# What post hoc test should I run for a significant interaction in a two-way unbalanced ANOVA?

I have data with two factors (Category and Treatment) and each factor has two levels (A and B; 1 and 2, respectively). The sample size for the combinations of factors and levels is unbalanced though (n = 3, 3, 6, and 6). Based on my search of the internet, I need to run a two-way unbalanced ANOVA with type III sums of squares (since I am interested in interactions). I used the following code in R to run the ANOVA:

Anova(lm(arcsin.mort ~  Category * Treatment, data = my.data,
contrasts=list(Category=contr.sum, Treatment=contr.sum), type=3))


Can someone confirm that I did this properly? I am uncertain about the contrasts. If so, both factors and their interaction are significant. What post hoc can I run for the interaction since my data are unbalanced?

• Have a look at the lsmeans package. Also could you add to your post that you use the Anova() function from the car package? – Stefan Jan 16 '16 at 15:41
• Since your effects each have 1df, I don't see why any follow-up tests would be called for. If the interaction is significant you might want to test simple effects. – David Lane Jan 14 '17 at 22:55