In addtition to the example I mentioned previously,
demo("MMC.WoodEnergy-aov", "HH")

Please also see
demo("MMC.WoodEnergy", "HH")

In this example, since anova(energy.aov.4),
shows that the Wood factor and Stove:Wood interaction are significant,
all possible pairwise comparisons of the 12 Stove:Wood terms are not
interpretable.  Only comparisons of Stoves within each of the Woods is
interpretable.  These estimates are shown with both tables and graphs.
Since the covariate is also significant, it is necessary to pick a reference
value for the comparisons.

Here is a simplification of the WoodEnergy example to ignore the covariate.
The 66 pairwise comparisons that TukeyHSD provides for the interaction
effect are not interpretable.  The significant interaction and one
significant
main effect together are an indicator that
main effects and interactions are not interpretable.
Only simple effects of one factor within
a constant level of the other factor are interpretable.

> energy.aov.4b <- aov(Energy ~ Stove*Wood + Stove:Wood,
+                      data=energy)
> anova(energy.aov.4b)
Analysis of Variance Table
Response: Energy
           Df  Sum Sq Mean Sq  F value    Pr(>F)
Stove       2   0.007   0.003   0.0078    0.9923
Wood        3 274.768  91.589 209.0130 < 2.2e-16 ***
Stove:Wood  6  34.570   5.762  13.1483 3.781e-10 ***
Residuals  76  33.303   0.438
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> energy.aov.4b.HSD <- TukeyHSD(energy.aov.4b)
> sapply(energy.aov.4b.HSD, dim)
     Stove Wood Stove:Wood
[1,]     3    6         66
[2,]     4    4          4
>




About a year after I wrote this example, Torsten extended glht to permit
an option of averaging over other factors and covariates.  I need to revise
the WoodEnergy example to use that option.

Rich

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