Exercises 26.7 and 26.8 of PSLS 3e
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26.7:
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(a) In Figure 26.7(a), the three curves for mean yield corresponding to
the two varieties and their average are perfectly parallel, meaning that
there is no interaction between the herbicide and variety factors. The
parallel curves imply e.g. that the comparison between the two varieties
V1 and V2 will be the same no matter which herbicide is considered; this
is exactly the opposite of what an interaction means.

(b) It appears from Figure 26.7(a) that the herbicides H1 and H3 have
produced the same mean yields; however, herbicide H2 has a a higher
average yield. Whether the difference between H2 and the two other
herbicides is statistically significant we cannot tell from the graph,
because we have no information about the precision of the average (e.g.
in the form of confidence intervals). If we were willing to say a main
effect exists if it just non-zero, regardless of statistical
significance, we would say that there is a main effect of herbicide.

(c) The figure shows the yields for V2 to be higher than those for V1
across all herbicides, and the same is therefore also true for the
averages across herbicides. As in (b) we cannot tell whether this 
difference will be statistically significant, but we could again say 
there is a non-zero main effect for variety.


26.8:
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(a) In Figure 26.7(b), the two curves for mean yield corresponding to
the two varieties are not parallel, meaning that there is an interaction 
between the herbicide and variety factors. The non-parallel curves imply 
e.g. that the comparison between the two varieties V1 and V2 will be 
different depending on which herbicide is considered. Indeed, that comparison
seems to be the same for H1 and H3, bot the difference between the varieties
is much larger for H2 than for the other herbicides.

(b) It appears from Figure 26.7(b) that the three herbicides have exactly
produced the same mean yields across herbicides (corresponding to a 
horizontal average curve). Therefore no main effect of herbicide is seen.

(c) The figure shows the yields for V2 to be higher than those for V1
across all herbicides, and the same is therefore also true for the
averages across herbicides. As above we cannot tell whether this 
difference will be statistically significant, but we could again say 
there is a non-zero main effect for variety.