Let's say that I want to look at the difference in average income between men and women working the same job, by using an ANCOVA.
My independent variable is therefore gender, while the dependent variable is income.
I want to control for the age covariate, to account for any differences in the average age between men and women in my sample.
If I see that there is an interaction between the gender and age variables, so that (for example), gender has a bigger impact on income for men than it does for women, do I need to add this interaction as an additional covariate, in addition to the age covariate?
I would think that the answer is 'no', since by adding age as a covariate, I'm already accounting for any age-related differences in the sample, but I'm not completely sure.