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Topic: Theorical question about inference
Replies: 1   Last Post: Jun 22, 2006 7:01 PM

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Richard Ulrich

Posts: 2,961
Registered: 12/13/04
Re: Theorical question about inference
Posted: Jun 22, 2006 7:01 PM
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cross-posted to, for general interest.

On 20 Jun 2006 17:32:09 -0700, "Eric" <> wrote:

> Hi all,
> I know it's a basic question, but I couldn't get an answer from the www
> resources.
> Since inference is about estimating population parameters from a
> sample, are correlation and khi-2 inference techniques or not ?

It took me Googling to get it -- khi-2 is chi-squared (or X^2).

I would say that inference, as I have used it in
research projects, is more often about "testing" rather
than about "estimation." We want to know whether there
is evidence that some effect *exists*, even though our
data may be too weak. Zero versus non-zero. If it is
non-zero, the mean-estimate is large enough to be
interesting, given small samples.

IF the sample size is large, then it becomes important
to consider whether the size of the effect is larger than
trivial sources of causation not controlled-for, and large
enough to be interesting. For large N, inference might
be more a matter of estimation.

So, I am denying your assumption, "about estimating
population parameters" as the root of inference.

The chi-squared distribution is used for testing in
various situations. It typically can be increased by
increasing the N, such as: in the tests on contingency tables.
- Thus, it is not a good measure of "effect size" except
for comparing tables (or other circumstances) that are
highly similar.

The Pearson correlation needs to be referred to a sample N
to get a test, so it comes closer (than the X^2 does) to measuring
an effect size of association. Any correlation is determined by
the variables, *and* by the choice of sample with its variances
on measures, but not by the N. Correlations *can* be compared
in tests between two samples (for example), but it is generally
preferable to test (for that example) the regression coefficients,
using a test based on pooling the samples.

> Since they're not estimating parameters, they shouldn't be considered
> as "inferential" techniques ?
> If so, how could one name them ? Please enlighten this troubled soul...

Chi-squared is a "test statistic". It does require reference
to the "degrees of freedom", which is often fixed for a design.

Pearson's r is a test-statistic that requires the N. Since it
needs N, it functions as an estimate of effect size for familiar
situations. Correlations are used "familiarly" in test-retest
reliability, just to mention one circumstance.

Cohen's d is used as an estimate for power analyses for
another sort of "familiar" situation, and it seems rather analogous
to the r, except that there is a separate test (t-test).

The Odds Ratio, at the other extreme,
is a more like a pure effect-size "estimate", since
it requires not just the total-N but the marginal-Ns
in order to generate a test. I started to say that it
is a "good" effect-size estimate -- it does emerge rather
naturally from logistic and log-linear modeling, but I'm
not sure what the standard for "good" ought to be.

Rich Ulrich,

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