If the
assumption of independence
of the sampled values is violated, then neither the chi-square test
nor Fisher's exact test is appropriate. If the same same subject
(or related subjects) produces more than one observation in the
contingency table, then this assumption will be violated.
For example, consider an experiment recording
the severity of a medical condition (severe or not) before and after
a treatment for that condition. Each subject in the experiment
would lead to two observations, one before and one after
treatment.
For such data, Cochran's Q test or
McNemar's Q test)
would be appropriate.
If the results of the chi-square analysis indicates that
there may be interactions between row and column effects,
then a more general logit or loglinear model will allow for the
inclusion of interaction effects in the model.
Agresti and
Bishop et al.
discuss logit and loglinear models. If you are not familiar with
logit and loglinear models, you should consult with a statistician
before proceeding.
The chi-square test and Fisher's exact test
are not designed for contingency tables with
structural zeroes.
A more general logit or loglinear model will allow for the
modeling of data that include structural zeroes.
Agresti and
Bishop et al.
discuss logit models. If you are not familiar with
logit/loglinear models, you should consult with a statistician
before proceeding.
The chi-square test ignores any possible
ordering of either the row or column variables.
If either or both of the row or column variables
is ordinal (having a natural order) or continuous,
then an alternative test to the
chi-square or Fisher's exact test may be more
powerful,
especially if one of the variables is an outcome variable (Y)
and the other an explanatory variable (X).
The list below gives some possible alternative tests
for the cases when X and Y are not both nominal.
This is not meant to be an exhaustive list, and
you should consult a statistician if you are
interested in applying a test with which you
are not familiar. Most of these tests
are usually calculated on data in the
form of individual observations instead
of in the frequency counts of a contingency table.
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