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

From: S Ellison <S.Ellison_at_lgc.co.uk>
Date: Mon, 14 Jul 2008 11:18:24 +0100

>>> Ted Harding <Ted.Harding@manchester.ac.uk> 14/07/2008 00:16 >>>
>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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