[R] Function to separate effect in AOV

[Ronaldo Reis Junior]

Hi,

I have a dummy question.

Suppose that I have two explanatory variable, T1 (A, B) and T2 (C, D) and one 
response variable.

> attach(dados)

> tapply(Y,list(T1,T2),mean)
         C        D
A 2.200000 10.20000
B 2.223333 20.26667

In this case, "A" and "B" inside "C" have no difference, but have differences 
inside "D"

I make this model:

> m <- aov(Y~T1*T2)
> 
> summary(m)
            Df Sum Sq Mean Sq F value    Pr(>F)    
T1           1  76.36   76.36  5617.9 1.119e-12 ***
T2           1 508.69  508.69 37426.7 5.704e-16 ***
T1:T2        1  75.65   75.65  5566.0 1.161e-12 ***
Residuals    8   0.11    0.01                      
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 


This result don't show the reality of the data, because I cant see that "A" 
and "B" inside "C" are the same.

The anova result is the same of an full different levels, like this:

> attach(dados2)
> 
> tapply(Y,list(T1,T2),mean)
         C        D
A 6.100000 10.20000
B 2.223333 20.26667
> 
> m <- aov(Y~T1*T2)
> 
> summary(m)
            Df Sum Sq Mean Sq F value    Pr(>F)    
T1           1  28.74   28.74  2114.3 5.529e-11 ***
T2           1 367.75  367.75 27056.7 2.088e-15 ***
T1:T2        1 145.81  145.81 10728.1 8.433e-14 ***
Residuals    8   0.11    0.01                      
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

In this case all level are different, C to D and A to B.

The question is:

The only way to find this real difference is:

1) make T1 and T2 like a Treatment variable with 4 levels (AC,BC,AD,BD)?

or

2) make 3 anova:
	a) Anova (A,B) inside C
	b) Anova (A,B) inside D
	c) Full factorial Anova (like this in the e-mail)

or

3) exist any other way to make this in only one analysis, to find all 
differences e interactions? In other words, to find differences in "A" 
and "B" inside "C", "A" and "B" inside "D", "C" and "D" inside "A" and "C" 
and "D" inside "B" 

Thanks
Ronaldo
--
> Prof. Ronaldo Reis Júnior
|  .''`. UNIMONTES/Depto. Biologia Geral/Lab. de Ecologia
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