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Hi, >How is this different from just testing the difference between S1 and S3. No difference. This is a consequence of only having 3 ratings to estimate the linear trend from (with more rating levels such a simple equivalence is not present). >Say if I have parameter estimates of 50, 150, and 100 for S1, S2, S3 >respectively, I will get significant map for the positive linear contrast. >But the relationship is not exactly linear among the three levels, right? this is because it does NOT exclude higher order relationships (quadratic etc). There is no easy way round this to my knowledge apart from looking at higher order terms if you have more rating levels - but then you would need to accept the null hypothesis (not achievable) to discount these terms. >So for a brain area to show positive linear modulation by the three levels, >should I get the conjunction between the following two contrasts? I know >that the sum of these two contrasts is equivalent to the above setup. yes > What >I am not clear is whether it should be the sum of the following two >contrasts or the conjunction of them to assert the linear relationship >among the three levels. > EV1(S1) EV2(S2) EV3(S3) >C1 -1 1 0 >C2 0 -1 1 You could do a conjunction like this as a necessary condition for a linear relationship- it just tells us something different about satisfying the condition of linearity. But just like the sum of C1 and C2 does not mean that the relationship is exclusively linear. In short: 1) the sum of C1 and C2 ensures that S3 is bigger than S1 2) the conjunction of C1 and C2 ensures that there is a monotonic relationship between S1, S2 and S3. The motivation for using the sum of C1 and C2 is that the resulting contrast of parameter estimates value IS the linear trend parameter m in y = mx + c. Hence its generalisablity to the case of more rating levels (e.g.5) in my last email. >Also how am I supposed to use the mean ratings (above) to test their >relationship instead of the categorical levels? Do I just replace 1/-1 to >the actual ratings or the inverse of the ratings (multiplied by 1/-1)? you have: C = [162 248 356] so you need to demean it: C = [-93.3333 -7.3333 100.6667] and optionally scale it: C = [-0.9601 -0.0754 1.0356] to get the contrast to replace [-1 0 1] and represent m in y=mx+c. For the conjunction (monotonicity) approach just stick with same as before. Cheers, Mark. Mark Woolrich. Oxford University Centre for Functional MRI of the Brain (FMRIB), John Radcliffe Hospital, Headington, Oxford OX3 9DU, UK. Tel: (+44)1865-222782 Homepage: http://www.fmrib.ox.ac.uk/~woolrich