# [R] Error term in aov

Simon Wotherspoon Simon.Wotherspoon at utas.edu.au
Mon Mar 29 04:36:45 CEST 2004

```Hi,
I'm trying to analyse a hierachical design and am running into some
trouble.  Clearly I don't fully understand "Error" and I was hoping someone
could set me straight.

We measure percentage algal cover in each of 5 quadrats from each of 16
patches where 4 treatments are randomly allocated to a patch.

First suppose patches are coded 1 to 16. then the following gives the
results I would expect.

> Algae <- c(0, 0, 0, 6, 2, 0, 0, 0, 0, 0, 0, 0, 0, 4, 1, 0,
+            0, 0, 13, 0, 23, 17, 0, 56, 46, 0, 79, 32, 51, 22, 5, 0, 0, 0,
+            0, 0, 56, 3, 0, 41, 0, 5, 8, 0, 0, 0, 0, 0, 0, 0, 43, 8, 69,
+            29, 39, 40, 63, 0, 71, 5, 46, 44, 41, 29, 11, 65, 55, 61, 74,
+            55, 0, 5, 0, 0, 6, 30, 82, 70, 27, 83)
>
> Treat <- gl(4,20)
> Patch <- gl(16,5)
>
> fit <- aov(Algae ~ Treat + Error(Patch),data=d)
> summary(fit)

Error: Patch
Df  Sum Sq Mean Sq F value  Pr(>F)
Treat      3 14429.1  4809.7  2.7171 0.09126 .
Residuals 12 21241.9  1770.2
---
Signif. codes:  0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1

Error: Within
Df  Sum Sq Mean Sq F value Pr(>F)
Residuals 64 19110.4   298.6

But if patches are coded  1-4 within treatments, then the following also
gives results I would expect,

> Patch <- gl(4,5,80)
>
> fit <- aov(Algae ~ Treat + Error(Patch %in% Treat),data=d1)
Warning message:
Error model is singular in: aov(Algae ~ Treat + Error(Patch %in% Treat),
data = d1)
> summary(fit)

Error: Patch:Treat
Df  Sum Sq Mean Sq F value  Pr(>F)
Treat      3 14429.1  4809.7  2.7171 0.09126 .
Residuals 12 21242.0  1770.2
---
Signif. codes:  0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1

Error: Within
Df  Sum Sq Mean Sq F value Pr(>F)
Residuals 64 19110.4   298.6

But in R-1.9.0 beta (27/03/2004) I get the error about the model being
singular, which I do not get in 1.8.1.  Why is this?

Secondly, I had the impression that "/" and "%in%" were loosely synonymous,
so why is the following different?
> fit <- aov(Algae ~ Treat + Error(Treat/Patch),data=d1)
> summary(fit)

Error: Treat
Df  Sum Sq Mean Sq
Treat  3 14429.1  4809.7

Error: Treat:Patch
Df  Sum Sq Mean Sq F value Pr(>F)
Residuals 12 21241.9  1770.2

Error: Within
Df  Sum Sq Mean Sq F value Pr(>F)
Residuals 64 19110.4   298.6

I had a look at the help for "formula" but that does not mention "/", and
the help for "Error" is not that enlightening either.

Any help is most welcome - sorry for yet again being a drain on everone's
time

Simon.

---

```