🚀 go-pugleaf

In <1992Oct26.090221.9754@vax.oxford.ac.uk> jnewman@vax.oxford.ac.uk writes:

>                   It is very hard to build a consensus with just two
>responses (thanks to both of you for taking the time). 

On the other hand, since nobody protested, the previous responses 
probably REFLECTED the consensus. I can only recall one of them, but
that one certainly was my thoughts almost exactly.

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

They can usually be regarded as random, and I would say that they 
generally should be. This applies even to the case when there are
systematic components in the block effects: Suppose you treat 10 blocks
with 10 different brands of fertilizer. You can then compare block X to
block Y, but if they are different, it won't tell you whether or not 
fertilizer X and Y are different.

One exception is when you really have a two-treatment situation, for
instance when you are investigating the effect of two substances in
different mixtures on, say, cell growth. If you make your preparations
in a randomized sequence, then you would not expect any common source
of variation to affect all preparations with substance A in concentration
x (assuming of course that you don't prepare your mixtures from a set of
"standard" bottles, one per concentration...).

>(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? 

First of all, it is NOT correct to use interaction for error, if it
contains systematic components. The discussion must assume that the 
interaction is non-systematic in character. Without this, it hardly
makes sense to test for main effects. One way of seeing the light is
to note that using A*B for error is exactly the same as analyzing
the single-obs-per-cell table of cell means. Another way is to inter-
pret the A*B interaction as 'variance at the cell level', i.e. as due
to a set of independent random variables, one for each cell PLUS 
something which is due to the 'variation at the units level'. If the
former is zero, the A*B interaction will not be different from the
residual. If you calculate the mean of the treatment Mean Square,
you will find that it is equal to the A*B interaction when treatments
are identical. I.e. the A*B interaction is the thing to compare with.

>(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? 

If you truly believe that there is no variation at the cell level, 
then you can pool the error term and the A*B interaction. Note that
this is distinctly different from just having a non-significant test
result.

	Peter Dalgaard