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Re: Second-level design - ways of analyzing a flexible factorial design

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Thu, 14 Jul 2016 17:13:10 +0100

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 ```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* > > > > UKA_banner > > > > Phone: +49 (0)241 80-85027 > > Fax: +49 (0)241 80-82401 > > [log in to unmask] > > Universitätsklinikum Aachen > > Anstalt des öffentlichen Rechts (AöR) > > Pauwelsstraße 30 > > 52074 Aachen, Germany > > Phone Call- & Service-Center: 0241 80-84444 > > [log in to unmask] > > www.ukaachen.de > > > > Aufsichtsratsvorsitzender: Dr. Robert G. Gossink > > Vorstandsvorsitzender: Professor Dr. Thomas H. Ittel > > Kaufmännischer Direktor: Dipl.-Kfm. Peter Asché > > > > Sitz Aachen > > Sales tax identification nmumber: DE 813100566 > > > > > -- Guillaume Flandin, PhD Wellcome Trust Centre for Neuroimaging University College London 12 Queen Square London WC1N 3BG ```