Monika
you can only get orthogonal contrast if they are the same size (so no F
vs T). Orthogonality means angle between vectors = 90 degrees - by using
the dot product you can check if two contrasts are orthogonal doing
theta = acosd(dot(v1,v2)/(norm(v1)*norm(v2))) so for instance contrast
v1 = [1 1] (average activation) is orthogonal to the contrast v2 = [1
-1] or [-1 1] since acosd(....) = 90 ; thus locating with v1 and testing
v2 is, a priori, fine
now having said that - contrast orthogonality is not enough to warranty
that you ROI analysis is valid because there might be a bias depending
on the data structure - see
http://www.nature.com/neuro/journal/v12/n5/abs/nn.2303.html and in
particular the supplementary material - depending upon the level of
analysis you should test the orthogonality using the design matrix - for
2nd level this is obtained simply by doing
v1'*pinv(SPM.xX.X'*SPM.xX.X)*v2, if 0 then you can proceed no problm.
Cyril
> Dear SPM users,
>
> As stated in Karl Friston's paper (http://www.ncbi.nlm.nih.gov/pubmed/16635579), an orthogonal contrast can be used as localizing contrast for roi analysis.
>
> I wonder if it could be used in my experiment which is two active conditions with an implicit baseline.
> I want to know if i want to perform roi analysis for condition-1 (contrast vector: 1 0) and condition-2 (contrast vector: 0 1); which other contrast can possibly be used as orthogonal contrast for constraining my analysis.
>
> I first thought of an F-contrast(1 0; 0 1) which would give me main effect of interest or F-contrast (1 -1; -1 1) which is supposed to give differential activation regions. But, i'm not sure whether any of these F-contrast vector are orthogonal to my T-contrast vectors (i.e. 1 0 or 0 1) from which i want to extract data for roi analysis.
>
> Also, i'm not sure whether these definitions of F-contrast vector are correct or not.
> how can we check orthogonality between T and F-contrast vector?
>
> Please help.
>
>
>
--
Dr Cyril Pernet,
Academic Fellow
Brain Research Imaging Center
http://www.bric.ed.ac.uk/
Division of Clinical Neurosciences
University of Edinburgh
Western General Hospital
Crewe Road
Edinburgh
EH4 2XU
Scotland, UK
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tel: +44(0)1315373661
http://www.sbirc.ed.ac.uk/LCL/
http://www.sbirc.ed.ac.uk/cyril
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