[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:B3 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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Re: [R] (no subject)

[Daniel Wagenaar]

Thank you all for your helpful responses. I apologize for the lack of 
subject line. That is certainly not my habit. It happened because my 
first email was refused because it was sent using an incorrect "From:" 
line (an aliases email address, daniel.wagen...@uc.edu) instead of the 
address I subscribed to the list with. When I resent it, I failed to 
copy the subject line. My apologies.


- Daniel

On 10/30/2015 03:12 PM, Kevin Wright wrote:

Maybe you want

summary(aov(Y ~ A + Error(A:B)))

Kevin


On Fri, Oct 30, 2015 at 9:32 AM, Wagenaar, Daniel (wagenadl)
mailto:wagen...@ucmail.uc.edu>> wrote:

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:B3 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? And, perhaps most importantly, how to
get the "textbook" result in the most straightforward way? (I'd like
to be able to give me students a simple procedure...)

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 <mailto:daniel.wagen...@uc.edu>
Web: http://www.danielwagenaar.net
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and provide commented, minimal, self-contained, reproducible code.




--
Kevin Wright


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