Several people have replied to me - thanks - and all agree that prima
facie there is a misapplication of statistics. I will therefore send the
following letter to the press in the hope of provoking further disclosure.
----
Yet again a massively impressive number has been adduced in a court case
to persuade a jury that there is "no reasonable doubt". That such numbers
do impress the lay public is evidenced by the emphasis placed on this
"fact" by the media. Yet again, however, both the number and its
interpretation are severely flawed.
The case, of course, is the lady convicted of killing two children. It
was suggested that the probability of two cot deaths in one family is 1
in 73 million. The basis for that figure was not reported, but I and
other statisticians guess that it was based on some calculation that 1 in
8500 children in the UK dies without explanation in their first year (SIDS).
That figure was squared to obtain the quoted "probability of two such
deaths in one family". [Can you confirm this from court reports?]
There are two major fallacies in this reasoning. First, the events are
not independent; the probability of a second sudden death *given the
first has occurred* is not the same as the first over the whole population.
The second, and more damning complaint, is that yet again lawyers are
using numbers to mislead the court, and probably themselves. Even if the
figure were correct, it would refer to the probability that a family
*selected at random* had suffered two SIDS. It says nothing about the
probability that two deaths, once observed, were of that type. The
distinction is comparable with the difference between picking the
winner of a horse race from the register of all racehorses, or by looking
in the winner's enclosure.
No doubt the figure will be ascribed to an expert witness. Perhaps
courts should start scrutinising the statistical qualifications of
witnesses who are experts in medical or forensic fields. According to
John Bibby#, the original version of the well-known phrase may have been
"lies, damned lies, and expert witnesses."
R. Allan Reese Email: [log in to unmask]
Lockington, East Yorks
[writing in a personal capacity, but as a Chartered Statistician, the
professional grade of the Royal Statistical Society.]
Office phone: 01482 466845
# Bibby J., "Quotes, damned quotes, and ...". An anthology of quotations
about statistics, 2nd ed 1986
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