Thank you all for your help.
Daniel,
I want to know if I really understand your answer. I calculated each group
mean and sub mean as below:
tapply(val,group,mean)
group1 group2 group3
4.215670 5.664411 7.210819
tapply(val,sub,mean)
abcd
4.856927 5.199305
The intercept is group=1, sub=a,
The interaction between sub=b and group=2 implies that both sub=b and
group=2 direct effects are included. That is, with the direct effects only
you are now at: intercept+group2+subb, which means the intercept (group1 and
sub=a) + the average difference between
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