[R] Treatment-Contrast Interactions

[Lorin Hochstein]

Peter Dalgaard wrote:

>Lorin Hochstein <lorin at cs.umd.edu> writes:
>
>  
>
>>I'd like to understand this approach as well, but I can't reproduce my
>>results using se.contrast. In particular, I get the same standard
>>error even though I tried to use different contrasts:
>>
>> > c1 <- c(1,-1)[A]*c(1,-1,0)[B]
>> > c2 <- c(1,-1)[A]*c(1,0,-1)[B]
>> > c3 <- c(1,-1)[A]*c(0,1,-1)[B]
>> > se.contrast(fit, as.matrix(c1))
>>Contrast 1
>>  14.24547
>> > se.contrast(fit,as.matrix(c2))
>>Contrast 1
>>  14.24547
>> > se.contrast(fit,as.matrix(c3))
>>Contrast 1
>>  14.24547
>>    
>>
>
>They could well _be_ the same if the design is balanced...
> 
>
Hmmm... One of my problems is that I don't know how to interpret the 
output of se.contrast.

Here's my example again.
 > score <- c(12, 8,10, 6, 8, 4,
       10,12, 8, 6,10,14,
        9, 7, 9, 5,11,12,
        7,13, 9, 9, 5,11,
        8, 7, 3, 8,12,10,
       13,14,19, 9,16,14)
 > n <- 6
 > A <- gl(2,3*n,labels=c("a1","a2"))
 > B <- rep(gl(3,n,labels=c("b1","b2","b3")),2)
 > contrasts(B) <- c(1,-1,0)
 > fit <- aov(score~A*B)
 > summary(fit, split=list(B=1:2), expand.split = T)
            Df  Sum Sq Mean Sq F value   Pr(>F)  
A            1  18.778  18.778  2.2208 0.146606  
B            2  62.000  31.000  3.6662 0.037629 *
  B: C1      1   1.500   1.500  0.1774 0.676621  
  B: C2      1  60.500  60.500  7.1551 0.011986 *
A:B          2  81.556  40.778  4.8226 0.015274 *
  A:B: C1    1  13.500  13.500  1.5966 0.216119     # <---
  A:B: C2    1  68.056  68.056  8.0486 0.008085 **
Residuals   30 253.667   8.456     

What I'm really looking for is that F value that's labelled A:B: C1, 
1.5966 in this case. (I'm not sure what to call this term, AB interaction?)

 I thought that it might be possible to use se.contrast to compute this 
(or at least, to get the numerator so that I could compute the F value 
once I had the mean square error of the residuals), but I'm not sure how 
to specify the contrast, and I don't know the relationship between the 
"standard error" output by se.contrast and the "mean square error" which 
is the fourth column of the output above.

Lorin