Ken kindly took the time to clarify problems in my understanding which
have more to do with my statistical ineptness than any problems with
the manuals or FAQs:
"[R] anova" page 43 (Version 8 manual) discusses the "/"
notation.
I admit that there may be better ways to word that discussion.
If anyone has some candidate better wording, send it my way. I
had hoped that the various nested and mixed models that followed
in "[R] anova" would have been enough to clarify.
If I can do better I'll send something! I'll eventually share my data
for the FAQ to include SP/RM[2,2], SP/RM[2,3], and SP/RM[2,4] ANOVAs.
For your 3 examples above:
> ANOVA y a b c/d tests each of a, b, and c, over d.
Yes.
> ANOVA y a/ b c/d tests a over error, and b and c over d
No. a is tested by b. b is not tested. c is tested by d.
Ah!
> ANOVA y a/d b/d c/d is disallowed syntax
It is disallowed because the term "d" appears multiple times in
the model, not because of the slashes.
First and foremost the -anova- command is supposed to indicate
which terms are in the model. Secondarily, the "/" notation is
helpful in getting many (often all) of the tests of interest when
the model is written in standard order.
None of my texts discuss "standard order". I assume this means ordered
by the same denominator. I don't have the Winer text. Yes, I should buy
it. Instead, I have an introductory text by George Cobb, which I like.
You can get any other tests you want using -test-. When you test
terms you can use the "/" to indicate the error term. See the
examples on pages 60-62 of "[R] anova".
For an example of this in a complicated ANOVA see
http://www.stata.com/support/faqs/stat/anova2.html#expand911
which is one example in a large FAQ filled with examples. In
this case, the "/" in -anova- obtained all but 3 of the tests of
interest. The -test- command using "/" was used to get those 3.
The -anova- command that was typed for that example was:
anova res A / G|A B B*A / B*G|A / S|B*G|A C C*A / C*G|A C*B C*B*A /
C*B*G|A / C*S|B*G|A D D*A / D*G|A D*B D*B*A / D*B*G|A / D*S|B*G|A D*C
D*C*A / D*C*G|A D*C*B D*C*B*A / D*C*B*G|A / , repeated(C D)
Imagine if instead of using the current "/" notation you had to
specify the error term for each instance. It would be even more
complicated, and I contend even harder to understand.
I totally agree.
One approach, if you dislike the "/" notation in -anova- is to
not use the "/", and instead do all tests of interest using the
-test- command after -anova-. That way, one by one you can
specify the term to be tested and the error term for that test.
Once you get used to the "/" notation, I am betting you will want
to use it again.
The facility to use both is very convenient. I look forward to using
your very cool ANOVA multiple test additions too!
With much customer satisfaction,
-Dave
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