> First off, I'd say "not enough information", as the ratio of
> actual positive to negative is not stated.

Which is the only correct answer. That rate is know as the 'base rate',
and ignoring it (what doctors are often reported to do) is knwo as the
'base rate fallacy'. There is a wiki entry for it, but I did not find it
very enlighting.

> Then I'd say "close enough to certain"

No, definitely not, at least not for all base rates. Assume for instance
that the base rate is 1 / 1e6, and assume for the moment that I am a
random sample. With such a low base rate the false-negatives can be
ignored, and nearly all positives are false-positives. The chance that I
indeed have the disease is only (approximatly) 1 / 1e4.

This simple calculation can fail dramatically when I am not a random
sample. After all, I decided to go to the doctor, maybe specifically to
have this test. So I might belong to a risk group, have the right age,
right sex, right eating habit, worked in a specific chemical plant, or
whatever. To do te calculation right (in a statistical meaningful way)
we must establish the base rate (rate of occurence of the disease) in
the group from which I am a random sample. If such a group does not
exist even the answer "not enough information" is not negative enough,
then it should be "can not possibly be calculated". Which is not an
answer politicians like, so it is often ignored even when it is correct.

The relation with cosmology (as already pointed out by others): *we* are
asking that question (about why the parameters happen to be such that we
can exist). We are definitely not a phenomenon in (a universe with ) a
random sample from all possible cosmological constants!

Wouter van Ooijen

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Van Ooijen Technische Informatica: www.voti.nl
consultancy, development, PICmicro products
docent Hogeschool van Utrecht: www.voti.nl/hvu
 
 

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