Rich Ulrich <[EMAIL PROTECTED]> wrote:
> Ron's post never showed up on my server.
> I especially agreed with the first paragraph of Steve's answer.
> No one so far has posted a response that recognizes the total
> innocence of the original question --
> This is not, "Why do we see two things that are almost identical?"
> This is, "Why do we see two things 'that don't mean anything to me'?"
> If you just want one number, why not "the p-level"?
> With the chi squared, you need to have the DF before you can look up
> the p-level. The chi squared is best used as a "test-statistic" but
> it is not complete all by itself.
> The Odds Ratio is not even a "test-statistic", but rather, an Effect
> size. Having the OR is like having a mean-difference where you also
> need N and Standard deviation before you have a test. With OR, you
> have to have the N, plus the marginal Ns, in order to get a Test.
Of course the Observed odds ratio *is* a test-statistic.
Anything composed out of the observed data, being that
they are themselves "random" quantities, is a statistical
quantity; which is to say, it has a sampling distribution.
The typical epidemiological usage treats log-Odds as if it
were an asymptotic normal variate; with a standard deviation
estimated from the cell values by the usual 1st-order part
of a moment expansion. They then proceed to place "confidence"
interval about log-Odds, and thus, about the Odds itself.
In my mind that certainly *does* treat the observed Odds-ratio
as a random variable, which is to say, as a statistic, whose
role is as an "estimator" of a putative "population odds-ratio".
Now, I have not gone through the math to see to what extent
and why log(ad/bc) *is* (and under what conditions) an
asymptotic gaussian, but I suspect that the argument is
similar to that one which establishes the asymptotic
normality of the log-likelihood of the observed table.
This, too, is analogous to the argument establishing
asymptotic "chi-squared-ness" of the observed chi-squared.
But that is a side-issue. The original question I had
was a hetergeneous one.
Now I think I see part of the answer. One can use chi-square
and N (the total cell number) to look up a tail probability
for the observed table, and use the odds-ratio as a measure of
effect size that is independent of N. On the other hand,
one *could* look the observed odds ratio up in a table
and compute *its* chance probability relative to the
"null" hypothesis that the true OR=1, and then use something
related to chi-squared (normalized somehow to N) as
the measure of effect size. It seems to me that the
choice of statistical indicator and effect-size indicator
is to a large part a matter of convention.
The other part of my question concerned the practise of
software packages printing out a slew of p-values based
on different algorithmic approaches to computing the *same*
test-statistic. They are then served up with their
authors names attached -- and the user is free to quote
them all, as if the prestige of that learned assembly
somehow inheres in his own individual decision. The
more voices in the room, perhaps the less anyone will
notice one's own indecisiveness?
At all odds, I myself must now defer to the collective
judgement...
Ron
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