I seek a textbook example of the application of chi square tests for main effects and interaction for categorical data, as in a 2x6 table. I plan to use this to help me be sure I can correctly use CTABLES in SPSS.
A $\chi^2$ test is a score test of nested (multinomial) logistic regression models, one of which just has an intercept and the other of which has a categorical predictor (much like ANOVA is a Wald test of nested linear regression models).
Consequently, if you want to extend this to something like two-way ANOVA with an interaction, you would do a (multinomial) logistic regression with multiple predictors. Then test the parameters with score tests, or “chunk” test to test multiple parameters at once (probably what you want if you have multiple levels in your factor variables).
R has a package that will do the score test for you if you know which regression models to pass in (totally analogous to F-testing nested models on linear regression). If you use another software, it likely has analogous functions.
Agresti, Alan. Foundations of linear and generalized linear models. John Wiley & Sons, 2015.
Agresti, Alan. Categorical data analysis. John Wiley & Sons, 2003.