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.wagen...@uc.edu
Web: http://www.danielwagenaar.net
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