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.
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.
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.
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