How to put someone in jail with statistics

BBC News – Dutch nurse Lucy De Berk acquitted of patient murders

The 49-year-old was first arrested in 2001 after the death of a baby in her care at a hospital in The Hague, which was thought to be a poisoning.

Afterwards, investigators found what they thought was a trend of suspicious deaths among 13 patients – all of whom were very young and disabled, or very old and in poor health – treated by Ms De Berk in the previous four years. Five others almost died in what investigators said were suspicious circumstances.

In 2003, she was convicted of four murders and three attempted murders, and sentenced to life in prison.

Part of the evidence against Ms De Berk was the testimony of a statistician, who said the odds were 342 million-to-one that it was a coincidence she had been on duty when all the incidents occurred.

Then in 2004, an appeals court convicted her of three additional counts of murder and upheld the life sentence.

Every time I see some number like “342 million to one” I cringe. When I see it from a statistician I growl. First, because it’s almost always based on false assumptions (like independence of all the things being looked at). Second, because it omits the universe in which these things are happening. In a world of 6 billion people, for example, events whose odds are 300 million to 1 against will happen, on average, to 20 people. (And if those are the odds for something happening on any given day, that means the thing whose odds are 300 million to 1 against will happen, on average, somewhere north of seven thousand times a year.)

This is also why I blenched when I saw that the idiots on Wall Street were using models that told them how much money they had at risk 95% of the time. Even if those models had been correct, that means one time out of 20 the risk would be bigger. If it was risk per trading day, that would mean a dozen times a year. If it was risk per trade, who knows? A dozen times a day?

People are lousy with large numbers.

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