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I have experimental data of individual sizes (continuous) as a function of two categorical variables (A and B) each with 2 levels (1 and 2), along with a control treatment. Each treatment condition was replicated twice, but these replicates were performed across 3 "blocks"

blocks

So the design is somewhat incomplete.

Using ANOVA, I would like to test for an effect on size of variables A and B (versus one another, and the control), the interaction of these factors, and whether there were any differences across the blocks (e.g. did the control vary across blocks, or did the relationship between A and B change across blocks?).

Because of the incomplete nature of the experimental design I am having difficulty specifying the ANOVA model. Including "block" as a main factor doesn't seem to make sense, as not all treatment combinations appear in all blocks. Missing factor combinations also generate a large number of invalid contrasts. Would it be better to specify "block" as a random effect, e.g. using lmer

lmer(Size ~ A + B + (1|block), data=mydata) 

Any assistance with this kind of data structure or direction to further reading would be a great help.

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  • $\begingroup$ anova(Size ~ A + B + Error(block), data=mydata) for random effect in anova. $\endgroup$ Jan 22, 2019 at 11:23
  • $\begingroup$ OK thanks. I'm more concerned with whether this data should be handled this way, or whether "block" should be included as a main effect in this case. $\endgroup$
    – allhands
    Jan 22, 2019 at 11:30

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