🚀 go-pugleaf

Consider a two-way anova in which factor A has 4 levels and factor B
has 8 levels and there are 3 replicates per treatment combination.  If
both treatments are fixed effects, then the error term for both main
effects and the interaction is the subjects within treatments term
which has 64 df.  However, if treatment B is a random effect then the
error term for testing A is the A*B interaction with 21 df, this is
sometimes called a mixed model.

Now, what if treatment B is really a blocking factor?  Would B be
considered a fixed or random effect.  According to some psychology
texts on the subject (e.g. Edwards: Experimental Design in
Psychological Research, 5th ed, chapter 16) nearly all blocking
factors must be considered random effects since we wish to draw
inferences about the population of blocks, not just these particular
blocks.  On the other hand, experimental design texts in the
agricultural field never mention the fact that blocks might be random
effects.   Our first question is: 

(1) Are there times in which blocks are clearly fixed effects and
times in which they are clearly random effects? 

Following up on this are two questions relating to the case in which
blocks are considered random effects: 

(2) Agricultural experimental design texts tend to recommend
purposefully confounding the interaction and the subjects within
treatments term by having only a single subject per treatment by
block combination. This circumvents the issue of whether blocks are
fixed or random effects because only one possible error term exists.
Why is it `correct' to assume no interaction term in this case but not
when the design is not confounded?  Or, is it always our option to
forget about the A*B interaction and use an error term with 85 df? 

(3) If the A*B interaction is included in the model but not found to
be significant, can we substitute the subjects within treatment term
in forming the F ratio? 

Thank you in advance for taking the time to answer these questions.

Jonathan Newman			Joy Bergelson
Dept. of Zoology		Dept. of Biology
University of Oxford, UK	Washington University, USA