Maybe this can help:

https://www.youtube.com/watch?v=qSLAaurrj7M

https://www.itl.nist.gov/div898/handbook/pri/section5/pri542.htm

or

https://math.montana.edu/grad_students/writing-projects/2012/12patchank.pdf

You can see this:

https://math.montana.edu/grad_students/writing-projects/2012/12patchank.pdf

It uses PROC LATTICE in SAS and PBIB.test() , which is in the agricolae package, in R. The agricolae package should be solid with this kind of analysis.

I also have a book which has the SAS code:

proc mixed

model y = treat

random rep block(rep)

Which I think is the same in R as

lmer(Y ~ Treat + (1|Rep) + (1|Rep/Block)

But I'm not entirely sure of this mixed effects model specification.

It might be worth trying the different methods and compare the results.

Use this frame man;

Fit the model

model