A double murder?

Statistics is like medicine – saves lives, but can kill when misused. That’s why we all should know at least the basics, no matter what we do for living. The lack of statistical knowledge can have tragic consequences.

On 26 September 1996 an English solicitor Sally Clark gave birth to a healthy son Christopher. Her happiness didn’t last long, as in December the baby became a victim of cot death. On 29 November 1997 Sally become a mother again. Unfortunately, eight weeks later her second son Harry died suddenly. And Sally’s nightmare was only about to begin…

Soon she and her husband were suspected of a double murder and arrested. He was cleared of charges, but Sally was prosecuted. Meanwhile she gave birth to their third son.

On 9 November 1999 Sally was found guilty with two murders and sentenced to life imprisonment. She lost with statistics, or rather with misused and completely false statistical calculations performed by the paediatrician Professor Sir Roy Meadow, former Professor of Paediatrics at the University of Leeds. According to the Care of Next Infant charity (CONI), on average cot death happens to one in 8,543 wealthy, non-smoking families. The doctor calculated that the probability of two children in the same family being a victim of this syndrome equals (1/8,543)^2, so about one in 73 million. It’s more than five times smaller than a chance of winning the UK National Lottery, so we can be pretty much sure that Sally was guilty. The only problem is that this reasoning is completely faulty.

Sir Meadow assumed that deaths of Sally’s sons were independent from each other, so Christopher’s death didn’t influence Harry’s chances of dying as a result of the same syndrome. However, CONI (yes, the same charity whose data were used against Sally) estimates that after one cot death in the family the second one might happen with the chance of one in 200 instead of 8,500. To be honest, one doesn’t need a degree in medicine to figure it out – diseases usually don’t happen without a reason and since in the family all children share both nature and nurture, such events shouldn’t be independent. Sir Meadow seems to have forgotten about it.

Journalists sniffed out a story and followed the whole trial. They reported that the chance of Sally’s innocence was only one in 73 million. So wrong! Even assuming that Sir Meadow was right (although he wasn’t), this figure doesn’t tell us anything about Sally’s innocence. In this case we would have to look at the odds ratio between two possible explanations of Christopher’s and Harry’s deaths: cot death or murder. Although the probability of cot deaths, assuming the validity of Meadow’s argument, is extremely low (1:73 million), the chance of a double murder is even lower, so the odds would be in Sally’s favour. This is another example of misuse of statistics called the prosecutor’s fallacy.

Sally Clark spent a few dreadful years in women’s prison with a stigma of a child murderer; we can only imagine how welcome she felt there… Accusations in the media definitely didn’t help her adjust to that new environment. Luckily, after the Royal Statistical Society’s intervention and the second appeal, in 2003 Sally was released from the prison. In fact, afterwards hundreds of similar cases were reviewed and three other “children murderers” were given freedom.

Sally’s traumatic experiences led to psychiatric problems and alcohol abuse. She died from alcohol intoxication in 2007, way too early.

Lawyers, doctors, and everyone else – please learn statistics. This can really save a life.