Buzz words in job requirement - ANOVA part 2

I am afraid there has to be ANOVA part 2 if change of more than one factor is conduct simultaneously. Another reason is that the title with part 2 is so cool. It sounds like a Kill Bill 2, Harry Potter and deathly hallows part2.

1. What problem can cool ANOVA part 2 can solve?
In one-way ANOVA, samples are different due to change of one variable. What if there are more than one factor/variable? In this case, there are 2-by-2 matrix, and each cell contains one sample with several observations.
In the context of marketing, imagine the marketer design a campaign with input of ads spending and discount level. He/she is not sure about how to fine tune the parameter, so he/she set different levels for each factor. impact of market is recorded. The question is if market really respond differently as factors change.

2. Idea of two-way ANOVA
Assume there are only two factors. And assume means of these samples are identical. Errors of each observation comes from four sources, factor A, factor B, interaction between A and B, randomness.

SS_A, SS_B and SS_AXB are all compared with SS_within. If they are relatively large, they causes difference more than randomness.

3. Formula of two-way ANOVA
Of course, there should be formula when there is no analyst supporting you. You can find formula here.