Is 3-factor Nested designs equivalent to 2-factor RCBD (if usable at all)?
How do they differ in how replication is done?
If I use nested design my experiment would have 1 nested and two crossing effects.
Eg. Nest/Block(?) = location, treatment X= 3 levels, treatment Y= 3 levels. All levels of X and Y crossed.
let's say you have 3 factors: A, B, and C. A is for the factor applied to the whole plots, B the sub plots and C the sub sub plots. assume there are Na treatments in A, Nb treatments in B and Nc treatments in C.
for one block what it looks like is Na large plots to which are randomly applied the Na treatments. those plots are subdivided Nb subplots to which are randomly applied the Nb treatments and the subplots are divided into Nc sub-subplots to which the Nc treatments are randomly applied.
each block is similarly established with unique randomization. Assume R blocks.
i'll show the Anova for A and B
source df
blocks R-1
A Na - 1
block * A (R-1)*(Na-1) this is the error to test blocks and A
B Nb - 1
A * B (Na-1)*(Nb-1)
block*A*B (R-1)*(Na-1)*(Nb-1) this is the error to test B and A* B
the sas model for plot glm is
Resp = Block A Block*A B A*B;
use test to test block and A and the SS for B and A*B are ok in the anova as they use (R-1)*(Na-1)*(Nb-1) as what's left over to test them.
with C it is just a bit more
i'm and old SAS user so i probably do it an inefficient way but it works
Another place to look is: Onyiah, Leonard C. Design and Analysis of Experiments, CRC Press., Section 10.6 explains this and has SAS code and examples. You might also look at Milliken and Johnson, Analysis of Messy Data Vol 1 Chapman and Hall, Chapt. 30 and perhaps 32. This is an older text but the SAS code should still be good. Best wishes.
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