I am really confused regarding 2-way Anovas. I think I did not understand something properly.
Let's say I have a 2x2 experiment design with 2 factorial variables (For the sake of an example let's say Letter and Number so A1, A2, B1, B2 as possible combinations) I would like to do a 2-way Anova since I hypothesise an Interaction between the variables Number and Letter. However, the sample sizes per group are quite small, unbalanced (n = 4-6) and not paired. As part of my experiment design I have 4 planned comparisons:
A1 - A2,
B1 - B2,
A1 - B1,
A2 - B2
Now two questions:
- As far as I understand I have two orthogonal contrasts?
- These are the simple main effects or are they interactions?
After the Anova I can NOT do a post-hoc test (because I have planned comparisons and not testing opertunistic?). So I would only test my planned comparison with a t-test with a correction for multiple comparisons (since I am doing more than 3 comparisons).
3. Which t-test should I do (pairwise, two-sample, or not a t-test at all)?
4. Am I doing the planned comparisons regardless of the significance of the Anova?
4.5 . But If so why am I doing the Anova in the first place?
5. Is it okay to just do a t-test with correction, without the Anova?
I looked at the following cross validation questions, but I am sill confused understand:
Calculating 'k' in the bonferroni procedure when there are both post-hoc and planned constrasts
Thank you for your help in advance!