12-01-2013, 11:51 AM
No problem - I made up the numbers! Perhaps someone can work out the actual probability? That said any probability simply based on the grading system are probably unreliable for the reasons outlined in the last paragraph of the article given below (taken from http://innocent.org.uk/cases/sallyclark/#watkinsbmj)
Anyway my point is best made by people remembering Sally Clark, the mother wrongly convicted and jailed for killing her two children largely due to an appalling misunderstanding of probabilities:-
Anyway my point is best made by people remembering Sally Clark, the mother wrongly convicted and jailed for killing her two children largely due to an appalling misunderstanding of probabilities:-
Quote:On 9 November at Chester Crown Court Sally Clark, a Cheshire solicitor, was convicted, by 10-2 majority, of smothering her two infant children. With conflicting forensic evidence, the Crown's case was bolstered by an eminent paediatrician testifying that the chances of two cot deaths happening in this family was vanishingly small - 1 in 73 million. This seriously misunderstands probability theory. It is speculation whether Sally Clark would have been acquitted without this evidence. But with this mathematical error prominent the conviction is unsafe.
Imagine an archery target with two arrows sticking in the very centre of it. This provides greater evidence of the skill of the archer if the target was in place before the arrows were fired than if it was drawn around them afterwards. Probability theory requires calculation of the probability not only of the event in question but also of all events that are as extreme or more extreme. When the target is drawn first you calculate the chance of both arrows hitting the centre of the target. But when the target is drawn round the arrows afterwards you calculate the chance of both arrows hitting the same point, whatever that point. With two independent arrows one probability is the square of the other.
Suspicion was drawn to Sally Clark by the occurrence of two deaths so the probabilities should not have been squared. The odds of 1 in 73 million shrink to 1 in 8500. But this figure is itself meaningless. There is in fact a wall full of arrows with the target drawn around the two that are close together and the others ignored. Mathematical formulas for this situation often surprise people. For example, with only 23 people in a room the odds are better than 50% that two of them have the same birthday.
From whole population data Reese calculates the square of the population risk of cot death as 1 in 2.75 million. There are 378 000 second or subsequent births each year in England. So if cot deaths are random events two cot deaths will occur in the same family somewhere in England once every seven years. But cot deaths are not random events. There have been several studies of recurrence. At least one study did show no increase in recurrence rates. But several others showed recurrence rates about five times the general rate, implying recurrence somewhere in England about once every year and a half. Two studies showed even higher rates.
The fact that studies of recurrence have been done means this event is not vanishingly rare. In a case series of recurrent infant death Emery classified two cases as recurrent cot death out of 12 cases occurring in Sheffield in 20 years. Wolkind et al found five cases in their unsystematic English case series of 57 recurrent infant deaths. Both these studies distinguished cot death from accident, illness, murder, and neglect.
The prosecution used the figure of 1 in 73 million rather than 1 in 2.75 million because of the family's affluence. Yet taking data from an epidemiological group and applying it stereotypically to all members is an example of the ecological fallacy. Social class is a complex reality of interassociated circumstances - education, work, income, lifestyle, culture, contacts, residence, opportunities, social class of origin, etc - statistically summarised for use in population studies by selecting the one variable which performs best as an indicator. This does not mean that individuals have the attributes of the statistical group.