Dutch nurse Lucia de B., convicted to a life sentence for the murder on 7 infants during her shifts, is now entitled to a re-trial. Why do I write about it here? Because one of the grounds she was convicted on was a statistical argument. A statistical argument that has been thoroughly contested by prominent statisticians, arguing that according to the court’s line of reasoning, one out of every nine nurses would go to jail!

I have written before about this statistical argument, but did so in Dutch. For those interested, I’ll give you a short recap, and a nice movie.

Lucia de B. has been convicted for murder on seven children on numerous grounds. Most of these have been contested or already been refuted. Ton Derksen, a Dutch philosopher of science, even wrote a book to discuss many of the court’s considerations. One of the main arguments has been, that an statistically highly improbable number of children died during her shifts. There are many arguments against this statement. For instance, after she was related to one unusual death, investigators specifically sought for other unusual deaths during her shifts. Clearly, this increases the numerator of the abovementioned chance. Later, it was discovered that the ‘unusual’ deaths actually didn’t need to be unusual, for the ‘unusual’ substance in the infants’ blood had been mixed up with a similarly named, but completely different, substance that is found in infants blood very often.

Nevertheless, one of the courts’ main considerations was that the chance that so many infants would die during or shortly after the shifts of Lucia de B. was so low, that she had to be guilty. Apparently, the court reasoned that the probability of these events (deaths during her shift) was so low, that other explanations would be highly improbable.

Clearly, something goes horribly wrong here. In the movie below a similar case is addressed by Peter Donnelly in a very accessible way. In the case that is addressed in the movie, a woman was convicted for the murder of her two children. These two children, independently, had died from sudden infant death syndrome. Sudden infant death syndrome is rather rare (and a tragedy for the family). As a matter of fact, it is so rare, that the chance that it happens to two babies of the same mother is so extremely small (according to the judge: extremely small chance times another extremely small chance), that this mother was sent to jail.

I’m not going to completely summarise Peter Donnelly’s arguments, but what it comes down to, is that we should interpret the court’s decision as a ‘test’. And we know of statistical tests that two errors can be made: we can erroneously conclude that an event is highly improbably, while it in fact is not. Or, we can erroneously conclude that something is not highly improbable, while in fact it is.

What this has to do with the case of the mother who lost two of her babies to infant death syndrome, and correspondingly to the case of Lucia de B., is made clear in the movie below. The basic argument, which relates to the case of Lucia de B., is that although some events are rather rare, if enough possibilities for the event to occur are present (lots of mothers have two babies, many nurses work with infants who die), the odds of the event to occur in the whole population isn’t that small at all. Watch and see how Peter Donnelly explains this eloquently:

And by the way: for the statisticians amongst us: the prominent statisticians “>I mentioned before basically argue that the assumption of homoscedasticity has not been met, which makes matters even worse!