Dear Ruben,

if you have a 4x4 factorial mixed design (one within-subject factor
"condition" with 4 levels, and one between-subject factor "group" with 4
levels), you can proceed in two ways:

* pooled error model: use a flexible factorial design with three
factors: subject, condition and group, and ask to include "main effect"
of "subject" [1] and "interaction" of "condition" and "group" [2 3]. You
can then test for the main effect of "condition" and the "group" by
"condition" interaction. If you want to test for the main effect of
"group", specify a new model without the "main effect" of "subject".
When testing for a factor with more than two levels, you have to use an
F-test.

* partitioned error models: create a specific model for each of your
questions of interest. For example, for the main effect of group,
compute for each subject the average of the 4 levels of the
within-subject "condition" factor and enter them in a one-way anova
(with 4 levels) at the second level. Then use F-contrast [1 -1 0 0;0 1
-1 0;0 0 1 -1] to test for the main effect of group. For the group x
condition interaction, compute at the first level 3 contrasts per
subject (using t-tests [1 -1 0 0], [0 1 -1 0] and [0 0 1 -1]) then enter
these 3 images per subject in a two-way ANOVA (using a full factorial
design)
and use this F-contrast to test for the group x condition interaction:
[kron(diff(-eye(4)),[1 0 0]);
 kron(diff(-eye(4)),[0 1 0]);
 kron(diff(-eye(4)),[0 0 1])]
a.k.a.:
 1 0 0 -1  0  0  0  0  0  0  0  0
 0 0 0  1  0  0 -1  0  0  0  0  0
 0 0 0  0  0  0  1  0  0 -1  0  0
 0 1 0  0 -1  0  0  0  0  0  0  0
 0 0 0  0  1  0  0 -1  0  0  0  0
 0 0 0  0  0  0  0  1  0  0 -1  0
 0 0 1  0  0 -1  0  0  0  0  0  0
 0 0 0  0  0  1  0  0 -1  0  0  0
 0 0 0  0  0  0  0  0  1  0  0 -1
Will described this approach in greater details in this post:
  https://www.jiscmail.ac.uk/cgi-bin/webadmin?A2=spm;2b10ca53.1510

Best regards
Guillaume.

On 12/07/16 13:11, Scholle, Ruben wrote:
> Dear all,
> 
>  
> 
> I am fully aware that these questions are asked on a nearly daily basis,
> but I got a question of how to conduct the ANOVA for my study. The
> study’s design is pretty simple, 4 subject groups, that conducted a
> 4-condition-paradigm each (1 control, 3 experimental condition).
> Resulting in a groupXcondition design, with each factor having 4 levels.
> So far, I assumed a flexible factorial design, with the factors
> ‘subject’ and ‘group’. For the GLM, ‘condition’ was included as the main
> effect. Subjects of group one were assigned to condition 1-4, Subjects
> of group 2 to condition 5-8, and so on.
> 
>  
> 
> Now I stumbled upon the paper of Jan Gläscher “Contrast weights in
> flexible factorial design with multiple groups of subjects”. According
> to this, 3 factors should be included: subjects, group and condition. So
> here are my questions:
> 
>  
> 
> 1)     Which approach is the “right” one to mainly focus on the
> interaction between group and condition (group comparison): Should I
> include the factors ‘subject’ & ‘condition’, as I did, or stick to
> Gläscher’s approach? Or is there an entirely different approach which
> fits the study best?
> 
> 2)     Which main effect & interaction should I model in the design?
> What is the meaning of including a main effect and/or in the interaction
> in the GLM?
> 
>  
> 
> Thank you very much in advance!
> 
>  
> 
> Kind Regards
> 
>  
> 
> *Ruben Scholle, M.Sc.*
> 
> *Scientific researcher / PhD candidate*
> 
> *Department of Psychiatry, Psychotherapy and Psychosomatics*
> 
>  
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-- 
Guillaume Flandin, PhD
Wellcome Trust Centre for Neuroimaging
University College London
12 Queen Square
London WC1N 3BG