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Hi Guido, > I am analysing some data where participants were exposed to a stimulus > on three different intensity levels. > So far, these levels are coded in the design matrix as three seperate > EVs. it seems to me that it is problematic to test for a linear effect > across ALL three levels, by using a contrast [-1 0 1] (assuming, > intensity increases from EV1 to EV3). However, this is the approach > suggested in the last 2 paragraphs on this fls web page: > http://www.fmrib.ox.ac.uk/fsl/feat5/glm.html. > My problem with the [-1 0 1] contrast is that the result of this test > is totally independent of the PE for EV2. The contrast would also get > significant, if the activation under medium intensity stimulation is > lower (higher) than under minimum (maximum) intensity stimulation. [-1 > 0 1] seems only to test, if activation increases from the minimum to > the maximum level. I agree that it can seem a little confusing, but it is actually correct. I think that the important thing to realise here is that the value of the second beta says nothing about _linear_ effect. First of all, what the contrast weight vector does is simply to create a linear combination of the betas. And the betas you can think of as the "activity" during the three different conditions. So, say for example that the betas are [1 2 3], the contrast [-1 0 1] would then give you 3-1=2, i.e. indicate the presence of a linear effect. Now say instead that the betas are [1 4 3], the contrast would again give you 2 and indicate a linear effect. Now this seems a little confusing, but if you sit down and plot the points [1 1], [2 4] and [3 3] (which is what we are really looking at) and then draw the best regression line through those points you will see that there is a linear trend. In fact you can change the middle beta (i.e. the [2 4] point) to any old value you like (e.g. [2 -4]) and you would still draw exactly the same regression line. Hence, the second point carries no information about the presence or absence of a linear trend. It does however carry information about a possible quadratic trend. > > It seems to me that in order to test for a linear effect, one would > need to use a different design matrix, where one EVs codes for the > presence of a stimulus and a second EV codes for the intensity (e.g., > with 1,2,3 for the linear assumption.). A linear effect could than be > tested with a contrast on the second EV. Would this be the proper way > to do it? You could in principle recode your design to have one ev to look for overall effecs and one that looks for linear trends. However, to make the "linear regressor" look exclusively for linear trends you need to orthogonalise it w.r.t. the the "overall effect regressor". So, lets saye we have three graded "tasks" and a baseline and lets say our two regressors look like [0 1 1 1 0 1 1 1] and [0 1 2 3 0 1 2 3] (i.e. a rather shortish experiment). Note also that the mean has been subtracted, which is equivalent to adding a regressor [1 1 1 1 1 1 1 1]. These three regressors are now quite correlated (e.g. the "linear" regressor can be used to model parts of the "overall" effect). However, the orthogonalised version of the linear regressor is [0 -1 0 1 0 -1 0 1]. I.e., the scans under "condition 2" are again (correctly) ignored. Just for accuracy I should mention that even if you did not explicitly perform the orthogonalisation any t/F-test you performed would still pertain to the orthogonalised version (though this is slightly less intuitive). Good luck Jesper