I agree with John Whittington's point that even if an event has extemely low
probability, guilt does not follow. (The inverse probability may be relevant
however).
Ray and John say that independent events are rare. That may be so. However,
if association is low, then multiplying probabilities may be 'nearly
correct. (Exam question: discuss).
However, if a common cause exists (e.g. common genetic defects), this may
impringe more on the VALUE of the one-event probability more than it does
on the independence assumption i.e. perhaps we should be multiplying
probabilities together, but the probability should be that of the event
GIVEN the commopn cause.
JOHN BIBBY
> -----Original Message-----
> From: email list for Radical Statistics
> [mailto:[log in to unmask]]On Behalf Of John Whittington
> Sent: 25 July 2005 09:47
> To: [log in to unmask]
> Subject: Re: Roy Meadow
>
>
> At 23:00 24/07/05 +0100, Ray Thomas wrote (in small part):
>
> >Lawyers and medics are getting a bit of a hammering here. But
> surely the
> >statistics profession must share the blame?
> >[snip]
> >The general point to be made is that it is actually difficult to find
> >meaninful statistice of human activities that are truly
> independent of each
> >other. Statistics of human activities are socially or organisationally
> >constructed not 'given'. Poetically put 'No man is an island'.
> >
> >Meadow's mutliplication to get a probability of one in 73
> million assertion
> >was obvously wrong. Two deaths in the same family cannot be
> considered as
> >statistically independent of each other because they occured in the same
> >family. But I don't recall the RSS or statisticians jumping up and down
> >when this figure of 73 millions was first used.
>
> As many have said, it's rather amazing that the defence
> apparently did not
> see fit to obtain any statistical expert opinion, which could well have
> resulted in the figure (hence quite probably the whole prosecution case)
> being challenged.
>
> However, having a defence witness who incorrectly quantifies the
> probability by the use calculations based on unreasonable assumptions is
> merely an added twist to the (essentially non-statistical) problem of the
> underlying 'unreasonable assumption' which has been played out in
> court (to
> the detriment of the defendant) many times before.
>
> There have been other highly publicised cases in which, without any
> statistical input or attempted quantification of probabilities, parents
> have been convicted of harming/killing children - because (without
> attempted quantification) it was considered 'beyond reasonable
> doubt' that
> a similar extremely rare fate could befall two or more children
> in the same
> family from 'natural causes'. We have heard of cases in which rare
> inherited diseases have resulted in two or more siblings being abnormally
> susceptible to breaking bones, brain damage, bruising etc. One
> (US) case I
> have seen repeatedly on TV ('Medical Detectives', on Discovery Channel, I
> think) was of a pair of siblings who, it turned out, both had a very rare
> genetic disorder which produced effects which simulated
> poisoning. ... and
> there have been many more.
>
> In all these cases, the underlying error has really been on the part of
> clinicians (and lawyers) who have failed to acknowledge the
> possibility of
> common genetic (or environmental) factors which might
> dramatically increase
> the chances of two incredibly rare events occurring in the same
> family. In
> other words, the clinicians who express such views are effectively
> asserting that there is no (clinical) way in which the events could be
> non-independent. If they briefed a statistician to estimate
> probabilities,
> they presumably would again make that same assertion - and unless the
> statistician were able to successfully challenge that 'clinical
> judgement',
> then I suppose the statistician would have little choice but to undertake
> the calculation on the basis of that asserted assumption.
>
> I certainly agree that it's a great pity that statisticians (individually
> or corporately) did not manage to somehow intervene in this case - but it
> seems to me that it's fairly clear that the underlying failings DID lie
> with the medics and lawyers.
>
> A more philosophical/sociological question relates to the issue of this
> sort of 'probabilistic conviction', even though one has to accept
> that the
> great majority of convictions (at least of contested prosecutions) are
> necessarily to some degree 'probabilitsic'. What if the chances of this
> being a 'natural phenomenon' really HAD truly been 73 million to
> 1? Do we
> think that the courts understand the nature of random processes -
> such that
> even an incredibly improbable event is equally likely to occur to
> Family A
> 'tomorrow' as to any other family in 500 years time? A similar mindset
> could easily result in winners of the Lottery (or roulette, or whatever)
> being automatically jailed, on the grounds that it was 'vanishingly
> improbable' that any given individual would win without cheating!
>
> Kind Regards,
>
>
> John
>
> ----------------------------------------------------------------
> Dr John Whittington, Voice: +44 (0) 1296 730225
> Mediscience Services Fax: +44 (0) 1296 738893
> Twyford Manor, Twyford, E-mail: [log in to unmask]
> Buckingham MK18 4EL, UK [log in to unmask]
> ----------------------------------------------------------------
>
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