[R] Specifying an appropriate error term in a hierarchical regression

[Chris Bergstresser]

Hi all --

   So I'm working through my statistics homework again, and trying to
reproduce the examples in the book (Kirk's _Experimental Design_,
third edition) in R.  This is a completely randomized hierarchical
design (CRH-28(A)).  The B factor is completely nested within the A
factor.  Pages 480-482, for those playing along at home.

   I can use:

summary(aov(value ~ a + Error(b), data = ex));

   to get the correct F value for the main effect of A.  I can use

summary(aov(value ~ b, data = ex));

   to get the correct values for B(A) and the within cell SS.  But I
can't find any documentation about constructing the Error term to get
this output in a single analysis (except for
http://www.psych.upenn.edu/~baron/rpsych/rpsych.html, but Kirk doesn't
talk about these tests in terms of Error strata, so it's a little hard
to figure out the correspondence).
   Also, the documentation on the Error term in ?aov is rather
perfunctory.  There's no mention of the "/" operator, for example.

ex = scan()
 3  6  3  3
 1  2  2  2
 5  6  5  6
 2  3  4  3
 7  8  7  6
 4  5  4  3
 7  8  9  8
10 10  9 11

a = factor(rep(paste("a", 1:2, sep = ""), each = 16));
b = factor(rep(paste("b", 1:8, sep = ""), each = 4));

ex = data.frame(value = ex, a, b);

summary(aov(value ~ a + Error(b), data = ex));
summary(aov(value ~ b, data = ex));