Re: Small probabilities

On 1/11/06, Randy Isaac <randyisaac@adelphia.net> wrote:
>
> Vernon,
>
> With all due respect to Iain, this is a point with which I disagree.
> Per our previous discussion, the only argument offered against coincidence
> is very low probability, which I argued is, in general, insufficient to
> prove that something is other than random or a coincidence. It can be a
> good "search warrant" or cause to search for other explanations but,
> lacking
> such evidence, coincidence is by no means ruled out.

As someone who works in probabilistic modelling, I'll have to take issue
with Randy on this one. It seems to me that many scientific deductions are
based on probability and statistics. You conduct a double-blind placebo
controlled trial of a new drug and collect the statistics on it. You want
to know if the drug has any effect. Sometimes it does and sometimes it
doesn't for individual cases. So you collect the stats for a large number
of patients, and determine the probability that the measured benefits could
have occurred by coincidence.

You said, Randy that coincidence is by no means ruled out. Of course, I
agree you can NEVER rule out coincidence, but if the probability of the
perceived beneficial effect of a trialled drug occurring by coincidence is
less than 0.01, then statistically it is deemed "highly significant".
Probably enough to justify the claim that the drug is useful. There is
nothing magical about the 0.01; probability is always a grey area and there
has to be some point where you draw the line in the sand, and say "we
believe this is a real effect".

Another example might be the link between smoking and heart disease/lung
cancer. I'll bet the tobacco industries are promoting the idea that it
isn't proven. Yes, of course it isn't proven, but the evidence is
overwhelming. But "evidence" is a probabilistic thing here (statistical
studies etc). Indeed, the term "evidence" has a specific mathematical
definition in Bayesian statistics.

Now Vernon's "evidence" might overwhelm or underwhelm different people, but
that just means they draw the line in the sand at different points. But I'm
afraid it won't do just to say "coincidence is not ruled out". I don't
disagree there, but then it's not ruled out in the examples I gave above.
Would you smoke 60 cigarettes a day because the evidence that it's bad for
you could be just a coincidence? Depends how badly you want to smoke, I
guess.

Best wishes,
Iain
Received on Tue Jan 10 23:04:06 2006