really important result that is. it will increase your chances of getting cancer. So if you go, oh, wow, statistically, it's a significant, sounds scientific.

I've got to, you know, maybe I don't eat bacon now. But then what if we said that the effect size of that is incredibly small? Like, in other words, every, you know, piece of bacon you eat, it increases your chances of cancer by a negligible amount. Saying that significant is a bit, I think that's a bit difficult in how we would, you think of it is language. Now, there may be a link, but the effect size is so small. I think saying statistically significant is very,

difficult. But I think statistical significance, what it's sort of generally people get confused about, is that they think it's sort of a probability, which it kind of is, but it is more to do with, and you can't really talk about this without talking about hypothesis testing. You're doing a test about the world. Do tell us, tell us what statistical significance is. All right, okay. I'll see if Let's see if this one works over the radio, shall we? All right, so if you... Let's imagine you've got a bunch of dice, and you want to see whether they are loaded.

Okay? So you... Dave, stop in, if I'm going this wrong, so I'm trying to do it from memory. But they... Let's say it's not like... If you roll a six, it might actually not be. You might have got somebody who's trying to play a trick on you,

and it's say more or less likely to roll a six. Yeah. So you're trying to test for this dice is loaded. If you roll it once and you get a six, does that mean it's biased? No, because you could have rolled a six by accident, just anyway, even if it wasn't. If you roll 100 sixes in a row, it would be very unlikely that that would happen on an unbiased dice. That was just, you're reaching into the, just, you know, greater, you know, longer odds than the number of atoms in the universe or something mad like that. So if you, so, but at no point can you actually say this dice is definitely loaded.

always roll one more six. The P value is the likelihood of seeing that result on an unbiased dice. You so what I mean? So if you roll three sixes in a row, that's one in 216 chance of seeing that on a fair dice. So your P value is one divided by 216

or about 0.0. I can't figure out of that. I can't think I've done all that. B0.0.0. 0. Very small. I think the crucial thing here is to think about the fact that it's sort of, it is an experiment, like a thought experiment. It's like a philosophical experiment. What would this, what would we expect to happen if this dice was unbiased? So I think

that's the way to think about it. When we think about p values, what would we expect to happen? So how likely would it be if the dice wasn't unbiased for us to roll 160 and roll, and we say, that's extremely unlikely. And what we'll do is we'll set a tolerance level beforehand when we think, and this is where we get the p equals 0.05 from, that's our tolerance level. How tolerant we are to say, well, if it's below that level, if that risk, that probability is so low, then we'll say, yes, it probably is the fact that it's very unlikely to happen in this world because, you know, is it really likely that we have, say, 1006s with, in our, with an unbiased ice, well, probably not. So it's this idea that it is a thought experiment,

and I think that's what probably people forget when they think about statistical significance. And so one thing that happens a lot with journals, which is this idea of P-hacking, is that people forget that it is this experiment. So they'll just keep on rerunning this thing lots of times, forgetting that, and then suddenly you'll just have this random result, that, oh, wow, I've got this, I think I've got statistical significance. But what you've actually done is run this thing so many times that by chance you've got this random result.

Because there is always a chance. I know this is going to be rid. There is always a chance that you do get 106s and well, okay, maybe not 1006s, but there is always a chance that this thing does happen. And that's how it works in medicine. That's exactly how we'll be thinking about the problem with the blood clots that we thought earlier. How many, for example, if we didn't see a link between vaccines and blood clots,

how many blood clots would we expect in the general population? So assuming that there's no link, what's the likelihood of the amount of times we get people with blood clots? And then we might be seeing now, as of evidence, that there is some. And so we're doing this, and it's difficult because there's low values, probability, and there's all sorts of things going on here. But that thought experiments is essentially what we think of as scientific proof. And I think people obviously think about cup up and falsification, but actually a lot of the time it's not. It's always a case that something could possibly be true.

We can't prove forever that gravity always exists. We just think it's extremely highly likely it does because every time I've done it, I see this thing falling down. And it's all about likelihood and probability. And I think that's reason why, you know, going back to everything we've said here, science is so important in schools, because this is what we think of as scientific proof. It's not the theory necessarily. And I think that's such an extremely important thing for people to know and to understand. I think that's, you've done a great job there of explaining that. And I think certainly in the book as well, you even use cats, Tom, to make your point. It's extremely important, yes. It is. And it's, you know, I think we're probably at Science Vegas, maybe a little bit guilty of not, you know, going into that too much.

Because it does, you know, if you have to explain it every time you mention a discovery, it's a bit laborious. But it is fundamental. So I want to just move on to another value. But I think it's interesting because, again, it's something we've all been talking about for the last year. And that is R in relation to the reproductability of the, of, COVID and we've been seeing, you know, our values shown all the time. I think I'd like to just talk about that because I think it's a good example of how

there's, in that example, there's no sort of intention to mislead, there's no sort of misrepresentation necessarily of numbers, but even then, you know, a number can hide another meaning or a deeper meaning, especially when it's a simple, single number that's quite neat and quite tidy like are, you know, so we're below one, so everything's okay. And I wonder if you could sort of talk us through that example of how the R rate can sometimes sort of hide important detail in the sort of reporting and the communication of what's going on with COVID. All right. Shall I go? Yep. Okay. Well, so there was this, there was, it was just, it was a really interesting thing that happened in, I think, May or so of last year. And,

that the John Edmonds, is it? The epidemiologist, who I think he's on stage, said, look, he told the Science and Technology Committee that the R-value, their estimates, the R-value had gone up, and this was written the depths of lockdown, and that sounded awful, right? And so, of course, the next day, you know, R-values gone back up might be as high as one,

the newspapers all over the place, but that if you paid a bit of attention to what he was talking, what he'd said, it was a bit more complicated than that, that actually he was treating it as though there were two epidemics going on, one in the wider community, you know, just among all of us, and one of us in the, in sort of care homes and hospitals. And in care homes and hospitals, the R value was a bit higher than it is in the society at large. It was spreading more easily in care homes and hospitals,

because they're more cramped environments. But what was happening in both of these environments was that the R-value was coming down. The number of cases was going down and the likelihood of it spreading was coming down in both of them. But because it was coming down faster in the wider community than it was in hospitals and care homes,

it meant that even though both of these individual places, these individual epidemics were slowing down and getting smaller, the slightly the care home epidemics was taking up more of the average. It was becoming a bigger part of the average. And therefore the average, when you look at the both them together, was going up. It was this weird,

it's this weird counterintuitive thing called Simpson's paradox that even though the numbers when you get a big data set and divided up, even though, and the smaller bits, the numbers can be going one way. When you add them together, it can look like the average is going the other. You can see this in some really interesting things.

What was, for those are a marvelous example that we've for example in if the me if your median wage is go the in the america a median wage for all of society was going up but if you broke it down to um people who had gone to university who hadn't gone to university people had gone to high school people who hadn't finished high school and each of the the median wage for each of those four segments was going down even while the society as a whole was going up and that was because more people were moving into the higher groups. So more people are going to university, more people are finishing high school. And so it became this really complicated thing, even though the overall number is going

one way, when you look at the subgroups, it goes another. And this was a really interesting thing, because what is the what is the, what is the correct way of looking at it? You know, what is, in the median wage example, if you are a person with no college degree, then you're likely that your wage has gone down over that period. But if you're an American, as a whole, it's likely that your wage has gone up. What is the correct way of telling that story? And I think in the case of the R value, at least,

there is, you know, you might only, it might be important to know that there's, to treat it as one big epidemic, or it might be important to look at these subgroups. The only honest thing you can do is say, look, this paradox is happening, this complicated story with the story, with the numbers is going on, and we need to sort of express that and let the readers understand

there's more to it than a simple number going up and down. And Dave, if you want to write something. I find the Simpsons Paradox extremely, I mean, if you're sort of slightly confused about how this can happen, don't worry, I still find it very difficult. It's actually when you get written down or you see a sort of page, we've got a nice table on it in the book, which is sort of advertisement, to buy the book. It's actually, oh, okay, that makes sense now. It's actually a lot to do how the group sizes change and then you can see how it happens. But I think just so one interesting point about the R number, which I always felt was so, so difficult, especially because it's just a number, you see 1.1 or 1.2. I'm used to dealing with sort of compound growth, exponential growth.

And I find it that people, well, it's very difficult is to know what's the big deal about 1.2, 1.3 or 1.4. They don't really seem like that bigger deal, right? But, When actually you write it down, and I suggest you do this if you're so inclined, if you're not really convinced, it's just to see it once and literally just sort of times, you know, take a number, say 10 and times it by one point and see how quickly it grows. And you'll be surprised that small, very small difference, like 1.1 to 1.3, how quickly it just completely gets out of hand. And I think this goes back to this idea of what's in our experience, which I think is important. We don't, unless we maybe see something like starting a fire and suddenly it sort of starts small,

and suddenly it completely takes off. We have very little experience of compound growth, seeing it in our lives. I think that's why it's so hard just to see from a number how can such a small difference really make this sort of big impact and how scary that is. And I think that was something at the time people probably didn't really have a good grasp of. I will say, though, it is astonishing.

I would love to do some research into this or something because I bet if you'd ask the British population 14 months ago, or certainly 18 months ago, what is the R value? I would bet that one person in 100 could answer it, you know? Professional epidemiologists, statisticians, you know, that sort of thing. I couldn't have done until I read a book about it, until I read Adam Kacharski's book in about January last year when this was all kicking off.

I don't think I'd have been able to tell you what it was. And now if you did it again, I know I'm just making up numbers here, I would be amazed if much less than half of people could, you know, couldn't tell, you know, we're able to tell you. I think it's now very much part of our common parlance. I think there's been... I think it gives you some definition. That was accurate. I think you know greater than one bad, best than one good.

Yeah, maybe. But I think they probably know that it's to do with the number of people that a person, you know, the number of people infected by the average person. Maybe half is optimistic. But I do think it's been, it has been, the pandemic has been a marvelous education in how people can get the hang of this. stuff. To a reasonable degree. They're not all going to be, you know, Professor to David Spiegelhalter, but they can get it to the degree where they can make use of it in their lives when they have to. And, you know, I think that has been somewhat heartening. I may be totally wrong, maybe no one has a clue what they're talking about, but I think that, I mean,

certainly when you watch the political journalists and people who've been thrown into having to deal with this stuff. It's been fashionable to sort of say they've got it terribly wrong, but I feel like going from a standing start, they've done a pretty decent job of having to, you know, go from rarely using numbers to do more than, like, look at how many votes they've got in the House of Commons to now actually working out our values and things. I think it's been a real education. I wonder if that's because maybe ours, it doesn't really have anything behind it, just says ours. You have to learn the definition where herd immunity, you're going to say that, what that means. I think probably people would make more mistakes than that.

And I talk about that a lot because it's sort of a mystical significant. It's sort of a misleading word that you think, oh, I know what this means now and then you sort of go off. Yeah. I think it would be fascinating, wouldn't it? Because I suppose there's a bit of both tied into that, isn't there? Because a lot of this is not intuitive. I mean, it's as far from intuitive with, you know, for example,

the paradox that we just sort of talked about. But then I suppose in the last year, we've had, we have had a very real example of what happens when R goes from, you know, 0.9 to 1.1. We've suddenly quickly seen these fluctuating numbers where very quickly you're suddenly not, you know, you're not following the news anymore because it's dwindling. And then the sunny, I'll go up. We all have to be inside with everything's, you know, terrible.

So, yeah, it would be a fascinating thing to see how people understand these sorts of things and how, you know, how much of the science communication got through and made difference. Yeah, it was a thing that, sorry, I've jumped in there, but I was saying, it's a thing that I've been, I've been asked a lot. The, the, when I, you know, just brush a bit of dust on my shoulder. When I won the Royal Statistical Society's statistical excellence in journalism award only a few months ago, the, the one of the things, they, you have to write a little thing afterwards and they, sort of, you know, about, about it all. And they said, do you think this last year has been a, um, people that has been an education for people. And I had to say, like, you know, as someone who likes, take numbers seriously. I don't know. I haven't done any surveys on this. I would love it if someone

did. But my fairly confident guess is that there have been a real improvement in understanding the relevant numbers, things like infection fatality rates, things like R, things like, you know, they're just a much larger percentage of the population could talk reasonably knowledgeably about these things and they could have done before. But sorry, I interrupted you. Do carry on it. And now I'm thinking how you go about looking at that. And I'm like, well, we don't have a I can't down. I was basically. Anyway.

Well, I mean, no, I think it's fascinating because I think, as well, before I put this back on the rails, I would be fascinated to see whether behavior changes as we return to, in drastic quotes, normal in terms of, you know, just simple things like how disease spreads. Will we shake hands? Will we keep masks on in public transport? will we, you know, now that people have from home. Exactly, this intimate knowledge of how disease spreads and what the risks are and etc. I wonder

if that will change. But anyway, to get to back to statistics that we know about, not the ones that we haven't found out yet, I just want to ask about a couple more before we wrap up. Another one,

not to keep it on coronavirus, but it's so pressing, I suppose, is how I enjoyed is one of my favourite is Good Hearts Law and there's some great comics if you Google Good Hearts Law about this by XKT and others like it.

Can you tell the listeners sort of how that played out in the pandemic a little bit and what it is? Yeah, sure. Okay, so Good Hearts Law is this very dry sounding but incredibly

profound thing I think which is it's The line is when a measure becomes a target, it ceases to be a good measure. And what that means is if you, you know, we use numbers, we use metrics, measures to measure what is going on in the world around us. You know, we want to know how is our education system doing. So we measure how many children get 5A star to see grades at GCSE, or we want to know how

hospital system is doing, so we say, you know, what's the survival rate of people 30 days after they are, you know, allowed out of hospital? And that's really good and useful. But then if you take that number and say, right, this obviously correlates with how good things are. So we think, okay, so we look at education and we say, oh, so children who get more, more, they start a C grades tend to do better in life. Therefore, if we push the number of children who get A-star to C grades up, more children will do better in life. So that will be our target. We will tell schools, if you don't get 50% of your children having five A-stars to C at GCSEs, then you will be punished, and it'll be rewarded if you do. You know, head teachers will lose their jobs, or you'll be put into special measures

if it doesn't happen, that sort of thing. And then, of course, what happens is that measure becomes a target, and so it ceases to be a good measure. So then you'll get things like, teachers will teach to the test. Or as genuinely did happen, they concentrated on the children on the C, D, grade boundary. So they're pushing children who are in D up to C and neglected everyone else because they're either going to fail or they're going to get the C to B or A, whatever. So the way of pushing up this arbitrary metric is to do it, to concentrate on those children hugely. It pushes up your metric, but it doesn't particularly improve the thing you actually care about, which is the sort of flourishing of all children and the whole grade pyramid. And what happened in COVID, which was, yeah, I was kind of weirdly proud of myself about this because it was, and again, April, I think last year, Matt Hancock declared that they were going to reach 100,000 tests by the end of April. I think I've got my numbers and dates right there. And I immediately thought, wait a minute, wait a minute, you're giving yourself a metric there, going to take yourself a target, you know. And this is going to be a bit of a hotbed for Goodheart's Law. And lo and behold, that's exactly what happened. They started counting antibody tests as COVID tests, even though that wasn't what we were using them,

you know, as PCR tests as that was, because that wasn't what we're doing. They started, Matt Hancock was sending out emails to all the Tory mailing list, saying, please go and get tested so that we can get our numbers up. there was, they started counting tests that had just been sent out in the post rather than actually taken as taken. So, you know, and then they started counting tests that have been, so if someone did a test, it didn't work and they tested again, they counted as two tests. And by doing all these things, they got it up to 100,000. And, you know, I'm not saying this was a bad thing. They did get, the testing regime got up really quickly and was impressive,

but they, they started, what we actually cared about was the number of people who needed a test and were able to get one. And what we didn't care about was whether exactly 100,000 people, 100,000, 99,99, that doesn't matter. The number on the thing was unimportant. And the Good Heart's Law nature of it meant that, of course, once we set this target, it was going to push us to getting these numbers as high as they possibly could.

I think what's interesting about that is Good Heart's Law is just so applicable in so many things. In fact, we've discussed a couple. One is, you know, would you say it's a good idea for, journalists to look at the amount of clicks on their, on their article. Now, you could say that's a good thing because it would incentivize some behavior to make sure they care about, you know, the really say the importance of their journalism, but also we could also say there's some negative behavior that would go in, maybe more sensationalist, same with academics and publishing, the idea that

maybe it incentivizes me to be more ambitious and work harder, or maybe it just incentivizes me to cheat. And I think what's really important is not, I don't think it should be that we should not necessarily set targets. They can be a good thing, right? To say, we should aim for this. I think saying that we should aim for something is okay. The problem then is that then if that becomes the only way you judge something, that's where you get into trouble. If you're then saying, look, we're only judges by the success of the 100,000 because that then, that measure has become something that we can't objectively say, this is what's going on with the vaccine. And I think it's important because I'm sure many of you, this thing will have this in your daily lives. It happens all the time. And I think

what's important is not to lose sight of what you are trying to achieve. And this is why I think people dislike numbers so much because when you get things like bosses or whatever looking, or why haven't you done this, you know, so many things, you get these numbers and people are trying to sort of show that as evidence or maybe even giving you that as a target. I think that really leads to something that is bad. It's a bad use of numbers. I think one of the things to do is when you get a number, rather than saying necessarily, this is what this thing says. This is what this shows. Think Why is it showing this? And think of all the possible reasons.

It's not just the good, it can be the bat. So that's probably a better way of thinking about numbers rather than just saying this immediately means you're rubbish at journalism, Tom, because he didn't get a thousand million clicks or whatever. I always got a thousand million to do that. Is that something else? And I think if you're too quick to jump to conclusions,

you're not really getting, you get getting really the most use out of the data. I am, funnily enough, I did a thing, another thing with the BBC last year and speaking to it, an education list and sports fan, Daisy Krista Dulu, who mentioned,

who's the woman who mentioned to me the D&C grade boundary thing, but she also said, you can see Goodheart's law in a really interesting way in sports. You have, for example, in football, you have a problem, like the game doesn't flow well because someone keeps standing,

you're just goal hanging, right? So you say you try and introduce a rule to stop someone goal hanging, introduce the offside rule, say, okay, you're not supposed to stand past this point past where the last defender is and then of course

that becomes part of the game. manipulating this new offside rule becomes part of the game and then so then lots of goals that would otherwise be good get ruled off, you get VAR looking at someone's armpit being offside by half a millimeter and all this sort of stuff and that but that's not really what

the rule introduced to care about if someone is a quarter of a millimeter offside. It's you care about the flow of the game and the you know, but anytime you introduce these new rules, you set these new targets, you set these new metrics, and that makes them useless for the thing you're originally trying to do. I really think that what a good heart's law is this, one of these things that when you see, when you've had it explained to you, you start seeing it everywhere, just everywhere. It just becomes this. I mean,

honestly, my last book was about how AI could go wrong in dangerous ways. And basically, I realized I could have written a lot of large part of the book was, like Good Goodhart's law, but more so. You know, like, if you tell a computer to do something to, like, build, you know, to cure cancer or make paper clips or something like that, you have to be damn sure that it's going to actually do the thing you want it to do and not just fulfill the metrics that you've set for it, because that's where it goes to disastrous wrong. I think Goodheart's Law is a really profound and fascinating thing that, honestly,

once you've seen it, you can't stop seeing it everywhere. So then finally, I just wanted to sort of end on an upbeat note. because maybe at points in this podcast or maybe in the book, you might think, oh God, can I trust anything? Can I, it's anything true? But I suspect you might have, you know, the view that actually, or a different view to that. But what do you think?

Can we trust anything anymore? Or is it just about the nature of the world as it is now? I think this is something, again, it's a worry. It's an action for us that we are worried about bad behavior that suddenly, you know, you see, you read everything in this book and you say everything is just completely nonsense, so I can't trust anything. And I think it's completely reasonable thing to do.

I really hope that people don't do that. And I would implore them not to. We're obviously highlighting certain events where things do go wrong. Okay? And I think it's more about how to interpret when you see things in the world, how to interpret that. And I do believe quite strongly that numbers are extremely important and can help us get to what we think is the truth or something, like along the way. lines. And even if you have stuff in the media that's not quite true, it doesn't mean we can't learn

something from that. You know, a lot of the times when I see something, I think, say, for example, oh, there's sampling bias here, even on Twitter. It doesn't mean I can't learn something from that thing. It might be that just that's a good representation of Twitter. It's maybe a bad representation of the population as a whole, but I might be able to learn something from that. So it's more, what can I take from this when I see a number? What can I learn from this? So rather than saying, oh, nothing is real, everyone's sort of lying to me. I think it's more, well, I mean, no, that is true. That's a really, you know, I can understand that people go, and I think it's a common thing, right?

Lots of people, when we mention this book, say, oh, yes, you know, lies, damn wise statistics and all that. And that's probably only true because we are letting people do that. We are, we know that, if we knew that how people did that, it'd be far harder for us to be tricked by it, because we would know, you know, basically, if we, if everybody knew or followed the rules in the back of the book about 20% increase, there'd be no, the sensationalism would go away because there'd be no point in doing it. Everyone would go, this is stupid. You know, that is, why would that just completely ridiculous? No one would believe it. So I think that's one of the reasons why, at the end of the book, we gave this idea of a style guide. We gave some concrete,

and it's a campaign that we're trying to do in terms of statistical history. If you're interested, you can sign up on how to read numbers. And it's just idea of this, if we have, the media that follows these simple rules about how to present numbers, then it's better. better informative for us. And what we want to do, it's not just journalists following them. It's we as the public want to demand people giving better numbers because that's what we're interested in. And we want it to be sort of demand-led thing. I will say this about the, firstly, I worry too about the, you know, the lies down lies and statistics thing because I think I think there's a counterpart to that which we quote in the book,

which I think is really important, which is while it's easy to lie with statistics, it is even easier to lie without them. Because if you're, at least, if you're using statistics, at least losing real statistics, at least you have to, it makes a little bit harder to falsify things, right? You can't just make stuff up in the same way that you could without them.

That said, like, I do think, and I completely agree with Dave, and this much such thing we would love you to do is go to how to read numbers.com and sign up to our campaign to get more, media outlets to use a statistical style guide, whether ours or their own, you know, something like that, we'd love it if the BBC wrote a statistical style guide,

like they have a, you know, a writing style guide. But I do think, while I can't trust anything in the media, any numbers, all these numbers of lies is an overreaction. I think that it would be good for readers to have a sort of an instinctive, well, they've given me a number. What should I do now? You know, what should, I trust but verify sort of aspect of thing, you know, like that to the thing. If you see, if you see a number, just knowing what

questions you should ask to interrogate that number, have they given me a context? Is it, you know, if they give me the absolute risk as well as the relative risk, is there, you know, is there, is there an effect size here? Do it if they just say, you know, there is a statistical, statistically significant link between eating fish fingers and developing a problem with snoring or something, you know, the, the, um, when they say there is a statistical link, how big is that link? How big is that link? they told me. And if they don't tell you these things, or if they don't tell you, you know, the sample size of the study or, you know, perhaps the confidence interval around the,

around their estimates or anything like that, it might be worth just to say, well, should be being a bit more willing to just not trust it or to go and find, go and look a bit more into it somewhere else, especially if you're going to base any decisions on it. I think that that would be a good thing to take away. That was Tom Chivers and David Chivers there talking to me about their new book, How to Read Numbers. The book's on sale now and it's published by Widenfeld-Nichelson. If you are interested in their advice on how to report statistics, do head to their site, How to Read Numbers.com.

We can find their statistical guide in full. Thanks for listening and if you've enjoyed the episode, please do leave us a review. This podcast was brought to you by the team behind BBC Science Focus magazine. In the April issue, which is on sale now, we dive into the missions that will take scientific, to new frontiers. For the magazine, we've talked to the teams exploring mountains under the oceans. We've taken a close look at the project that will attempt to take an actual photo of an exoplanet. And we've explored how cosmic rays are allowing scientists to see deeper into ancient pyramids than ever before.

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