I have three site temperature types: cold, medium, and hot. This is a fixed effect - I am specifically am testing if temperature affects my response variable. I believe temperature type is my 'block'.
I will have three sites for each temperature type. I think site is a random effect. Within each site, I will have a factorial design, where two other fixed factors, A and B, are crossed.
I am interested in the interaction of all three fixed effect (tempxAxB).
From reading my stats book, I think this is a split plot design, but my stats book does not have information about factorial design (the cross of A and B) within blocks. Is what I just described a split plot design or a three way ANOVA? And if it is a funky split plot, could someone point me to an ANOVA table (how to calculate sum of squares) with a similar set up?
Here is a schematic of the setup: