Could you explain what you mean by "balance" and "dimensions"?  Are A and B discrete (categorical) variables?    In the ANOVA setting,  "balance" refers to the number of observations in each level of a categorical variable. For example, if a study has 50 males and 50 females, then the SEX variable is balanced.   When you say "dimension," do you mean the number of levels of a categorical variable? Please give an example of data where "two or more dimensions of A may happen at the same time." ... View more