[R] Anova - interpretation of the interaction term

From: michael watson (IAH-C) <michael.watson_at_bbsrc.ac.uk>
Date: Fri 22 Apr 2005 - 19:46:30 EST


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



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