[R] "Reasonable doubt" - was "Re: shapiro wilk normality test"

[S Ellison]

>>> Ted Harding <Ted.Harding at manchester.ac.uk> 14/07/2008 00:16 >>>
>said:
>What constitutes "reasonable doubt" can become a very interesting
>question, but there are some crimes for which it has a definite
>statistical interpretation

Warning for potential courtgoers: "reasonable doubt" NEVER has a direct
statistical interpretation in a UK court. "Beyond reasonable doubt" is a
state of mind in the jury or the presiding magistrates. While a
statistical test may indicate the strength of some part of the relevant
evidence, and thereby reduce the remaining doubt in the minds of the
jury/magistrates, UK law requires that the jury (or magistrate) to judge
whether doubts are reasonable or not on common-sense and not on
statistical grounds.

The two can be very different, because the doubt in the minds of the
jury must take into account such factors as whether the sample can be
shown to be associated with the defendant; whether the test equipment
was properly calibrated and functioning correctly at the time of the
analysis; whether the sample could have been tampered with or affected
since being taken; whether the blood alcohol was at that level at the
time of driving (and indeed whether the defendant was driving at all);
whether the defendant's second defence test sample result was also over
the limit; whether the arresting officer had it in for the defendant and
so on. 

So a more accurate interpretation of ted's example would be that after
the positive analysis and statistical test result, there was strong or
very strong evidence (you'd need at least 3sigma to say even that much
actually, and the UK convention is exceedence by at least 6mg/100ml)
that the sample as tested showed contained an amount of alcohol over the
legl limit. With suitable supporting evidence, the strength of that
evidence would, for a 'reasonable man' (ie the proverbial man on the
Clapham omnibus),  leave no reasonable doubt of the defendant's guilt.
But the 'reasonable doubt' test is not in itself statistical.

In terms of the 'absence of evidence<>evidence of absence' debate, of
course, it's not so relevant. The law generally requires evidence of
_presence_ - although there's some contaminant legislation that causes
problems by requiring demonstrated absence. 

Steve Ellison
Lab of the Government Chemist


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