## 7 Conviction By Maths Error

October 20, 2009

On 9 November 1998 at Chester Crown Court Sally Clark, a Cheshire solicitor, was convicted, by 10-2 majority, of smothering her two baby boys.Clark’s first son died suddenly within a few weeks of his birth in 1996. In 1998, when her second son died in similar circumstances she was arrested and tried for the murder of both sons. The prosecution used paedeatrician Prof Roy Meadows as a expert witness. He had discovered Munchausen Syndrome by Proxy (MSbP) which every student will have seen in some cop show. It relates to an adult, often the mother, inflicting injury or medicating a child to make them sick and to get attention. Sally Clark was found guilty and spent 3 years in jail.

The Maths Error: Not Understanding Statistics!

Prof Roy Meadows testified that the chance of two children from an affluent family suffering sudden infant death syndrome was 1 in 73 million. He arrived at this number by squaring 1 in 8500 for likelihood of a cot death in similar circumstances.

Multiplying the probability of two events only works if the events are independent like flipping a coin. But a Cot Death gene, for instance, would dramatically increase the likelihood of 2 Cot Deaths in one family.

The Royal Statistical Society later issued a public statement concerning the “misuse of statistics in the courts” and arguing that there was “no statistical basis” for Meadow’s claim. The journalist Geoffrey Wansell called Clark’s experience “one of the great miscarriages of justice in modern British legal history”. Prof Meadows was struck off the medical registrar in 2005. Sally Clark died of acute alcohol poisoning in her home in 2007. (Ref: BMJ )

Article Left: The Observer UK

1. While you are correct in asserting that underlying medical/environmental factors will greatly influence probability of a fatal event, I think you have explained the statistics incorrectly.

If two identical events are independent then the probability of each event occurring is the same.

If I flip a coin the probability of landing heads is 1/2. If I flip it again the probability of heads is still 1/2.

The probability of the second toss being 1/2 x 1/2 = 1/4 is only true if I predict in advance that both tosses will land heads. So to square the probability the two events are RELATED. Not independent.

So. The first baby is born. The probability (assuming this figure to be correct) of a cot death is 1 in 8500 – unfortunately the baby dies. A second baby is born. The probability of a cot death is still 1 in 8500. The two events are independent.

The only way that the figure of 1 in 73 million could be arrived at is if someone had predicted in advance, before both babies had been born, that two cot deaths would occur in that family.

So your comment about the “cot death gene” is, in a way, irrelevant because the two events were statistically independent to begin with.

• HI Quentin,
Thanks for your thoughtful comment. Full marks for clear thinking. Unfortunately, I’ve found students don’t understand the concept of independent events. This is a useful example because you can state reasons why events are NOT independent. It adds clarity even if mathematically not necessary. Thanks again. Cheers Mathspig

2. […] Sally Clark dies several years later of alcoholic poisoning. More information. […]

3. […] Two cot deaths in one family are not independent events. A Cot Death gene, for instance, would dramatically increase the likelihood of multiple Cot Deaths in one family. Sally Clarke spent 3 years in jail. Protests from the Royal Statistical Society followed. Prof Meadows was struck off the medical registrar in 2005. Sally Clark died of acute alcohol poisoning in her home in 2007. ( See Conviction by Maths Error) […]