In March 2003, when nurse Lucia de Berk faced trial in a Dutch court for charges of murder and attempted murder, the statistical evidence against her seemed compelling. Investigators had identified a number of “suspicious” deaths and near deaths in hospital wards in which de Berk had worked from 1999 to 2001, and records showed that she had been present when many of those events took place. Henk Elffers, a statistical expert working for the court, reported that the chance her presence was mere coincidence was only one in 342 million.

On the basis of this number and limited forensic evidence — traces of toxic substances found in two of the exhumed bodies — the court found de Berk guilty, and sentenced her to life in prison. But some Dutch mathematicians now say that the figure cited was incorrect, and that the case offers a classic example of how statistical reasoning can go horribly wrong. “The magical power of the big number led everyone at an early stage to be totally convinced of Lucia’s guilt,” says mathematician Richard Gill of the University of Leiden in the Netherlands. “Then they went to work to confirm their theories.”

I recently wrote about this case for the science journal Nature (reference is Nature 445, 254-255 18 Jan 2007). As it turns out, the physical evidence is also strongly disputed (it was retrieved from badly decomposed bodies exhumed months or years after burial) and many people now believe that Lucia may be innocent. The entire case looks to be an example of "instinctual" human thinking gone horribly wrong -- with decision making being based on the emotional power of a big number (even though the logical irrelevance of such numbers is well known), and with the opinions of everyone involved, lawyers, judges and the public pushed by the irresistible social force of everyone knowing that she was guilty, which led to the systematic suppression of doubts. The sad but remarkable thing is that statisticians and psychologists know the dangers of these human social habits very well, yet we're still unable to get adequate safeguards into the legal framework to prevent outcomes such as this one, or that in the famous Sally Clark case a few years ago in the U.K.

Several Dutch scientists deserve enormous credit for their tireless exploration of the way Lucia's case was handled, and especially for exposing the flawed nature of the statistical arguments. Richard Gill has an extensive summary of the details of the case on the web. Philosopher of science Ton Derksen has written a book critical of the case. Both have submitted presentations to a Dutch committee of legal "wise men" which is now considering whether the case should be reopened. I'm told (by Lucia's lawyer) that a decision could come down as soon as April.