# interpreting the drop1() function

Bill Shipley (bshipley@courrier.usherb.ca)
Mon, 2 Feb 1998 14:33:28 -0500

I am struggling to understand how one interprets the drop1() function in the
context of unbalanced ANOVA. On page 173 of Venables & Ripley, I read: "A
term such as A:B is said to be marginal to any higher order term that
includes it, such as A:B:C. If both occur in the model then discarding
marginal terms does not affect the statistical meaning of the model, only
the way it is parameterized."

General Question 1:
Now, what does this mean? Consider a case with two factors (A & B) and a
completely balanced design. In an ANOVA table one can obtain the MS and F
values for A (ignoring B), B (ignoring A) and the interaction of A and B.
However in this case the two main effects (A and B) are marginal to the
interaction (A:B) and each source of variation can be interpreted clearly.
So what does it mean to say that "discarding marginal terms does not affect
the statistical meaning of the model"? Surely, this cannot mean that if A:B
is significant, then so must A and B taken seperately? If so, can someone
provide me with a good citation for this?

General Question 2:
Some have suggested that using contrasts is better than looking at TYPE III
sums of squares. How could this be done, using the above model as an example?

Specific Question:
my data set contains three factors: light (hi/low), nutrients (hi/low) and
species (22 unordered species); individuals within species serve as
replicates. Now, the data set is completely balanced when considering only
the light vs. nutrients subset, but is unbalanced when including species
because a few species were missing from some light:nutrient combinations. I
want to test for the presence of the main effects and the interactions.
When I use drop1(myfit,~.) [which is supposed to give TYPE III SS using the
SAS terminology] I only get values for the species main effect and the
interactions involving species. Is this because the TYPE I and TYPE III
sums of squares are the same for the light & nutrient terms and the
light:nutrient interaction (these being balanced)?
Thanks for any help.
Bill Shipley
Departement de Biologie
Universite de Sherbrooke
Sherbrooke (Quebec)
bshipley@courrier.USherb.ca
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