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It was “feeble”. It was “very unsatisfactory”. It was, in short, “terrible”. If you wish to annoy a statistician, ask them about the trial of Lucy Letby, a British nurse. Statisticians will, typically, take no view whatsoever on the guilt or otherwise of Ms Letby, who in August 2023 was found guilty of murdering seven very young babies in a hospital near Liverpool between 2015 and 2016, and given 15 life sentences without the chance of parole.
They do, however, have very strong views on the way her trial—which relied in part on analysis of hospital rotas—proceeded. “The conviction is unsafe,” says Peter Green, a maths professor at Bristol University. It was the kind of case “that leaves a bad taste in the mouth,” says Philip Dawid, a statistics professor at Cambridge University. Statisticians were “shocked”, another eminent professor explains, by the way the trial weighed the probability of seemingly extraordinary events.
Britain has a problem. Not, in fact, a murder problem (with 1.1 murders per 100,000 people, Britain is not bad by global standards). Nor does it have a problem with producing scientists who can work out such things—and considerably more besides (with eight Fields medals and around a hundred science Nobels, Britain is above average at higher-level maths). Instead, it has a problem with producing non-scientists—such as politicians or, say, lawyers in a murder case—who can understand data. When it comes to this, says Sir Adrian Smith, the head of the Royal Society, Britain is “very bad” indeed.
This is not a new diagnosis. In a 1959 lecture called “The Two Cultures”, the scientist and writer C.P. Snow warned that society was “being split into two polar groups”: those who understood science and those who did not. Worse, the bookish types did not even know what they did not know. Literary intellectuals smirk at the illiteracy of scientists but, Snow said, ask them to describe the second law of thermodynamics (“the scientific equivalent of ‘Have you read a work of Shakespeare’s?’”) or even to define mass (“the scientific equivalent of saying, Can you read?”) and the answer would be a “cold” negative.
Snow felt, 65 years ago, that this smirking incomprehension was a “joke which has gone sour”. It is sourer still in 2024. The trial of Ms Letby is one example. Covid furnished far more: such as how Boris Johnson was, as one adviser put it, “bamboozled” by science and “struggled with the whole concept of doubling times”; or how politicians failed to grasp concepts like absolute and relative risk. Dame Kate Bingham, who chaired Britain’s vaccine taskforce, was “pretty shocked” by the level of scientific ignorance in the civil service. Worse, she felt that, for some, it is almost “a badge of honour”.
Mr Johnson is paradigmatic of what has gone wrong. He is not—despite what his actions often imply—a stupid man and certainly not, after Eton and Oxford, an ill-educated one. His education was etiolated; it was not ineffectual. He could read Archimedes in the original; he could not begin to understand Archimedes’s maths. He is the product of what Snow called Britain’s “fanatical belief in educational specialisation”. And that belief, says David Willetts, a former universities minister, is “as acute as ever”.
The problem is not that A-levels are very bad. It is worse: they are very good. An A-level physics student “probably knows more physics than any other 18-year-old in any other Western country,” says Lord Willetts. Arts students are similarly specialised: when cramming for university, the would-be historians in Alan Bennett’s play, “The History Boys”, debate such arcane topics as the 14 foreskins of Christ found in medieval reliquaries. They do not touch on chemistry. This matters. To evaluate an education system, the crucial question is not whether someone who is studying physics understands it; it is whether someone who is not does.
And that is the question Britain cannot get right. In 2010 the Nuffield Foundation, a think-tank, decided to test whether Britain was really so bad at offering educational breadth by comparing it with 24 other countries, mostly drawn from the OECD, a rich-country club. In England fewer than one in five students studied maths after 16. In 18 of the countries more than half did; in eight, everyone did. Government data suggest that almost half of the working-age population in Britain have the numeracy skills of a primary school child.
Not all of Snow’s thesis has dated well. He over-emphasised scientific knowledge; having a scientifically literate population is actually less about knowing facts than having “an attitude of mind”, says Sir David Spiegelhalter, emeritus professor of statistics at Cambridge. But Snow’s analysis of English education still stands.
The solution is not to get everyone to do A-Level maths: it is too hard and, besides, there are too few teachers. Instead, as a forthcoming Royal Society report will argue, maths and data analysis should be woven into all education up to 18. Something is certainly needed: for people in positions of authority not to have basic quantitative literacy is “unacceptable”, says Professor Spiegelhalter.
And yet it is widely accepted. Newspapers frequently run stories on the percentage of politicians, judges or civil servants who went to private schools. There are far fewer stories on what percentage are from arts rather than science backgrounds. But it is high—and always has been. The original Victorian civil service exams, designed by the classicist Benjamin Jowett, gave the most marks not to science but classical literature. “Name the first and last of the 12 Caesars,” ran a typical question.
Arts students still dominate. Statistics on the numbers of civil servants with STEM qualifications are hazy; but most estimates put them at around 2–7%. In America, it is almost 16%; in South Korea, around 30%. How, asks Dame Kate, could you possibly run a business department in a 21st-century government with “nobody who knows anything about business or science?”
Lawyers are little better. Even before Ms Letby’s trial began, statisticians were “apprehensive”, says Professor Green. There had been recent miscarriages of justice in which so-called “health-care serial-killers” had been convicted using bad statistics. Moreover, the history of law and statistics in Britain is dismal. In the 1990s, a mother was convicted of murdering her baby sons after Roy Meadow, a paediatrician, claimed (erroneously) that the chances of their deaths being accidental was 1 in 73m. Professor Dawid was called to counter this claim. Before he could speak, the judge dismissed him: it was “hardly rocket science”.
Professor Dawid was “disgusted”—but not surprised. What alarms statisticians is not merely lawyers’ knowledge of stats (which, says Professor Dawid, is usually “dire”). It is, says Professor Spiegelhalter, their lack of awareness. Before the Letby trial, Professor Green and some colleagues therefore produced a booklet titled “Healthcare serial killer or coincidence?”
In previous cases, says Professor Green, rotas would be used to show that a particular nurse was always on duty when people were killed. Non-experts would then say: “You can’t possibly believe this could happen by chance. Therefore she is guilty”. The reasons why this logic is wrong are complex—and outlined in that booklet, now on the Royal Statistical Society website. But suffice to say that statisticians call this “painting the target around the arrow”.
Yet, in the Letby trial, a chart was used to show that she had been on duty when babies had died or collapsed unexpectedly; the jury was not told about other deaths for which she was not charged. The statistical weaknesses of this were not sufficiently pointed out. The target was painted around the arrow. She was convicted.
In 1959 Snow wrung his hands. But recognition of the narrowness of British education and the problems caused by statistical ignorance are growing. Snow observed that most felt our education system was bad but “nearly everyone feels that it is outside the will of man to alter it.” With luck, in 2024, it will not be. ■
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This article appeared in the Britain section of the print edition under the headline “Two cultures”
Britain August 24th 2024
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From the August 24th 2024 edition
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