This message to allstat is a statement of my appreciation for
something that seems to me right and laudable, happening this
week within the UK statistics academic community. As such, my
message does not demand an answer -I suggest that anyone thinking of
a response should consider the possible merits of addressing their
response, at least in the first place, to myself directly only and
not to the whole of the allstat list.
Here's the business :
In 1999 Louise Woodward, of Cheshire UK, was convicted of murder.
This was based upon the fact that two successive infants of
hers had died with diagnosis of 'cot death'. This was widely
reported at the time and I recall feeling uneasy about the
statistical arguments which might have been considered in the case.
In 'The Sunday Times', 07-May-00, there is news of an appeal. The
report states that the conviction rested *heavily* upon an argument
that as the statistical risk of a single cot death for someone in
the mother's/defendant's situation was known to be around 1/8500,
then the corresponding risk of two cot deaths should be taken
as the square of this figure - around 1/73000000 - a figure so
small that it was unconvincing as a chance outcome.
The Sunday Times article also mentions that Professor P Dawid,
of University College, London, now provides comments that the
above-summarised calculation based upon statistical independence
between such a pair of events was inappropriate - a reasonable
person might estimate that if one child in a particular family
situation had experienced the accident of cot death then the
estimated risk of a second death of this kind within the same
family situation should be greater than the unconditional
background rate (of 1/8500) - there might be a common situational
risk, possibly unknown in character, which need have nothing to do
with murder.
(I should add that the newspaper report of Professor Dawid's words
is clearer than my wording used here!)
So - when you see arguments about combining probabilities being
apparently misused, do consider speaking out - it may not be
evident how much weight assessors may put on the outocomes, and
this seems the proper social responsibility of a statistician!
Norman Marsh
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