I'd like to do an ANOVA on the following problem:
The only dependent variable is the number of children a person has. The two independent variables are the person's age and the person's income. Of course there might be a non-negligible interaction between age and income. We want to neglect the fact that neither age nor income (I presume) are actually normally distributed as I learned that ANOVA is quite robust to violation of that condition (or is it?).
Let's consider persons aged 20 to 70 with incomes from 0 to 250k/year.
I am wondering how the sizes of the factor levels can change the results of the analysis, i.e. can I expect analyses that consider 10 age groups (20 to 25, 25 to 30,..., 60 to 70) to yield "better/worse" results (be more/less statistically significant) than analyses that use only 5 age groups (20 to 30, 30 to 40,...)?