[R-sig-eco] Balanced split plot analysis in R

[Dixon, Philip M [STAT]]

Markus,

The presence or absence of an interaction has no bearing on the choice of analysis.  If you're a design-based person, as I am, you have two sizes of experimental unit (main plot and split plot).  If you're a model-based person, the multiple measurements (the split plots) on each main plot induces a correlation between split plot observations that needs to be accounted for in the model.  Both facts are different way of saying the same thing.  The presence or absence of an interaction doesn't change either fact.  You're concerned about appropriate comparisons of the main plot marginal means.

You're lucky that your design is balanced (equal numbers of observations for each combination of main plot and split plot factors).  Otherwise, the appropriate R analysis gets very hard very quickly.  (and there is considerable disagreement about what that appropriate analysis should be).

My suggestion:
Leave the interaction in the model.  It is part of the treatment design.  Test and do multiple comparisons among the split plot levels using the model you have.  If you are comparing cell means, the only correct comparisons are those between disturbance treatments within a grazing treatment.  If there is no evidence of an interaction, you're probably not comparing cell means, so that limitation is not an issue.
To get comparisons among levels of the main plot treatment: compute the average Y for each main plot, i.e. average over the split plots in each main plot.  There is now only one treatment factor (grazing regime) and one blocking factor in the analysis.  The error in this analysis is the variability among main plots, which is what you want for comparisons among grazing levels.  Straightforward test and multiple comparisons.

Best wishes,
Philip Dixon