Statistics, Storks, and Babies - Numberphile

Key Takeaways

today's topic is one of the most famous stories in statistics uh it's also about where babies come from um i know you know where babies come from but there used to be this tale that's what i grew up with that babies come from stalks if a child is asking awkward questions of his or her parents the parents would say well you know the stalks bring the baby in draped from their bill in a blanket that's where your baby brother or your baby sister came from have you figured out where that came from why stalks were associated with babies at all so there's a theory it's something to do with um stalks being a traditional symbol of fertility a religious symbol of fertility and another theory is that stalks when they go fishing they're looking for embryonic life forms in the water so that is that is two theories um i don't know i'm i'm an economist you know i'm not a not a sort of a studio of mythology and ritual anyway anyway to get back to the important stuff which is the statistics so stalks deliver babies this is the old story let me try to prove that to you statistically i've got my i've got my paper here so and this is just going to be a um illustrative plotting if you imagine two axes and here this is babies per year and here we have the number of stalks and if you just take a a bunch of european countries and i have actually seen the data what you find is turkey if i remember and this is poland and then you might have germany here and then you've got a whole bunch down here a couple there and it's not the world's best correlation but it's it's not the world's worst correlation loads down here with not many babies not many stalks you've got these big outliers here you've got nothing here you've got no places with um loads of babies and no stalks you've got no places with loads of stalks and no babies and you can draw a best fit line and it goes like that and there is actually an academic paper about 20 years ago with the title stalks deliver babies p equals 0.008 and without going into the technical details you probably know that according to the conventional standards of statistical significance that means this relationship is not a coincidence there is definitely a correlation between stalks and babies now you're probably thinking to yourself okay so what's the trick because surprise surprise talks don't actually deliver babies um email me if you actually want me to explain where babies do come from when i get a reply well maybe um so so what's going on here what's going on here is basically as i said i think this is turkey this is poland there's there's monaco there's luxembourg there's lichtenstein down here lots and lots of places with very small amounts of land there are no stalks and there are no kids basically and here are places that are really big lots of stalks lots of babies and that's what's going on that's enough to drive that statistical correlation the amount of land is the hidden uh is the hidden factor yes the secret thing that's driving both a large population which means a lot of babies and it is driving the large number of stalks because bear in mind i'm not i didn't say birth rate i'm sure there's well i expect there's no correlation for the birth rate what i'm talking about is the the number of babies born each year in this in these countries which is very closely correlated to the population so you would also perhaps expect a correlation with trees yeah yeah probably number of trees versus number of babies a year trees also deliver babies i mean you could you go in all kinds of places like this and there were lots of these um these spurious correlations out there actually there's a website maintained by a guy called tyler viglen i think called spurious correlations full of all kinds of fun stuff like this but i said at the beginning that this is one of the most famous stories in statistics it was made famous by a fellow called darrell huff and here for me is where this gets really interesting so dewell half was a journalist and in 1954 he published a book with the title how to lie with statistics it got a rave review in the new york times it became many people say the best selling book about statistics ever written and i loved it when i was a teenager reading about all of these tricks all the different ways you could be deceived he's got the stalks and babies in there it's got loads and loads of great examples it's got dodgy maps it's got dodgy graphs it's got all sorts of great great examples it's a very funny book um i'm not the only person who likes it ben goldacre who wrote bad science and many other great books about numbers he praised darrell half charles whelan who wrote a book called naked statistics he said it was an homage to daryl half there are loads of fans of drell huff out there this book is in praise of statistics though this this book is supposed to be doing a service to statistics presumably so that i think is where the important question uh lies it it is loved by nerds but it is not really in praise of statistics because what dual half is doing is in chapter after chapter example after example he's debunking dodgy statistics and he just doesn't have a lot of positive examples of statistics being used to illuminate the world and that's where i start to get a little bit queasy because that book was published in 1954 and you know what else happened in 1954 two great statisticians epidemiologists richard dole and austin bradford hill provided some of the first solid evidence that smoking cigarettes might well give you lung cancer because the same year two different visions of what you can do with statistics darrell huff is saying it's a bit of a joke it's a bit of fun i'll tell you the story about the stalks and the babies um but don't don't ever take statistics too seriously because they're just a way for people to lie to you austin bradford hill and richard doll are using this vital tool to find out the answer to one of the key medical questions of the 20th century and when you think about it they couldn't have done that in any other way than using a the statistical lens so even to notice that lung cancer cases were on the increase and they were massively you need to be systematically counting cases of lung cancer i mean you maybe there'd be some anecdotes but you know you need the numbers you need the data and then to show compellingly that uh there's there's evidence of causation you really need to work hard with the statistics a lot of people at the time thought it was something to do with cars which is not crazy you think about it between the beginning of the 20th century and the 1950s lung cancers on the increase so are cars loads of cars maybe it's something in the tarmac maybe it's uh something you know coming out of the exhaust is not a crazy idea but it turns out it wasn't the cars it was the cigarettes this is so important this is such a key fact understanding that this thing is true this has saved literally tens of millions of lives possibly hundreds of millions of lives and you've got to rail half and remember this the the best-selling book ever published about statistics saying don't ever take statistics too seriously because they're basically liars will use them to lie to you there's a twist in this story because in the 1960s the us senate held hearings to decide whether cigarette packets should have warning labels on them should smokers be warned you know maybe this is going to kill you and they got all these expert witnesses in to discuss the evidence and one expert witness came in and he told the senators look don't worry too much because there are a lot of funny correlations out there let me tell you about stalks and babies and he sat there and he told the senators all about how you could demonstrate this correlation between babies and stalks he used a slightly different example but the same basic argument and it's the same with with cigarettes and lung cancer and the senator who was chairing the commission said do you seriously mean to tell me that there is as as casual a relationship between smoking and lung cancer as there is between stalks and babies and the expert witness says yeah they seem to me to be about the same and his name you may have seen it coming darrell huff the guy who published how to lie with statistics he was actually working on a sequel which was never published called how to lie with smoking statistics so he'd taken this you know this you know funny witty skepticism about statistics in this great little book and he'd soured it into this nasty cynicism that everything out there is fake news you can't believe a single thing you're told and he'd then gone to work for the tobacco lobby who found him to be the perfect witness for their case if you'd like more great stories like this from tim harford check out his book how to make the world add up this is what it looks like just in case you need to know the links in the description include a chance to get yourself a signed copy you can also catch tim talking with matt over at stand-up maths again links in all the usual places