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I have a strip-split experiment:

Vertical = TrtA, 2 levels
Horizontal = TrtB, 5 levels
Subplots = Trt C, 20 levels

I know how I would usually run this, but there are so many levels of treatment C and I want to know if subplots are significantly different between the two levels of TrtA. Is subplot C6 greater in A1 or A2? Is subplot C13 greater in A1 or A2?

What is stopping me from running a model on each subplot and treating TrtA and TrtB like split-plots? This is what I have done, but I feel like I shouldn't:

fit_mod <- function(df) {
lm(response ~ ordered(TrtB) * TrtA, data = df, random = ~1 | 
block/TrtA)
} 

Then I run this function for each TrtC. I get output telling me whether TrtA, TrtB or their interaction were significant for each TrtC.

My question is simply, can I do this?

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