[R] Testing significance in a design with unequal but proportional sample sizes

[Christophe Pallier]

Prof Brian Ripley wrote:

>On Fri, 5 Mar 2004, pallier wrote:
>
>...
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>  
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>>Actually, the different types of main effects defined above just 
>>correspond to different
>>contrasts on the cell means. So if there is an easy solution to compute 
>>arbitrary contrasts
>>on the cell means in a factorial design, this could an approach to this
>>question. (Anyone?)
>>    
>>
>
>There are at least three such ways.  ?contrasts (for the assignment
>function contrasts<-)  and ?C, as well as the contrasts= argument to aov 
>(the function you were discussing ...).
>  
>
Thanks.
I know the existence of 'contrasts' and I read the  section about 
contrasts matrix in your book (MASS 3rd edition), as well as
in the R online documentation, but I probably do not understand them 
well: It still escapes me how to proceed to compute
"arbitrary" contrasts, such as, say:

a1b1 a1b2  a2b1 a2b2
   1       1      -1      -1

a1b1 a1b2  a2b1 a2b2
  .5      .5       -1       0

in a model "x~ a * b"  where a and b are two binary factors.

(the contrasts should be on the cell means, ignoring the sample size of 
subgroups. I know how to compute the size of the contrasts from the 
table of means returned by tapply, but I whould also need the associated 
MSE).

Sorry if the solution is obvious.

Christophe Pallier