Sally Clark had two sons. Both died within weeks of birth, a year apart, apparently of sudden infant death syndrome (SIDS), sometimes called cot death. SIDS is — mercifully — rare; in England, at the time, it struck roughly one in 8,500 babies. That statistic led to Clark being prosecuted for double murder in 1998, despite there being little to no forensic evidence for her guilt.
A paediatrician, Roy Meadows, called as an expert witness for the prosecution, told the court that the probability of the two deaths happening by chance was one in 73 million: that is, 8,500 times 8,500.
As it happens, that’s not true. This calculation assumes that the deaths are entirely uncorrelated, but we know that SIDS can run in families and be affected by environmental conditions. If you have one case of SIDS in your household, while incredibly rare, you are more likely to have a second; the 73 million figure is orders of magnitude too high. But that wasn’t Meadows’s big mistake.
His big mistake was the following: he assumed that if the probability of the two deaths happening by chance was one in 73 million, then the probability that Sally Clark was innocent was one in 73 million as well.
But this is wrong. Crucially, catastrophically wrong. As wrong as assuming that because only one human in eight billion is the President of the United States, there’s only a one-in-eight-billion chance that the President of the United States is human.
Nonetheless, Meadows’s testimony helped convict Clark in 1999. She spent three years in jail before her conviction was overturned on appeal. Her life was, obviously, ruined. It will not surprise you to learn that she drank herself to death four years later, alone. It’s a haunting story.
The danger of convicting with statistics: Courts have a bad history of using probability
American Buddhist Net 