Which test? is there chi cubed? I have a Chi-Sq test, which is 2 x 4. I would like to try to fit another variable. Is there any such thing as Chi-cubed? I would like 2 x 4 x 3. My 2 is the dependent variable, do i have to group the others to make 2 x 12? The groups are categorical. Should I collapse the groups or is there another suitable test?
 A: The chi-square test can be used in any situation when you want to see if the observed numbers of cases among a set of categories differ significantly from the numbers expected, often from the numbers expected based on some null hypothesis. So you certainly could apply a chi-square test to your 2 X 3 X 4 contingency table. You will have 24 possible categories overall; the shape in which you organize them doesn't matter except perhaps as an aid for calculating the numbers of cases expected in each category under the null hypothesis.
The chi-square test in that case, however, would not take into account the different roles that you have assigned to your categorical variables: the 2-level variable is an outcome while the others are considered independent variables whose values might be predictors of that outcome. In that case a logistic regression would be much more in line with what you are trying to accomplish. That would specify the 2-level variable as the outcome while incorporating the other 2 variables (and, if you wish, an interaction between them) explicitly as predictors.
