Lies, damned lies, and statistcs.

Lying seems to be a popular theme at the moment. Both in the real world, where's it's been rebranded as post-truth, and within the Skeptics 'movement' (which is, of course, part of the real world anyway). July last year saw Dr Gordon Wright rock up in Greenwich for his fascinating talk about secrets, lies, and our quest to uncover them and last night the same Star & Garter hosted Dr David Robert Grimes with his talk Lies, damned lies, and statistics - How we get science coverage wrong.

Dr Grimes is a physicist and writes regular opinion and analysis pieces on scientific issues for the Irish Times and the Guardian as well as being a regular panellist on science issues on radio and television. He was joint-recipient of the 2014 Maddox Prize for Standing up for Science and he's an all round amiable fellow with an easy delivery, conversationally going on off on tangents and, occasionally, ending up in rabbit holes of his own making.

It was a scattershot approach and the talk went on for quite a bit longer than the usual Skeptics event but there was a lot to take away from it. The basic gist of Dr Grimes' argument was that people didn't really understand statistics. In most cases through no fault of their own but in some, more egregious, instances because they were being lied to.

An early example was that of Bertie Ahern, the former Irish Taoiseach, who once tried to claim 10% growth (of what I'm afraid to say I didn't catch but that's not the point) on the basis that something that had dropped 50% had then gone up 60%. If you take a base figure of 100 and take away 50% you have 50. 60% of 50 is 30. 50 + 30 = 80. So what had actually happened was a drop of 20%. Ahern had mixed up, either intentionally or not, the base figures. He'd either not understood statistics or he'd used them, on purpose, to present false figures. Or, to put it more simply, lie.

That's what Dr Grimes was getting at when he titled his talk after that hoary old chestnut "Lies, damned lies, and statistics". A quote that has been ascribed to both Mark Twain and Benjamin Disraeli yet remains officially unattributed.

Dr Grimes showed us a graph listing deaths caused by breast cancer. He said that about 4% of all women will die of breast cancer compared to 42% who die due to cardiovascular reasons. Whilst not belittling the seriousness of breast cancer he went on to contend that, when factoring in the chances of false positives in tests, it is actually inadvisable for women under 40, maybe even under 50, to have tests as they could do more harm than good. I'm no doctor and, thus, feel a bit uneasy even passing these thoughts on but Dr Grimes (you can tell by his name, it's not just his initials) is.

He simplified some complicated looking maths to show that even if there's only a 0.01% chance of a false positive in any test that still doesn't mean you only have a 1 in 10,000 chance of getting an incorrect diagnosis. It could be as high as a 4/5% chance.

Equally serious was the case of Sally Clark, a corporate lawyer, whose first two children both died suddenly, and of unexplained circumstances, before they were 12 weeks old. The odds of this happening were reported to be 1 in 73,000,000. This figure was arrived at by the now discredited paediatrician Roy Meadow and played a huge part in sending Sally to prison. She spent three years in jail as a child murderer. Clearly spending time incarcerated for the homicide of your own children is about as low as it gets. When she was found innocent and released her life had been ruined and she was found dead of alcohol poisoning three years later.

Meadow's quote "one sudden infant death is a tragedy, two is suspicious, and three is murder, until proved otherwise" became known as Meadow's Law. He acted as an expert witness in Clark's court case. He claimed that, for an affluent non-smoking family like the Clarks, the probability of a single cot death was 1 in 8,543 so the probability of two cot deaths in the same family was around "1 in 73 million" (8543 × 8543). Given that there are around 700,000 live births in Britain each year, Meadow argued (wrongly) that a double cot death would be expected to occur once every hundred years.

Whilst Clark was in prison the Royal Statistical Society wrote to the then Lord Chancellor, Lord Irvine of Lairg, pointing out that the calculation leading to 1 in 73 million was invalid and that there were several reasons why. First, Meadow's calculation was based on the assumption that two SIDS (Sudden Infant Death Syndrome) deaths in the same family are independent. The RSS argued that "there are very strong reasons for supposing that the assumption is false. There may well be unknown genetic or environmental factors that predispose families to SIDS so that a second case within the family becomes much more likely than would be a case in another, apparently similar, family".

Second, it is likely that the court committed a statistical error known as the "prosecutor's fallacy". Many press reports of the trial reported that the "1 in 73 million" figure was the probability that Clark was innocent. However, even if the "1 in 73 million" figure were valid, this should not have been interpreted as the probability of Clark's innocence. In order to calculate the probability of Clark's innocence the jury needed to weigh up the relative likelihood of the two competing explanations for the children's deaths. Although double SIDS is very rare, double infant murder is likely to be rarer still, so the probability of Clark's innocence was quite high.

In case that evidence is not overwhelming enough for you the probability of a child dying of SIDS has since been changed from 1 in 8543 to 1 in 1300. Clark was, as I've written, eventually released from prison and exonerated of all charges but not before it ruined, and finally ended, her life. This is where the abuse, or misunderstanding, of statistics gets very serious indeed.

Dr Grimes also told the example of a man who was walking home one night in Los Angeles and was stopped by police as a suspect in a rape case. Despite having a cast iron alibi of having been with his family, including his new born child, that day, a pubic hair was found on the woman's body and the statistical likelihood, according to the prosecutors, of this belonging to the new father the police had stopped were overwhelming. Seemingly on the basis that it was a 'negroid' pube.

It was enough to see the main jailed for 30 years until further research revealed that the hair actually belonged to a dog. A further test on a semen sample taken at the time was found to fit with another man already in prison. So our man was innocent and three decades later he was released from prison having completely missed his child's entire youth because he'd been wrongly placed on the sex offender's register. There were hundreds of cases that depended on this incorrect (statistically and morally) evidence. Many were looked into. But for 32 people it was already too late. They'd already been executed. So much for the death penalty.

 Dr Grimes seemed to jump from the sublime to the ridiculous when he went on to talk about Melinda (who he kept calling Melissa) Messenger who's received quite a lot of publicity for refusing to give her daughter the HPV vaccine (a vaccine that has been estimated to prevent 70% of cervical cancer, 80% of anal cancer, 60% of vaginal cancer, and 40% of vulvar cancer) because of her concern about possible side effects.

It's worth noting that Melinda Messenger is not an immunologist nor a scientist of any kind. It doesn't mean her point of view is worthless. It just means it doesn't hold as much weight as someone who has actually studied, and knows about, this kind of thing. I know Michael Gove says we've all had enough of experts but I bet he still expects an experienced doctor to treat him when he goes to hospital and an experienced pilot to fly his plane. Though I'd be happy for Melinda Messenger to carry out both these jobs for him.

This brought Dr Grimes to his pet hate of 'false balance'. When a media outlet, be it television or newspaper, presents pseudoscience they like to get a scientist in to offer an alternative view. But if 99.9% of evidence says one thing and 0.01% hints at another these two things shouldn't be presented as equally possible. It's patently nonsense yet such is the rush to sell newspapers, get clicks, or get viewers media outlets don't have time to check details as much as they should and we, as the customers, the end users, are most to blame for not checking, and insisting on checks being done, ourselves.

Dr Grimes' talk was circuitous and took in many, many different examples of where statistics have been bodged, fumbled, and outright made up. It was worth attending even if a lot of it was actually quite depressing. I'll try, in future, to be a bit more circumspect when presented with information that looks too good to be true. We're all, after all, guilty of confirmation bias.