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On Fri, 2 Jun 2006, Stephen Montgomery-Smith wrote:
After reading Jon's explanation of how much care is put into creating
exit polls, I am nevertheless struck at how creating good exit polls is
an art rather than a science. It requires intelligently guessing what
the sources of bias might be, and working as hard as possible to remove
them. But there may be other sources of bias that they didn't think of,
and which only appear in elections somewhat rarely.
Sure. And the Bush camp had that base covered by running at least one
advertisement where they encouraged people to vote for Bush but to say (to
friends and family) that they were voting for Kerry. When I saw that ad,
I thought, "they are going to cheat." Didn't anyone else see an ad like
that one? I think it was targeted at women with the idea that "Bush will
keep you and your family safe from the terrorists."
And a problem with calculating a p statistic that is way small is that
this is the chances of such a thing happening in any one election, when
you really need to be computing the chances that it would happen in any
of the huge number of elections that have had exit polls computed for
them.
That is not hard to deal with if you assume that the different elections
have independent outcomes.
Also, from an anecdotal point of view, I wouldn't expect the exit polls
to be consistently wrong across the board unless there were a large
scale effort to subvert the results of the election, and to do such a
thing in total secret without someone somewhere spilling the beans is
just not feasible as far as I can see.
I wonder about that. Why couldn't a few hundred (at most) people keep a
secret for at least this long? There is a lot at stake and they would be
in a world of trouble if they ever revealed what they had done.
But more than that, I have spent some time thinking in general about
statistics. Some of the large data problems that people are dealing
with (e.g. microarrays that Jon told me about recently) is revealing to
me just how ad-hoc statistical methods are. As best as I can see the
only statistical method with any pretension to any kind of solid
foundations is the Baysian method, but my impression is that for large
data problems it tends to give way worse results than the other more
ad-hoc methods.
I don't see it that way. Here are two good books on inference:
Edwards AWF (1972) Likelihood. Cambridge University Press,London
Royall, R. (1997). Statistical Evidence: A Likelihood Paradigm. London: Chapman & Hall
Here is a review by geneticist/statisticians:
http://taxa.epi.umn.edu/~mbmiller/journals/ajhg/199807_Vieland_Hodge_Likelihood.pdf
(the first 7 pages of that PDF)
I read Edwards very thoroughly and thought he had great ideas. I haven't
read Royall, but I think his ideas are much like those of Edwards.
I personally question the very assumption that the laws of probability
can be applied to real life questions like "how likely is it that
Macbeth was written by Shakespeare?"
The problem with that is that the question isn't posed in a way that leads
me to a reasonable statistical model.
Probability theory has had a very fine development, and works extremely
well for computing chances that certains hands will appear in poker.
There is an example where the model is close enough to the reality that
the Kolmogorov axioms work beautifully.
And indeed if you try playing games of chance without knowing the laws
of probability, a clever person can rip you off big time. But I think it
has been simply assumed that these same laws can be applied to problems
like how effective medications are, and I am now wondering if this
assumption is truly warrented.
The reason that they can be applied to things like clinical trials is that
we use randomization in trials. The use of random assignment of patients
to conditions is the key to how to develop statistical models for clinical
tials. If we didn't have that, we'd really be in the dark.
Much more could be said about these topics but I'll leave it at that for
now. I'll just add that it would be great to have a dialogue about
likelihood and statistical inference. It's a great topic. I have a lot
of work this summer preparing a tenure dossier that might easily fail, so
I might have to wait until fall to really get into it. This probably
should be done on a different list -- one that I make for us or we might
just use CC because it might just be me and you or maybe Jon too.
Mike
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