[R] Nested ANOVA yields surprising results

[Daniel Wagenaar]

Dear R users:

All textbook references that I consult say that in a nested ANOVA (e.g., 
A/B), the F statistic for factor A should be calculated as

F_A = MS_A / MS_(B within A).

But when I run this simple example:

set.seed(1)
A <- factor(rep(1:3, each=4))
B <- factor(rep(1:2, 3, each=2))
Y <- rnorm(12)
anova(lm(Y ~ A/B))

I get this result:

   Analysis of Variance Table

   Response: Y
             Df Sum Sq Mean Sq F value Pr(>F)
   A          2 0.4735 0.23675  0.2845 0.7620
   A:B        3 1.7635 0.58783  0.7064 0.5823
   Residuals  6 4.9931 0.83218

Evidently, R calculates the F value for A as MS_A / MS_Residuals.

While it is straightforward enough to calculate what I think is the 
correct result from the table, I am surprised that R doesn't give me 
that answer directly. Does anybody know if R's behavior is intentional, 
and if so, why? Equally importantly, is there a straightforward way to 
make R give the answer I expect, that is:

      Df Sum Sq Mean Sq F value Pr(>F)
   A   2 0.4735 0.23675  0.4028 0.6999

The students in my statistics class would be much happier if they didn't 
have to type things like

   a <- anova(...)
   F <- a$`Sum Sq`[1] / a$`Sum Sq`[2]
   P <- 1 - pf(F, a$Df[1], a$Df[2])

(They are not R programmers (yet).) And to be honest, I would find it 
easier to read those results directly from the table as well.

Thanks,

Daniel Wagenaar

-- 
Daniel A. Wagenaar, PhD
Assistant Professor
Department of Biological Sciences
McMicken College of Arts and Sciences
University of Cincinnati
Cincinnati, OH 45221
Phone: +1 (513) 556-9757
Email: daniel.wagenaar at uc.edu
Web: http://www.danielwagenaar.net