[R] main effect & interaction in 2-way ANOVA

Gabor Grothendieck ggrothendieck at myway.com
Fri Feb 25 02:31:03 CET 2005

array chip <arrayprofile <at> yahoo.com> writes:

: Hi,
: I am just a little confused of mian effect in the
: analysis of variance (ANOVA) when you include or do
: not include an interaction term. Let's assume a simple
: case of 2-way ANOVA with 2 factors A and B, each with
: 2 levels. If it shows that main effect for A is
: significant when the interaction between A and B is
: NOT included, and the main effect for A is NOT
: significant when the interaction is included, what
: simply does this difference mean? I understand that
: main effect for A generally means averaging over
: levels of B, is this explanation for the situation
: when interaction is included or is not included or is
: irrelavant?
: And if my interest is in the main effect of A, in the
: above senario, should I include the interaction (thus
: lose the significance) or not include the interaction
: (thus keep my significance)?

There are simplified interpretations if you restrict yourself
to hierarchical or graphical (graphical are a subset of hierarchical)
models.  These require that if an effect is set to zero that all
higher order effects that include it must be set to zero too.
Thus if A is set to zero you would have to set AB to zero too
if you wish to follow that philosophy (and also if you want to use
any of the R packages that support it).

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