# Re: st: Three-way Chi-square test

 From Ronan Conroy <[email protected]> To [email protected] Subject Re: st: Three-way Chi-square test Date Wed, 31 Jul 2002 09:39:54 +0100

on 30/7/02 9:27 PM, Wendell Joice at [email protected] wrote:

> I am contemplating running some 3-way chi-squares (chi-square tests on
> three-way tables). Unfortunately, they aren't all nice neat 2X2X2 tables. In
> some cases, a factor may have as many as 4 categories: thus yielding a 2X2X4
> table.

A chi-squared test is a measure of general association. The more complex the
data, the less the result tells you. In fact, the general rule is that a
statistical test is informative in inverse proportion to its degrees of
freedom.

I suggest that the first thing is that you need to think about a measure of
effect size, rather than a statistical test, unless you are in the unusual
situation that you have a meaningful hypothesis which says that there is a
generalised association, of an unspecified pattern, over the three factors.

Can any factor be thought of as the dependent variable?
Where independent variables have more than two categories, do they represent
ordered or unordered categories? This is important, because you may be able
to create a model in which an ordered categorical predictor can be measured
using the odds ratio associated with a one-unit increase.

As a general approach, I suggest logistic regression. If your predictors
have three or more categories and are unordered, you could use dummy
variables to contrast against a logical baseline category (and -test-
afterwards to see if odds ratios were different).

This is all I can think of as a general principle. If you describe the
design more, perhaps we can come up with more concrete suggestions. As it
stands, however, I think that the procedure you are trying to follow does
not test any definable hypothesis. But correct me if I'm wrong!

Ronan M Conroy ([email protected])
Lecturer in Biostatistics
Royal College of Surgeons
Dublin 2, Ireland
+353 1 402 2431 (fax 2329)

--------------------
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