arcniz, your restating of my statistical inferences were by-and-large on
the mark but could use some fine-tuning in spots and even a correction in
one place.
All tests, even those that are correctly calibrated, are subject to
"variance." Statistics is the branch of mathematics that concerns drawing
inferences in the face of variance. A BAC test value X is a Gaussian random
variable whose mean is the subject's true but unknown BAC. The
variance of X is much smaller than you would expect - or, more accurately,
than I expected - but still nonzero. Taking more than one test, say N samples
X1, X2, ... , XN, decreases variance. If Xbar denotes the average
(X1 + X2 + ... + XN)/N then the variance of Xbar is 1/N'th the variance
of X. Therefore by increasing the sample size more control over variance
is obtained. The Law of Large Numbers, a theorem in probability theory,
shows that as N tends to infinity Xbar tends to true BAC with probability 1.
The one point with which I would disagree with arcniz is the statement
"If both blood tests turn out clearly on the wrong side, then your goose is
cooked. Maybe yes, maybe no. Nobody should find themselves in such a
position but if it happens, then I would suggest instructing your lawyer
to hire a competent statistician. (I regret to say that expert statistical
opinion can be obtained much more economically than either medical
opinion or legal counsel.) For example, if your two tests were 0.046 and
0.042 and if the accuracy of the tests did not improve much in the last
fifteen years, then I doubt if I would have trouble convincing a jury that
the hypothesis "true BAC greater than 0.04" could not be accepted with
the certainty needed for a criminal conviction. Well, juries can be tricky
but the line of reasoning that I would use has been accepted by appellate
courts.
Incidentally, some jurisdictions attempted to avoid the variance issue
with laws that read "BAC tests at 0.10 or above" instead of "have
a BAC at 0.10 or above." I'm refering to motor vehicle laws of course
and I'm not sure whether those legislative dodges worked.
PaperTiger, You are right about the name but when I saw the movie on
Canadian TV long ago I think it went under the title "Danger in the Skies."