My comment was meant as a reductio ad absurdum to show the fallacy of the
original argument, not as a serious argument about the innocence or guilt
of the mother. I'm sorry if this was not clear.

Martin

Quoting "Dr. Robert Newcombe" <[log in to unmask]>:

> 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.
>
>



Prof J M Bland
Dept of Public Health Sciences
St George's Hospital Medical School
London SW17 0RE, UK

Tel 0181-725 5492
email [log in to unmask]

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