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Date sent: Fri, 12 Nov 1999 09:58:17 GMT Subject: Statistics and Justice From: [log in to unmask] To: Allstat UK list <[log in to unmask]> > Allan Reese has written about the case of the woman convicted of killing her two > children, apparently partly on the basis of a statistical argument. > > I thought members might be interested in some data. In 1996, the most recent > year for which data are available, there were 649,489 live births in E&W. > There were 4,959 deaths in the first year of life, including 394 sudden infant > deaths (SIDS or cot deaths) and 14 homicides. Thus the probability of a cot > death is 1 in 649489/394 = 1,648. If deaths were independent, which they are > not because there are familial risk factors, the risk that a fimily of two > babies would have two cot deaths would be 1 in 1,648*1,648 = 2,715,904. > Presumably some other adjustment was applied for social factors as the figure > given in the press is said to apply to `well-to-do families'. > > But the same calculation for homicide gives a risk that that two baies will both > be murdered as one in (649489/14)^2 = 2,152,224,291. If the first figure is > relevant, so is the second. As Allan says, neither is relevant. A very interesting argument - but might I suggest that bringing in the homicide argument is irrelevant in a different way. I know one could conceptualise this as a decision problem in which the two possible hypotheses are 2 SIDS and 2 homicides (disregarding all other possible causes of death and the somewhat perverse possibility of one death being of each kind). But surely the *rareness* of homicide as an event in the population would be a quite inappropriate argument to adduce in order to support an assertion of innocence! In a society with a low homicide rate, this fact would not be taken into account when assessing a prima facie case of homicide. Any statistical argument would have to depend critically on whether the case was brought to the attention of the prosecution system solely because of the statistically rare nature of such a "coincidence" or because there were other factors that independently pointed to intentional killing. If just the former, then it practically becomes automatic that when a high SC couple lose two children in this way there is strong suspicion of infanticide - yet if they had been low SC, smokers, and a few years back when incidence was higher, the "p-value" would have been less extreme. So much for p-values again ... Besides, the population data are recognised to be likely to be biased downwards, as coroners are reluctant to give verdicts such as homicide (the same applies to suicide) unless they feel the evidence is very strong indeed. This is as well as the arguments of non- independence and of ascertainment which makes the probability of 1 in 1648 more relevant than its square. Robert Newcombe. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%