I am encountering an issue using the aov() function in R. I have a two factor randomized block model and would like to perform anova following the model presented in the book "Analysis of variance and covariance" (P. Doncaster and A. Davey). They have the following example :
4.2/6.2/7.2 Two-factor randomized complete block model Y = S'|B|A
aovdata <- read.table("http://www.southampton.ac.uk/~cpd/anovas/datasets/R/Model4_2.txt", header = T)
attach(aovdata)
S <- factor(S) ; A <- factor(A) ; B <- factor(B)
Commands for Model-1 factorial analysis
model4_2i <- aov(Y ~ S + A*B + Error(S + S:A + S:B))
summary(model4_2i)
(available on http://www.southampton.ac.uk/~cpd/anovas/datasets/ANOVA%20in%20R.htm#model4_2)
This renders the following table :
> summary(model4_2i)
Error: S
Df Sum Sq Mean Sq
S 3 9.075 3.025
Error: S:A
Df Sum Sq Mean Sq F value Pr(>F)
A 2 745.4 372.7 67.58 7.68e-05 ***
Residuals 6 33.1 5.5
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Error: S:B
Df Sum Sq Mean Sq F value Pr(>F)
B 1 91.65 91.65 4.134 0.135
Residuals 3 66.51 22.17
Error: Within
Df Sum Sq Mean Sq F value Pr(>F)
A:B 2 186.37 93.18 7.819 0.0213 *
Residuals 6 71.51 11.92
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
My issue is that when I try to use this same model with my own data, I don't have the expected structure :
model <- aov(Y ~ S + A*B + Error(S + S:A + S:B),data)
summary(model)
I get :
> summary(model)
Error: S
Df Sum Sq Mean Sq
S 3 0.05215 0.01738
Error: S:A
Df Sum Sq Mean Sq F value Pr(>F)
A 3 0.18511 0.06170 5.286 0.0266 *
B 1 0.01334 0.01334 1.143 0.3163
Residuals 8 0.09339 0.01167
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Error: S:B
Df Sum Sq Mean Sq F value Pr(>F)
B 1 0.025230 0.025230 19.162 0.0484 *
A:B 1 0.003853 0.003853 2.927 0.2293
Residuals 2 0.002633 0.001317
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Error: Within
Df Sum Sq Mean Sq F value Pr(>F)
A:B 3 0.01858 0.006194 1.164 0.382
Residuals 8 0.04255 0.005319
I don't understand why factor B is in the "Error S:A" term, or why the A:B interaction is in the "Error B:S". I don't know what I do differently or where I go wrong. Any ideas?
Here is the dataframe :
> data
B A S Y
1 1 1 1 2.64
2 1 1 2 2.60
3 1 1 3 2.54
4 1 1 4 2.56
5 2 1 1 2.63
6 2 1 2 2.54
7 2 1 3 2.62
8 2 1 4 2.57
9 1 3 1 2.74
10 1 3 2 2.70
11 1 3 3 2.81
12 1 3 4 2.67
13 2 3 1 2.59
14 2 3 2 2.62
15 2 3 3 2.80
16 2 3 4 2.58
17 1 2 1 2.63
18 1 2 2 2.54
19 1 2 3 2.73
20 1 2 4 2.76
21 2 2 1 2.48
22 2 2 2 2.68
23 2 2 3 2.57
24 2 2 4 2.73
25 1 4 2 2.50
26 1 4 3 2.75
27 1 4 4 2.44
28 2 4 1 2.34
29 2 4 2 2.34
30 2 4 3 2.54
31 2 4 4 2.45
