[R] nested anova not giving expected results
Matthew Norton
matthew.norton at umontreal.ca
Mon Apr 15 16:12:48 CEST 2002
Hello all. This may be a trivially simple question to answer, but I'm a little
bit stumped with respect to the calculation of the F statistics in nested
anovas in R. If I understand correctly, the F statistic for the
among-subgroups but within groups hypothesis is calculated as
MS_subgroups/MS_error, while the F statistic for the factor is calculated as
MS_factor/MS_subgroups (I'm getting this from Sokal & Rohlf's _Biometry_).
However, as I understand the output from R, it calculates the F for the
factor as MS_factor/MS_error, which can significantly change the results.
As an example, I took the values from Sokal & Rohlf's example on mosquitos,
which are as follows:
cage animal length
1 1 a 58.5
2 1 a 59.5
3 1 b 77.8
4 1 b 80.9
5 1 c 84.0
6 1 c 83.6
7 1 d 70.1
8 1 d 68.3
9 2 a 69.8
10 2 a 69.8
11 2 b 56.0
12 2 b 54.5
13 2 c 50.7
14 2 c 49.3
15 2 d 63.8
16 2 d 65.8
17 3 a 56.6
18 3 a 57.5
19 3 b 77.8
20 3 b 79.2
21 3 c 69.9
22 3 c 69.2
23 3 d 62.1
24 3 d 64.5
Using the following R commands, I get this output for a nested anova:
> model<-lm(length~cage/animal)
> anova(model)
Analysis of Variance Table
Response: length
Df Sum Sq Mean Sq F value Pr(>F)
cage 2 665.68 332.84 255.70 1.452e-10 ***
cage:animal 9 1720.68 191.19 146.88 6.981e-11 ***
Residuals 12 15.62 1.30
---
Signif. codes: 0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1
According to the book and my understanding of nested anovas, the F statistic
for the cage:animal component is correct, but the F statistic for 'cage'
should be 332.84/191.19, giving a value of 1.741 which is not significant,
and highly different than 255.70.
Perhaps I've misunderstood, but could someone explain to me what R is doing?
In order to guide you, I'm running linux and my R-version is:
R 1.4.1 (2002-01-30).
Copyright (C) 2002 R Development Core Team
Thanks in advance,
--
Matthew Norton
nortonm at magellan.umontreal.ca
Dépt. des Sciences Biologiques, Université de Montréal
C.P. 6128 Succ. centre-ville, Montréal, Qc H3C 3J7
(514) 343-6111 x1233
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