The excellent Ben Goldcare, a science blogger, writes about a nurse in Holland who is appealing her conviction for killing six patients. There isn’t much to say about the article, and it doesn’t just highlight what seems to be a miscarriage of justice but also examines how statistics can be misused in circumstances like this:
The case against Lucia was built on a suspicious pattern: there were nine incidents on a ward where she worked and Lucia was present during all of them. This could be suspicious but it could be a random cluster, best illustrated by the “Texas sharpshooter” phenomenon: imagine I am firing a thousand machinegun bullets into the side of a barn. I remove my blindfold, find three bullets very close together and paint a target around them. Then I announce that I am an Olympic standard rifleman.
This is plainly foolish. All across the world, nurses are working on wards where patients die, and it is inevitable that on one ward, in one hospital, in one town, in one country, somewhere in the world, you will find one nurse who seems to be on a lot when patients die. It’s very unlikely that one particular prespecified person will win the lottery but inevitable someone will win: we don’t suspect the winner of rigging the balls.
And did the idea that there was a killer on the loose make any sense, statistically, for the hospital as a whole? There were six deaths over three years on one ward where Lucia supposedly did her murdering. In the three preceding years, before she arrived, there were seven deaths. So the death rate on this ward went down at the precise moment that a serial killer moved in.
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