[R] Anova - interpretation of the interaction term

[michael watson (IAH-C)]

Hi

So carrying on my use of analysis of variance to check for the effects
of two factors.  It's made simpler by the fact that both my factors have
only two levels each, creating four unique groups.

I have a highly significant interaction term.  In the context of the
experiment, this makes sense.  I can visualise the data graphically, and
sure enough I can see that both factors have different effects on the
data DEPENDING on what the value of the other factor is.  

I explain this all to my colleague - and she asks "but which ones are
different?"  This is best illustrated with an example.  We have either
infected | uninfected, and vaccinated | unvaccinated (the two factors).
We're measuring expression of a gene.  Graphically, in the infected
group, vaccination makes expression go up.  In the uninfected group,
vaccination makes expression go down.  In both the vaccinated and
unvaccinated groups, infection makes expression go down, but it goes
down further in unvaccinated than it does in vaccinated.

So from a statistical point of view, I can see exactly why the
interaction term is significant, but what my colleage wants to know is
that WITHIN the vaccinated group, does infection decrease expression
significantly?  And within the unvaccinated group, does infection
decrease expression significantly?  Etc etc etc  Can I get this
information from the output of the ANOVA, or do I carry out a separate
test on e.g. just the vaccinated group? (seems a cop out to me)

Many thanks, and sorry, but it's Friday.

Mick