Statisticide II: Crushed Innocence

This is the first follow up in the Statisticide thread. Discussed here, is the Sally Clark trial.

Sally Cark’s first son died a few weeks after his birth in 1996. She gave birth to another child in 1997, who also died subsequently, at the age of eight weeks. The latter death aroused suspicion, and Sally was charged with the murder of her two kids. While there was no definite evidence of Sally’s having murdered her children, the prosecution’s case rested on the claim that two natural cot deaths in the same family are extremely unlikely. There was evidence of physical trauma in both cases. However, this could have been related to Sally’s efforts at resuscitation.

The prosecution’s expert witness, Sir Roy Meadow, former Professor of Paediatrics, University of Leeds, stated that “one sudden infant death in a family is a tragedy, two is suspicious and three is murder unless proven otherwise”. He further deduced that for a family like the Clarks (affluent, non-smoking), the probability of a single cot death was 1 in 8,543, so the probability of two cot deaths in the same family, was around “1 in 73 million” (1 / 8543 × 8543, obtained by the product rule for probability of independent events). This small likelihood of an innocent mother facing two cot deaths, seems to have caused the jury to have considered Sally the murderer beyond reasonable doubt. Sally was convicted and sentenced to life imprisonment. (I can discuss the media reviling the killer mother and hostility in prison, but that is not my point here).

In this case, its not merely an issue of transposed conditionals (discussed in my last post), but also sheer miscalculation of the probability figure to obtain ’1 in 73 million’. It was only in 2002, that the Royal Statistical Society expressed its concerns about Prof. Roy’s calculation.

The first lacunae pointed out, was that the assumption of two cot deaths in a family being independent events, was ill conceived. It could be the case that genetic or environmental factors are involved and the events are highly correlated. The second concern was related to the fallacy of transposed conditionals. The RSS stated that the ’1 in 73 million’ figure should not have been interpreted as the probability of Clark’s innocence. What was required of the jury was to weigh up the relative likelihood of two competing explanations for the deaths: double cot death is very rare, but double murder is likely to be rarer still, so the probability of Clark’s innocence was quite high in absence of any other available evidence! This is also referred to as prosecutor’s fallacy.

Another objection raised, was regarding the probability figure for a single cot death also not being 1 / 8543. This figure ignored the male gender of the Clark babies. Among males this probability is about 1 / 1300.

The prosecution’s statistical argument contains all the lacunae school students are guarded against in probability classes: wrong base probabilities, unfounded assumptions of independence, and misinterpretation of conditional probability. Further, misrepresenting the facts to an equally naive jury, compounded matters. It took two appeals, intervention by elite statisticians, and three years in prison, for Sally Clark to undo, to a limited extent, the damage statisticide caused her.

References:

1. Sally Clark: Home Page
2. Wikipedia page on Sally Clark
3. Plus Mathematics magazine article on the case
4. RSS public statement about the case