
A&E waiting times have been making the headlines - Tim Harford takes a look at some of...
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Thank you for downloading More or Less from the BBC. This is the version of the programme first broadcast on Radio 4 on Friday 7th June 2013. Here's Tim Harford.
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Hello and welcome to More or Less Sliding the statistical master key into the great mortis lock of life. This week, the statistics of pregnancy, of having three pairs of twins and of course, of what comes before that.
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If indeed it were true, I'm really not sure how most men would get anything done because their brain would just be so clogged with thoughts of sex.
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And we'll be setting Evan Davis the most fiendish challenge of his career, trying to find simple economic data on the website of the Office for National Statistics. But first, let's talk about how long people have to wait for emergency treatment in English NHS hospitals. Research suggests waiting times for accident and emergency departments have reached a nine year high.
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The King's Fund.
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That headline was from the Radio four bulletins. Actually, a lot of the reporting we've seen here looks perfectly reasonable to us, but it is worth clarifying a teensy what is a waiting time? So often on more or less, we hear statistical claims, but then it's easy to jump to a conclusion about what the statistic is describing. You might assume that your waiting time at Accident and Emergency is how long it takes for a medical professional to see you. Not so. The clock starts when you register at the desk and it stops when your case is resolved, which means you've been treated and discharged or you've been admitted to the hospital. Now, here's another claim from Sarah Montagu on the Today programme.
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There have never been so many people trying to use accident and emergency services in this country. Last year the number reached 21.7 million. That's up 50% in a decade.
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Now, this is true, but it doesn't mean that more and more people are going to traditional A and E hospital units. About 10 years ago, the National Health Service developed lots of new walk in clinics and minor injury units. And from 2004, people presenting those new units have been counted as having shown up at Accident and Emergency. The numbers of people accessing these types of services has increased over the last nine years, while the numbers attending traditional A and E units in hospitals has risen only very slightly. One more thing to watch out for when you hear numbers about the nhs, just remember it's a pretty big organisation. Here's the Shadow Secretary of State for Health, Labour MP Andy Burnham. We've seen around 4,000 nurses jobs lost under the coalition and a survey came out like this, pressure on AE will get worse and worse unless the government changes course. Fair enough. 4,000 fewer nurses is 4,000 fewer nurses. But a bit of context never hurts. There are 300,000 nurses across the entire entire NHS in England, so that's a reduction in nursing levels of 1.3%. Now, last week I teased the Daily Telegraph. Worrying news on the front page of the Daily Telegraph on Wednesday. If you take 15 people having elective surgery in any English hospital, including relatively common procedures such as hip replacements, tonsillectomies and hernia operations, one of those 15 will be dead within the month. It's an astonishing mortality rate of 6.7%. Or alternatively, the Telegraph put the decimal point in the wrong place. Now, I could have stopped there, but I may have got a little carried away. Something of a trend for the Telegraph, which made a similar front page error almost exactly three years ago. Misplaced one decimal point might be considered a misfortune. To misplace two looks like carelessness. The National Health Service suggests that the risk of death for a kidney donor is around 1 in 3,000, which is low. Unless, of course, the Daily Telegraph gets involved, in which case it could increase tenfold at the stroke of a journalist's calculator. Till we return next week, or for Daily telegraph journalists in 10 weeks time. Goodbye. Who's there?
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It's me. I'm a headline from the Daily Telegraph. I want to point out in last week's program, at the same time as making fun of me, you made a decimal point error yourself. You said the Crown prosecution pays about 5p to print the paper for each case, when in fact it was £5.
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Oh, jealous statistical gods, how cruel you are. I was wrong. Very wrong. Wrong by a factor of 100. Now, that's as wrong as two Daily Telegraph headlines multiplied together. The gist of our story was right. The Crown Prosecution Service isn't as extraordinarily wasteful of paper as you might at first think, and using paperless systems isn't going to reduce radically the costs of the CPS. But printouts cost around £5 per case, not $0.05. So while the story was right, my maths were wrong, as several loyal listeners emailed or tweeted to point out. This is embarrassing, given that we're a program about getting the numbers right. And doubly embarrassing because I was mocking the Daily Telegraph for making a very similar error. Awkward.
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I'll say it's awkward. What have you got to say for yourself, you smug hypocrite? Sorry, Sound like you mean It.
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Sorry.
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That's better. Apology accepted. Good afternoon.
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You're listening to More or Less with me, Tim Harford. Last week, the Commons Public Administration Select Committee released the findings of its investigation into the way statistics are communicated in the uk. The report covered plenty of ground, including the way the Office for National Statistics responds to requests for bespoke or ad hoc statistics and what the UK Statistics Authority does when politicians misuse official statistics. It's hard to believe that's possible, but I am told it does happen. But we couldn't help noticing that the Select Committee raised an issue which we've struggled with ourselves over the years, the idiosyncratic performance of the Office for National Statistics website.
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I'm not going to put too much in the search bar because I think that I could put goods, but. Well, actually, why don't I put goods?
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Yeah, you know what you're looking for. Let's not make it OK. One man who has a serious beef with the ONS website is Evan Davies, once the BBC's economics editor, now the statistical wing of the Today Day Programme. Surely Evan, with economics related degrees from Oxford and Harvard, years working at the Institute for Fiscal Studies and two decades of experience as an economics journalist, isn't going to be flummoxed by the following simple challenge. Relying only on the ONS website, find me the latest figure for UK Weekly household spending.
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Household spending. Okay, so let's search for that. Put it in the search bar. You get a huge number of options.
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2,468 results. The first bold entry is consumer trends, climate changing spending patterns of households. It's not clear why Climate Week is.
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That is completely irrelevant. Basically, this is what I would call a random selection.
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Retail sales has come up here.
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Retail sales has come.
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I've now got a document in front of me. No, there isn't actually a total figure. They've broken it down into food, non alcoholic drink, alcoholic drink, clothing, etc. So I could at this point get a calculator and add up all the categories.
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Well, I'm not sure that would help because that's not clear whether those categories are exhausted or not. You have failed in your challenge, but you have, I think, successfully illustrated your point. You're not exactly an amateur. You do use this site regularly. What chance does an ordinary member of the public have faced with the ONS website?
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The one good thing about the website is if you want to know one or two very basic statistics, they can generally be somewhere close to the front page. If you want to know the population or the AS I say the latest inflation rate, but basically this is not a website for those sort of faint hearted people who are dabbling in data. This is really a website for people who've got a lot of time and a lot of patience.
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Indeed. And so Evan went home, apparently a beaten man. But no. Despite having been up obscenely early to prepare for wrangling with politicians on the Today programme, the indefatigable Mr. Davis dropped us an email shortly after our discussion. He hadn't been able to let the challenge lie and through an alternative strategy, he had found the right number. In seconds, he just typed the request into Google, which managed to find the correct official statistic. On the double. For those of you keeping score, that's
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our new Californian overlords.
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One Office for National Statistics website nil.
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UK household spending was £484 a week in 2011 as it happens in. But what does that number mean? Is it going up or down? Is that adjusted for inflation or not? What counts as spending anyway? Or indeed, what counts as a household? To really understand what that data point is telling us, we need context. And that, alas, is another bone of contention for the Public Administration Select Committee. Context is important, and it can be hard to get proper context out of the ONS website, or for that matter, out of ONS publications and press releases. For example, if we return to our household spending figure, the ONS put out a press release with that number, the title of which was Household Spending Edges Higher.
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While spending patterns differ by income.
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And who would doubt the accuracy of that? Well, Chris Giles, economics editor at the Financial Times, that's who. So what was the problem with the way the ONS press release had headlined the topic?
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Now, the first half of that Household Spending Edges Higher was based on its finding that in 2011, households spent £483.60 on average per week, it said, an increase of 10 pounds on the level recorded in 2010. Now, the trouble was, this is a nominal increase. This is in cash terms. Well, in 2011, inflation was 5%. So that 2% rise, they said, was actually a big cut in spending. And we worked it out to be the lowest level of real spending after adjusting for inflation in 14 years. What the ONS put into the press release was actually very important in the way it was reported. So, for example, the Telegraph headline was,
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household spending rises as fuel prices soar.
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The Guardian reported it as household spending
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at record high, fuelled by rising petrol prices.
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And the Mail reported it as it
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cost £483,80 a week.
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To run a British home.
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In 2011, the FT's headline was Household
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spending falls to a 14 year low,
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which is actually, I think, what the truth in the statistic actually was.
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Chris Giles of the Financial Times. I put Chris's point to Laura Dewis, the ONS deputy director responsible for digital publishing.
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Chris has raised some really good points there and we are making changes here because we're going to get our statisticians and our communications expert to work much more closely together around this to make sure that the story is clear. I mean, it's important to say we don't get these kind of criticisms very often. We release hundreds of statistical bulletins and analysis every year and this is a rare complaint.
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I also asked Laura what on earth was up with the ONS website.
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There have been some issues, particularly with the search and navigation of the ONS website, and that's something we're working really hard to resolve at the moment. In Evan's example, if he was looking for household expenditure that was last released in December, and what our search is currently set up to do is actually to bring back the. The most recent search results, because that's what users have told us they wanted. They want us the latest figures. But actually that means that it doesn't always bring back the most relevant search results for some of the older content.
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That's the latest relevant figure would probably be ideal.
H
Exactly. And that's what we need to get to. And part of that is about making sure that we have the right metadata in our search engine.
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So what is metadata?
H
So metadata is the descriptive data around our content. So effectively, where you have household expenditure but somebody searching for family spending, we need to make sure that all of those words are connected to that statistical content. And that's a piece of work that we need to do. What happened in 2011 that we moved from print publishing to online publishing and that was a significant operation for the Office. We didn't get it 100% right. And so we've been working since then to make improvements. The improvements have largely focused on productivity for people working in the publishing system and looking at areas of compliance around the site. So we've only really made a small inroad into improving the user experience.
B
So I'm just trying to translate that. Does that mean basically you haven't focused on making the site easy to use for people who rock up and try to get data, you focused on making it easier for ONS staff to publish stuff to it?
H
Exactly, because we have some really challenging deadlines here around publishing statistical releases to 9:30 publishing deadlines. So we've really been focused on trying to make sure that that works as effectively as possible. What we now have in place, it's
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important, but is it not possible to do two things at once or is it not possible to have a team sorting out the search function?
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What we now have in place is a program for the next two years looking very much at the user experience. And so the next stage of work is to do with the search engine, but also the navigation and we'll be making improvements there.
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Laura Dewis from the Office for National Statistics. Now we receive lots of questions from loyal listeners and last weekend, in amongst the complaints about my arithmetic, we got quite a few emails to more or lessbc.co.uk about this.
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A woman from Renfrewshire has denied the odds to give birth to her third set of twins. Karen and Colin Roger, who just left hospital with their new arrivals, were told that the chances of conceiving three sets of twins were one in half a million.
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Well, the question you all wanted answering, of course, was are the odds of a woman having three separate sets of non identical twins really half a million to one? Well, Ben Carter's here. Ben, I've always suspected your twin is Big Bird from Sesame Street.
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Very droll, Tim. Big Bird is not my twin.
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Well, that would explain why I never see the two of you together then. Now, Ben, if we can stop talking about you and your problems for a moment, what's the story with Karen Roger and her 500,000 to one against brood of three pairs of twins?
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Okay, before we start, let's put twins conceived through in vitro fertilisation to one side because that's quite common for children conceived without ivf. The chance of a pregnancy being non identical twins is 112 to 1 against.
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Okay, so to get the chance of two such pregnancies, now normally we'd just multiply these odds together. So the chance of throwing a six on a die is one in six. The chance of throwing two sixes on two dice is one in 36.
G
Well, if we trusted you maths, Tim, but we don't. So I can do that calculation. 112 to 1 would be the odds for the first pregnancy. 112 to 1 squared would be the odds for the second pregnancy and it would be 112 to 1 cubed, which is about 1.4 million for the third pregnancy. So that suggests that Karen's feet is a 1.4 million to one shot. But that's not actually the calculation we want to do.
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Why not?
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Because non identical twins come in clusters. Rolling a six doesn't suggest that another six is on the way. But having twins suggests a tendency to have more twins. There are genetic factors involved. Older women are more likely to have non identical twins and being on the tall side or the heavy side are also predictors.
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Now, we would never be so rude as to ask Karen's body mass index. And although we know her age, we are gentlemen and we don't intend to reveal it. So, Ben, cut to the chase.
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When Karen had her first non identical twins, we could then conclude that further twins were More likely, around 1 in 28, four times more common than the base case.
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So we should multiply 112. That's the odds against the first twin pregnancy by 28 for the second pregnancy. And then what? By 28?
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Again, maybe less than that. But let's err on the side of caution. 112 times 28 times 28 is 88,000. So Karen's feat was about a 1 in 88,000 fluke.
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Now, we've been talking about non identical twins throughout. I deduce therefore, Ben, that identical twins are different.
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They are less likely. One in 227 pregnancies, again excluding IVF conceptions, and they don't come in clusters. So the chance of three sets of identical twins is 11.7 million to one against.
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Now, very roughly though, there are a million births in the UK each year, so even that it's not unimaginable.
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And Karen Rogers feat 1 in 88,000 in a country where a million babies are born each year looks almost commonplace.
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Will you say that, Ben? I'd like to see you do it. You're listening to More or Less now. Are you nervous about making life's big decisions? Don't be, because I have a large yet portable bag full of numbers to help you out. They come from a new book, Naked Statistics, which aims to show how statistics can be used to answer many of life's questions. I called up the author, Charles Whelan, and asked him whether he could serve as my statistical guide through life, or more specifically, through parenthood. Let's start with examining one of those pieces of advice commonly given to expectant mothers. Try to avoid caffeine. What does the evidence say?
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There's a new book by Emily Oster called Expecting Better that summarizes a lot of the data around healthy pregnancies, and she casts serious doubt on that particular piece of advice. And the reason is that the causality may go in fact, the other direction. So we're taught to think that, well, caffeine may be bad for the baby, but in fact, one of the things we know is that nausea is a sign of healthy pregnancies. We don't fully understand why that's the case, but it's been quite clearly established. And of course, women who are nauseous are far less likely to drink coffee. So it stands to reason that it may in fact be healthy pregnancies causing people to drink less coffee rather than the other way around. And in fact, one corroborating piece of evidence for that is, is that women who drink less decaf coffee also have healthier pregnancies. And of course, if caffeine is the important ingredient, then decaf shouldn't make much difference.
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Of course, it's not just what the numbers can tell us, but what the numbers can tell about us. If you use store cards, you probably know you're giving retailers quite a lot of information about yourself, but maybe more than you realize. Here's a tale about the aptly named U.S. department Store Target in the United States.
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Maybe other places when you get pregnant, you're about to have a baby, often there'll be a baby shower. People give you presents so you can register as you can for bridal registries for the particular presents that you'd like to get. And you can register at places like Target. Now, when you do that, what you are telling them is I'm pregnant. And you're often telling them even when you're due so how far along in the pregnancy you are. Target took that information and cleverly began to look at the shopping habits of the women who had said they were pregnant. They bought more cotton balls, they switched to unsatisfied lotions, they started buying certain kinds of vitamins. And then they made the logical leap. Wow, if these pregnant women are doing those things, then other women also doing those things. And they came up with a pregnancy prediction indicator of 25 different behavioral changes. Well, the other women doing that must also be pregnant too. So they looked across all of their shoppers and made an inference about which ones are pregnant. Now, they could then send pregnancy related coupons to those women. We fast forward to a fellow in Minneapolis who was a father of a high school girl and he was not happy that his daughter was getting pregnancy related coupons in the mail for baby wipes and cribs and those kinds of things. So he called the store, complained loudly. The manager felt very bad. In fact, the manager felt so bad, he actually called the guy back three days later to apologize again. At which point this father said, well, it's my turn to apologize. And this is the quote in the magazine. There have been some things going on in the house that I wasn't aware of. It turns out his daughter was pregnant. Not only was his daughter pregnant, the statisticians at Target had figured it out before her father had.
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And then what about that question which obsesses many parents from almost the moment their child is born? Where should we send them to school? Here, Charles Whelan says the numbers provide some comfort.
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The data here are really, really important. If you are indeed a good middle class parent as you describe yourself, then your children are probably going to be quite fine no matter what you do. So there's quite compelling evidence that just by virtue of being relatively well educated, caring parents of a certain means, you're going to speak a lot to your baby. You're going to do all the things that lead to a healthy, smart young child. One of the things that still has my mother lying on a couch with a cold compress on her head is that I send all three of my children to the Chicago public schools, which may be notorious even around the world, but certainly in the United States are notorious for being some of the most strike ridden, gang prone and so on. And so I did make that decision because when I looked at the aggregate statistics for Chicago, what I realized is that most of the really, most like 80% of the students were coming from low income, disadvantaged backgrounds. That wasn't my background and I thought my kids would be fine. In fact, they've turned out swimmingly.
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Charles Whelan AUTHOR OF Naked Statistics Stripping the Dread from the DATA now, as everyone knows, men think about sex every seven seconds. But how do we know this or indeed is it even remotely plausible? We decided, Sorry, I was miles away. We decided to find out how often men really do think about sex. And so I spoke to Terry Fisher, professor of psychology at Ohio State University, and I asked her, where does this statistic come from?
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I really have no idea. I've looked at all the research that I could find on this topic and nobody has found a number that remotely resembles that. So I have no idea the origin of it. And yet it seems to appeal to people. The fact that it's become a well known urban myth suggest that people think it's true and they think it's possible if indeed it were true. I'm really not sure how most men would get anything done.
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I'm actually extremely proud of my ability to multitask now, how did. Sorry, I was a little distracted. Professor Fisher and a few of her students decided to do their own study. To test this idea, they recruited a few hundred college students, both men and women aged between 18 and 25. They divided them into three groups and set them off with golf score counters. The first group had to click their little counter every time they thought about sex, the second to click when they thought about food, and the third when they thought about sleep. Obviously, American college students aren't particularly representative of the world population as a whole, but they might not be a bad place to start if you're launching a quick and dirty study into how often people think about sex. Now, I estimate, and I used a calculator for this one, so it should be right this time that if you're awake for 16 hours a day and you think about sex every seven seconds, you think about sex 8,229 times a day. Well, I asked Professor Fisher how the men fared. In her study.
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The average number of thoughts about sex was 34 during the day. The median number, which is a statistic I actually prefer in this context because it eliminates the influence of outliers. The median was a little bit less than 19 thoughts per day.
B
So every hour or so.
C
That's correct.
B
And was there anybody who didn't think about sex at all or some sex monster who just thought about it constantly?
C
Well, we had quite a range, especially among the men. The average number of thoughts per day about sexuality ranged from 1 to 388.
B
So 388 is quite a lot, but it's well short of 8,229.
C
It certainly is, yes.
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Now, what about women? Were they very different?
C
Well, they were somewhat different. They had a more narrow range. So their thoughts ranged from one per day to 140 per day, with the average or mean number a little less than 19, the median just a little less than 10. And so they were reporting sexual thoughts about half as often as the men
B
did, but a huge range and 140 times a day. I mean, it's nothing like every seven seconds, but that's thinking about sex quite a lot. It sounds a bit like my wife, to be honest, but don't worry, I won't let her listen to this program. What about food? How often did men think about food? How often did women think about food or, indeed, sleep? Was it similar to thinking about sex or was it very different?
C
It was similar. It wasn't exactly the same. But in general, men were thinking about all of those things. More than women. We analyzed the data. What we found was a significant gender difference, but not a difference in terms of type of thought. And so the men were just reporting overall more of those thoughts than were the women.
B
Do you think that that's a reasonable way of doing it? Because, of course, it is slightly artificial to get people to constantly monitor their own thoughts and chalk up, oh, yeah, I thought about hamburgers again. Click.
C
I agree it's artificial, but it's an advance over the previous techniques that were used, which, with the exception of one study, just consisted of asking people to retrospectively estimate how often in a 24 hour period they think about sex. And human beings just are not really capable of making good estimates. And so we didn't believe that we were really capturing every single thought about any of these topics. However, by asking people to carry the tally counters and to keep track each evening, we were, at the very least increasing awareness of the frequency of these particular thoughts.
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Professor Terry Fisher of Ohio State University, we thought this was an experiment worth replicating. So the More or Less production team has been supplied with golf clickers and asked to record the frequency of sexual thoughts. Here's a recording we made earlier. We do, after all, share office space with Radio 4's Moneybox team. We're only human and they're irresistible. And that's all we have time for this week and indeed this series. If you go to our website BBC.co.ukmoreallshowever and subscribe to our free download, you'll hear the secret episodes that don't get broadcast on Radio 4 featuring Ruth Alexander. If I can get her to put down her golf counter. If you know the origin of the urban myth that men think about sex every seven seconds, then please email us at more or lessbc.co.uk or any other thought that you'd like us to investigate. We promise to read your emails before we return in the summer. Until then, goodbye.
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More or Less was presented by Tim Harford. The producer was Charlotte MacDonald, the editor was Richard Varden and audio production was by James Beard. The programme was made in association with the Open University and you can Download many more BBC Radio 4 programmes for free@BBC.co.uk radio4.
Episode: A&E, and the chances of having twins
Date: June 7, 2013
Host: Tim Harford
This episode explores the reliability of statistical claims found in news, politics, and everyday conversation—with a particular focus on how numbers about the NHS, pregnancies (especially multiple births), and human behavior like sexual thoughts are often misunderstood or misrepresented. Tim Harford and his guests dissect headlines, challenge urban myths, and look at statistical errors in the media, all while maintaining the show’s characteristic wit and skepticism.
(Starts ~00:24)
The show analyzes media headlines about NHS Accident & Emergency (A&E) department waiting times.
Key Clarification: The A&E waiting time statistic isn’t about how long it takes to see a doctor—it’s the time from registration to resolution (either discharge or admission).
“You might assume that your waiting time at Accident and Emergency is how long it takes for a medical professional to see you. Not so. The clock starts when you register at the desk and it stops when your case is resolved...” (Tim Harford, 00:57)
Tim explains a reported rise in numbers (21.7 million visits, up 50% in a decade) is partly due to counting new walk-in clinics and minor injury units as A&Es after 2004.
Context on NHS Nurse Numbers:
(Starts ~02:42)
(Starts ~05:37)
(Starts ~14:03)
(Starts ~17:05)
(Starts ~18:38)
(Starts ~20:34)
(Starts ~21:44)
On media errors:
“Misplaced one decimal point might be considered a misfortune. To misplace two looks like carelessness.” (Tim Harford, 03:19)
On ONS website’s challenge:
“This is really a website for people who've got a lot of time and a lot of patience.” (Evan Davis, 07:59)
On household spending ‘increase’:
“It was actually a big cut in spending. And we worked it out to be the lowest level of real spending...in 14 years.” (Chris Giles, 10:19)
On twin pregnancy odds:
“Roll a six doesn’t suggest that another six is on the way. But having twins suggests a tendency to have more twins.” (Ben Carter, 15:39)
On pregnancy and caffeine:
“So it stands to reason that it may in fact be healthy pregnancies causing people to drink less coffee rather than the other way around.” (Charles Wheelan, 17:46)
On Target’s pregnancy prediction:
“It turns out his daughter was pregnant. Not only was his daughter pregnant, the statisticians at Target had figured it out before her father had.” (Charles Wheelan, 19:54)
On the ‘every seven seconds’ myth:
“I'm really not sure how most men would get anything done because their brain would just be so clogged with thoughts of sex.” (Terry Fisher, 22:51)
This episode of More or Less demystifies and debunks persistent myths and misunderstandings lurking in media headlines, statistics around the NHS, pregnancy, and even everyday trivia about human behavior. From the misreporting of NHS statistics to the real odds of twin births and the truth about how often men think about sex, Tim Harford and guests bring humor and clarity to the numbers—always with an eye for the context missing from headlines.
Contact/Episode Feedback:
Email: moreorless@bbc.co.uk
Key Guests:
Recommended Read:
Naked Statistics: Stripping the Dread from the Data – Charles Wheelan
Find More Episodes:
https://www.bbc.co.uk/programmes/b006qshd/episodes/player