Sally Clark case was notorious for the prosecution’s misuse of statistics in respect of Sudden Infant Death Syndrome (SIDS). In particular, the claim made by Roy Meadows at the original trial – that there was “only a 1 in 73 million chance of both children being SIDS victims” – has been thoroughly, and rightly, discredited.
However, as made clear by probability experts who analysed the case, the key statistical error made was to consider the (prior) probability of SIDS without comparing it to the (prior) probability of murder of a child by a parent. The experts correctly focused on the critical need for this comparison. However, there is an oversight in the way the experts built their arguments. Specifically, the prior probability of the ‘double SIDS’ hypothesis (which we can think of as the ‘defence’ hypothesis) has been compared with the prior probability of the ‘double murder’ hypothesis (which we can think of as the ‘prosecution’ hypothesis’). But, since it would have been sufficient for the prosecution to establish just one murder, the correct hypothesis to compare to ‘double SIDS’ is not ‘double murder’ but rather ‘at least one murder’. The difference can be very important. For example, based on the same assumptions used by one of the probability experts who examined the case, the prior odds in favour of the defence hypothesis over the prosecution are not 30 to 1 but rather more like 5 to 2. After medical and other evidence is taken into account this difference can be critical. The case demonstrates that, in order to use probabilities in legal arguments effectively, it is crucial to identify appropriate hypotheses.
My published article on this is here.