# [R] anova question

Peter Dalgaard BSA p.dalgaard at biostat.ku.dk
Fri Mar 3 23:04:23 CET 2000

```Ulf Mehlig <umehlig at uni-bremen.de> writes:

> I have a probably very naive question about the R anova/aov functions:
> I've found in several text books with descriptions of anova procedures
> that, in nested anova (specifying the model "X~A/B", B being a factor
> specifying treatments, and A groups of samples within each treatment),
> the mean square for "among treatments" is divided by the mean square
> "within treatment among sample groups"; R seems to divide by the
> residual mean square. So, in the following (silly) example I would
> have expected a F value of 1.496/0.785=1.905732:
>
>   > test <- data.frame(x=rnorm(12*5), a=rep(1:12,rep(5,12)), b=rep(1:5,rep(12,5)))
>   > summary(aov(x ~ factor(a)/factor(b), data=test))
>                       Df Sum Sq Mean Sq F value  Pr(>F)
>   factor(a)           11 16.456   1.496  1.8357 0.07647 .
>   factor(a):factor(b)  4  3.142   0.785  0.9638 0.43689
>   Residuals           44 35.859   0.815
>
> As I am certainly misunderstanding something, I would appreciate a
> hint, and maybe a literature recommendation!
>
> Many thanks,
> Ulf

Um,

If B is the treatment you want B/A, I believe?

I don't think the data frame looks like I think you think it looks:

x  a b
1   0.9421894166  1 1
2  -0.6615090815  1 1
3   0.6659020398  1 1
4   0.6384607529  1 1
5   0.2785534174  1 1
6  -0.5093066357  2 1
7  -0.1765458342  2 1
8  -0.0003846756  2 1
9  -0.5523574783  2 1
10  1.4351543109  2 1
11  0.2338159511  3 1
12  0.2701585951  3 1
13  0.3781168982  3 2

I think you expected this:

> test <- data.frame(x=rnorm(12*5), a=rep(1:12,5), b=rep(1:5,rep(12,5)))
> summary(aov(x ~ factor(b)/factor(a), data=test))
Df Sum Sq Mean Sq
factor(b)            4  5.367   1.342
factor(b):factor(a) 55 56.619   1.029

I.e the b:a effect leaves no DF for residuals. So you remove the term
and use that SS for residual.

--
O__  ---- Peter Dalgaard             Blegdamsvej 3
c/ /'_ --- Dept. of Biostatistics     2200 Cph. N
(*) \(*) -- University of Copenhagen   Denmark      Ph: (+45) 35327918
~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk)             FAX: (+45) 35327907
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```