Hi,
You are right that the middle point is ignored in this case, which is the best that can be done with finding a linear slope based on only three points. If the middle point moves then the slope of the linear trend does not change. The mean value changes and the quadratic fit changes, but the linear part does not change. That is why it gets a value of 0 in the contrast. The same is true for any odd numbered set of data points (e.g., with 5 points the contrast would be [-2 -1 0 1 2]). With an even number of points all of the values are non-zero (e.g., [-3 -1 1 3] for 4 points). But it does mean that in the specific case of three points there is no difference between high > low and looking for a linear trend (slope) > 0.
All the best,
Mark
> On 2 Nov 2017, at 19:34, Hallvard Røe Evensmoen <[log in to unmask]> wrote:
>
> We want to do a 1-factor 3-levels linear trend analysis. In the feat3 lecture and “Appendix_A:_Brief_Overview_of_GLM_Analysis” document, linear trend across levels is investigated for three levels (low medium high) using the t-contrast [-1 0 1]. Is that really a linear trend analysis? Is it not the case that when condition medium is set to zero then it does not contribute to the contrast, and that t-contrast [-1 0 1] therefore reflects high > low?
>
> The contrasts must be orthogonal to each other, e.g. to not mix average activation with linear increase. Is it then only possible to do a linear trend analysis for an even number of levels?
>
> Any feedback will be highly appreciated.
>
>
> Best regards
> Hallvard
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