The dummy variables for the factors in balanced designs are orthogonal.
The treatment dummy variables are not orthogonal to the block dummy variables
for unbalanced designs. That is essentially what the term "balanced" means.
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I have a factor SAMPLES which is at the lowest level (within) of a split plot
anova model but this factor also appears in the ANOVA table at the block
level. This happens for unbalanced responses but not for balanced responses.
I would be grateful for an explanation of this.
The block error term
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