Statistics

Lucy Letby and the problem with statistics

First Fred West, now Lucy Letby. At this rate, it won’t be long before Herefordshire has produced more serial killers than it has miles of dual carriageway. You might assume growing up in one of England’s loveliest counties would make people placid, but then you haven’t spent half your life stuck behind a caravan on the A465. They may not all kill people, but Herefordshire people overtake like psychopaths. It only takes one dodgy assumption to reach a conclusion that is diametrically wrong But I’m going to park my Monmouthshire prejudice here and suggest that something about the Lucy Letby conviction seems off to me. I’m not going to talk

Bayes’s Theorem: the mathematical formula that ‘explains the world’

Here’s a profound question about beards: is the number of acrobats with beards the same as the number of bearded people who are acrobats? Go with your gut instinct. It’s not a trick question. If you answer ‘yes’, then you’ve understood the central idea behind Bayes’s theorem. If you’re one of those people who likes to titter about how bad you are at mathematics, stop it. Retake your GCSE, learn how to pin this obviousness down in symbols, and you can produce artificial intelligence, forecast stock market collapses and understand this: P(A|B) = (P(B|A)∙P(A))/(P(B)) This is Bayes’s equation, the formula which, as Tom Chivers insists in this remarkable, bold book,

The genius of More or Less

In a week of slim audio pickings, I spent time reacquainting myself with some of the BBC classics and can confirm that, yes, More or Less still warrants a place in that category. Like Thinking Allowed, which also drew me back, the programme works wonders with data and statistics, and benefits from having a calm and unobtrusive presenter. While most of the questions put to the stoical Tim Harford are delightfully pedantic, some have that special quality of convincing you that, while you’ve never given the topic a second thought, you are in fact deeply invested in it, and absolutely must know whether or not the thing that’s been alleged

What is behind the increase of non-Covid related deaths?

The latest data on weekly deaths in England and Wales, published today by the Office of National Statistics, show what could be the beginning of a disturbing trend. From mid-June to mid-July, the number of excess deaths has been running at below the five-year average. But for the second week running, that has reversed: in the week ending 21 August there were 9,631 deaths, 474 higher (5.2 per cent) than the five-year average for this week of the year. The rise does not appear to have been caused by any increase in deaths from Covid-19, however. On the contrary, there were just 138 deaths for which the death certificate mentioned

Why are more people dying at home?

The death drought continues. For the eighth week in a row the Office of National Statistics (ONS) has recorded fewer deaths in England and Wales than would be expected at this time of year. In the week ending 7 August, 8,945 people died, one fewer than the previous week and 157 (1.7 per cent) lower than the five-year average for this week of the year. There is, however, a geographical divide: deaths in the East Midlands are running five per cent higher than the five-year average. While deaths in the North East and North West are slightly higher than usual. What should be worrying the government is the sharp rise

Covid statistics are just politics by other means

Statistics is the continuation of politics by other means, to misquote Clausewitz. One hundred and fifty years after the crushing of the revolutionary Paris Commune, historians still clash aggressively about the death toll. Was it as high as 40,000 or as low as 10,000? It matters because the Paris Commune is a shibboleth, a great left-wing site of memory and martyrdom, made famous by Karl Marx’s pamphlet The Civil War in France. He presented the Paris Commune as the first great experiment in communist government. Its crushing by the army of the conservative Adolphe Thiers is depicted in left-wing folk memory as the ‘reactionary, repressive forces of capitalism’ ending an idyllic

Covid deaths – direct and indirect – will now be over 45,000

This week, the government has published a better measure of Covid-19 deaths by widening it out from hospital deaths to all settings. But what about those who have died without having had a test? Does the ‘improved’ estimate go far enough?  I think the simple answer is no. The mortality data is rising at a rate that suggests many more are dying who have not been tested. But there are ways of estimating and, as the former head of health analysis at the ONS, I have conducted my own study.  As of Wednesday 29 April, my figure is 45,290 deaths linked to Covid-19 in Great Britain. This is far higher than the

It’s a mistake to compare our Covid death toll with Spain and France

Covid statistics are like complex machinery; if you don’t read the instructions you won’t operate them properly. Which is why the claim by some media outlets that the UK now has the second highest number of Covid deaths in Europe, should be handled with caution. It is true that on Wednesday the official UK Covid-19 death toll increased by 4,419 to 26,097 after the government included deaths outside hospitals for the first time. The figures were revised respectively by Public Health England since the first UK death in March. According to the Guardian, ‘The change comes after weeks of criticism of the way that the UK had been reporting its

Macron’s updated coronavirus statistics will test French morale

On Saturday night France’s Prime Minister spoke to the French people flanked by the Health Minister, the Director General of Health (DGS) and three epidemiologists, to reassure the public that the government would be more transparent about the spread of coronavirus. Despite President Macron’s increasing media appearances in the ‘war on corona’ a 25 March opinion poll showed 90 per cent of the French public are anxious, 39 points more than on 11 March before the lockdown. Although 64 per cent claimed their morale was holding up, 56 per cent said they had lost faith in the executive’s management of the crisis. This is very different to a poll on

How to understand – and report – figures for ‘Covid deaths’

Every day, now, we are seeing figures for ‘Covid deaths’. These numbers are often expressed on graphs showing an exponential rise. But care must be taken when reading (and reporting) these figures. Given the extraordinary response to the emergence of this virus, it’s vital to have a clear-eyed view of its progress and what the figures mean. The world of disease reporting has its own dynamics, ones that are worth understanding. How accurate, or comparable, are these figures comparing Covid-19 deaths in various countries? We often see a ratio expressed: deaths, as a proportion of cases. The figure is taken as a sign of how lethal Covid-19 is, but the

Vital statistics

Scientists, it turns out, are really bad at statistics. Numerous studies show that a startling proportion of academics consistently misunderstand the statistics they’re using, and the conclusions that can be drawn from them. A computer algorithm that highlights basic statistical errors was recently set loose on a huge sample of published research papers in psychology  and found that almost half contained a mathematical mistake; 13 per cent had a serious screw-up that meant their reported results might have been completely wrong. If scientists — who use statistics all day to analyse their experiments — are so innumerate, what hope is there for everyone else? Enter Sir David Spiegelhalter, Winton professor

Too many facts get in the way of truth

One dietary fad that never made sense to me was the campaign against the consumption of eggs. Now call me an old Darwinist, but here we are having spent a few million years evolving into a bald monkey with prehensile thumbs, perfectly optimised as an egg-stealing machine, and yet the digestion of an omelette somehow came as a horrible shock to our cardiovascular system. What next, I wondered. Perhaps they’ll discover that 45 per cent of cows are allergic to grass, or that sharks are largely sea-food intolerant. And it seems that the opprobrium directed at eggs was mostly wrong. It was based on the assumption that, since some cholesterol

Want greater diversity? Try being less fair

In its hasty dismissal of James Damore, Google showed a worrying disregard for one of the most important freedoms within a company — the freedom to ask: ‘What if we’re wrong?’ A business culture that can attract and accommodate people with complementary talents benefits everybody. So even if you don’t believe Damore’s theories (in which case you probably shouldn’t hire any systems geneticists), he’s surely right to speak up if he believes the complex question of diversity has been hijacked by wishful dogma. It should be the province of first-rate scientific inquiry, not second-rate social theory. If the diversity agenda is pursued badly, the cure may well be worse than

Barometer | 23 March 2017

Princes among men British DJ Mark Dezzani was hoping to be elected prince of Seborga, a self-proclaimed independent state in Italy. Some other self-declared nations not recognised by others: — Hutt River in Western Australia declared independence in 1970 after farmer Leonard Casley complained he hadn’t been granted a large enough quota for growing wheat. He later proclaimed himself Prince Leonard but abdicated last month in favour of his youngest son, Prince Graeme. — Sealand, previously known as Roughs Tower, is a gun emplacement built to defend the Thames during the second world war but then abandoned. In the 1960s it was occupied by businessman Roy Bates, who ruled as

Barometer | 24 November 2016

Bucks for Bucks Buckingham Palace is to be renovated at a cost of £369m, funded through an increase in the sovereign grant. How much have home improvements to the palace cost over the years? — The original house was built by the Duke of Buckingham in 1706 for £7,000. — In 1761, George III spent £21,000 to buy it, and £73,000 on remodelling it. — In 1826, George IV hired John Nash to remodel the building for £450,000. He was fired in 1828, having spent £496,169. — In 1845, Queen Victoria complained it wasn’t big enough for her growing family and added the east wing, using £53,000 raised by selling

Britain’s trade deficit will be a useful Brexit bargaining chip

Britain’s trade deficit – the difference between what we import and export – widened in the run-up to Brexit. Figures out today show that we imported £5.1bn more goods than we exported to the rest of the world. That gap widened by nearly £1bn between May and June, according to the ONS, in a picture which the Guardian have said is pretty ‘ugly’. But there is a flip side. Firstly, these figures don’t reflect anything about the referendum – they were compiled in the build-up to the June vote, so they tell us little about the impact of Brexit. Secondly, it’s worth mentioning that whilst the deficit has, indeed, got bigger,

The deceptions behind George Osborne’s Brexit report

Sometimes, George Osborne’s dishonesty is simply breathtaking. Let’s set aside the way he has positioned himself over the years (if he believed that leaving the European Union ‘would be the most extraordinary self-inflicted wound’ he might have told us – and his constituents – earlier, rather than proceeding with the farce of renegotiation). But it’s his maths, today, which shames his office – and his use of this maths to make the entirely false suggestion that the Treasury thinks Brexit would make you £4,300 worse off. For anyone who cares about honesty in politics, and the abuse (and reporting) of statistics, this is an interesting case study. His chosen date is 2030. By then,

The truth about black teenagers, prison and university

A few months ago, David Cameron made an incendiary claim that splashed the Sunday Times and set the news agenda for days: black boys, he said, were more likely to go to prison than university. It was a shocking statement, that quite rightly sparked much discussion. But there was one flaw: his claim was nonsense. I had to submit a Freedom of Information request to find the real story: black men are twice as likely to go to a top (i.e., Russell Group) university than to prison. Include women, and it’s five times as likely. Include all universities, and there’s no comparison – black teenagers have a higher university entry rate than

Barometer | 17 March 2016

Name that town The representative of Slough in the UK Youth Parliament called for the town’s name to be changed to rid it of negative connotations. Other towns with an image problem which have done a Stalingrad (now Volgograd) and changed their identity: STAINES Now Staines upon Thames KILIWHIMIN, HIGHLANDS Now Fort Augustus ALLIGATOR VILLAGE, FLORIDA Now Lake City WANKIE, ZIMBABWE Now Hwange PILE O’ BONES, SASKATCHEWAN Now Regina Residents in the Austrian village of FUCKING voted against a name change in 2004 Over a barrel During the referendum campaign, Alex Salmond proposed that Scotland would become independent on 26 March 2016, and said it would have £7.5 billion of

Who killed murder?

Pity the poor crime writers. Our earnings, like those of all authors, are diminishing for reasons far beyond our control. Our fictional criminals and detectives are being outsmarted by genetic fingerprinting, omnipresent security cameras and telltale mobile phones. Who needs Sherlock Holmes to solve a tricky crime when you have computers, with their unsporting ability to transmit and analyse enormous quantities of data and identify culprits? But the bigger problem for us novelists (if not for everyone else) is that murder itself is dying. The official homicide rate peaked in 2002, thanks to Dr Harold Shipman, and has since fallen by half — from 944 then to 517 last year.