Fact: between 2008 – 2014, the bodies of 60 young men have been found in the canals around Manchester.
Scott Hesketh, Crime Editor of the Star on Sunday newspaper, investigated; he asked psychologist Professor Craig Jackson for an opinion: ‘It’s extremely unlikely that such an alarming number of bodies found in canals is the result of accident or suicide,’ he said. He went further: the fact that a few victims were found in Manchester’s Canal Street, famous for its gay bars, led him to believe that a serial killer may be targeting gay men.
More or Less contacted the National Water Safety Forum, which keeps a record of deaths of British waterways. Over a period of five years, more than 1500 people died on our waterways – mostly through accidents and misadventure. So what does that mean for Manchester? First, let’s put this in context: the bodies turned up in the Greater Manchester area, and not just in the canals in the city centre. Central Manchester has a population of about half a million, but Greater Manchester’s population is 2.6 million and has a whopping 175 miles of waterways – which puts those 60 deaths in a less sinister light. So, More or Less asked the question: what number of people would you expect to be found drowned on 175 miles waterways if there weren’t a serial killer on the loose? The answer: 61 deaths – and that was the number expected over a period of five years – so in fact, Manchester had seen fewer deaths than expected.
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It’s often said, ‘There are three kinds of lies: lies, damned lies, and statistics.’ But it isn’t the numbers that lie – it’s the people who misinterpret, misrepresent, or mangle the numbers that cause the real mischief. Nick Fennimore, the forensic professor in the A.D. Garrett novels, despises bad science – he’s even written a book called Crapshoots and Bad Stats all about the way numbers can be messed with and mishandled. Like most forensic scientists, Fennimore uses a statistical approach called Bayesian Analysis.
Fennimore first meets Josh Brown, his enigmatic protégé, over coffee and a bit of Bayes in Everyone Lies.
Josh is interested in miscarriages of justice, and is currently researching Sally Clark, the solicitor wrongly convicted of murdering her two infants. The Clarks had tragically lost two children to cot death syndrome, but their mother was brought to trial charged with their murder. Professor Roy Meadow, acting for the prosecution, pointed to the stats: the chances of a middle class, affluent family losing one child due to cot death was minuscule, but losing two babies to the syndrome was a 1 in 73 million chance.
The equivalent of betting on an 80-1 outsider in the Grand National for four years running and winning every time.
Wow – that sounds convincing! Maybe… but it is wrong. Professor Meadow was a paediatric specialist, not a statistician, and he made a basic error of mathematics, compounding the error by ignoring biological factors that may have explained the deaths. This wilful refusal to look at the context of the situation put an innocent woman behind bars for 3 years.
So, what were these biological factors? Both babies had been vaccinated shortly before they died; one child had a staphylococcus infection which might have contributed to his death; and it is now known that babies born to older women are more susceptible to cot death (now known as Sudden Infant Death Syndrome, or SIDS). Sally Clarke was 35 years old.
Context, as Fennimore is fond of saying, is crucial.
Bayesian Analysis looks at probability of something happening from both sides, and it absolutely, unswervingly demands that context is considered. ‘If they’d done a Bayesian analysis of the evidence, the case would never have come to court,’ Fennimore says. ‘Bayes would ask what is the likelihood that the deaths were caused by SIDS compared with the likelihood that they were caused by murder. Statistically, it’s more likely that two children will die of SIDS in the same family, because of predisposing factors.’
There’s an excellent assessment of the flawed use of statistics in Sally Clark miscarriage of justice at Understanding Uncertainty