The power
of the test depends on the total sample size in the
contingency table, and the
expected cell frequencies
depend on the overall total and the row and column marginal totals.
Observed values of 0 may be either sampling zeroes or
structural zeroes.
If they are structural zeroes, the chi-square test and Fisher's
exact test are not appropriate, although an
alternative test
may be available.
If a set of marginal totals is fixed, then the more nearly
those marginal totals equal each other, the more powerful the chi-square
test will be for the same total sample size.
The chi-square test involves using the chi-square
distribution
to approximate the underlying exact distribution.
The approximation becomes better as the
expected cell frequencies
grow larger, and may be inappropriate
for contingency tables with very small expected cell frequencies.
For tables with expected cell frequencies less than 5,
the chi-square approximation may not be reliable.
A standard (and conservative)
rule of thumb is to avoid using
the chi-square test for contingency tables with expected
cell frequencies less than 1, or when more than 20% of
the contingency table cells have expected cell frequencies
less than 5.
The table of expected values will reveal whether either
of these conditions is true, and Prophet will also generate
an appropriate warning in the test results.
The table of standardized residuals gives the value for
each cell
of the difference between the observed and expected
values for the cell, divided by the square root of the
expected value for the cell, assuming the model of
independence of row and column variables is true.
If there are standardized residuals greater than 2 or
less than -2, those cells are not being fitted very
well by the model of independence. A large residual
may mean that a particular cell is an
outlier,
or that there is an
interaction
between that particular row and column.
When the categories have a natural order, then a pattern
to residuals (e.g., large negative ones in one corner of
the table, with large positive ones in another corner
of the table) indicate the possibility of interactions.
If you are unsatisfied with your purchase, you may return it within 30
days for an
exchange, credit or refund.
This guarantee does not cover electronic download products, special requests requiring photocopying
or
engineering aids; however, if you cannot
edit our document(s) in your MS Word, Excel or Visio program we will fix
it or give you a refund.
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