I’ve just finished reading Bad Science by Ben Goldacre. It was published in 2008 but is still relevant today. Indeed I think it should be compulsory reading for high school students and all journalism undergraduates.

There’s a fascinating chapter on the placebo effect, an eerily familiar chapter about the denial by some that HIV causes AIDS which reminded me of covid, the unscientific claims made by the homeopathic and nutrition industries, and how the media is to blame for the MMR vaccine scare. I was shaking my head in disbelief throughout.

Perhaps what stood out to me the most and what I will never forget is how a failure to understand statistics led to the incarceration of an innocent nurse in the Netherlands. Lucia de Berk was sentenced to life imprisonment in 2003 for four murders and three attempted murders of patients in her care. She was eventually exonerated in 2010.

The prosecution’s case relied heavily on flawed statistical arguments that no one at the time seemed to notice. They claimed the chance of a nurse working at three hospitals being present at the time of so many unexplained deaths was one in 342 million, therefore she must be guilty. But they had calculated this value incorrectly and it was actually only 1 in 25.

In addition, if a court is going to weigh up the probability of something being a coincidence to prove guilt they must compare this value with the probability of the other explanation happening: murder. For instance, it may be there is a 1 in 100 million chance that 8 patients will all die from unexplained causes while one particular nurse is working. That is pretty rare and so it’s tempting to assume guilt. But what are the chances that someone is guilty of murdering 8 patients? That may be 1 in 500 million – even rarer (I’m just making these numbers up for the sake of an example). They not only bungled their statistical calculation, but they also failed to present the court with both probabilities, and without the second, the first is meaningless.

Phillip Dawid, Professor of Statistics at the University of Cambridge, later described them as having “made very big mistakes”. I think he was being generous there. They monumentally fucked up. Another British mathematician, Richard D. Gill, later started a petition to reopen Lucia’s case and in 2007 the signatures were presented to the Dutch Minister for Justice and the case reopened. Eventually, Lucia de Berk was exonerated and paid an undisclosed sum in compensation. The lesson here is to pay attention in high school maths. It might save your life one day.

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