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Hi,

See my responses below...

> I am new to FSL and had a question about how to set up a parametric modulation design for a habituation experiment. So the experiment consists of 2 runs and each run has 3 blocks. The main block of interest is a passive fear task and we want to look at habituation over the course of 6 blocks. Specifically we are interested in seeing if the habituation is a linear trend or curvilinear (quadratic) trend.
> 
> Linear:  3 1.8 0.6 -0.6 -1.8 -3
> Curvilinear (Positive U) : 3 -1 -2 -2 -1 3

These contrasts look fine, *but* if you have acquired things in 2 runs then that complicates things as we normally do not recommend concatenating runs in time since it causes problems with filtering and intensity normalisation. So we would recommend analysing each run separately, forming contrasts for each "block" that is present in them, and then in the second level do a fixed-effects analysis that combines the runs and forms these contrasts at that level.  It is possible that your definition of a "run" and a "block" isn't quite what I have in mind though - as for us a "run" represents one fMRI scan, and then there would be a gap (which might be short) before another run occurs.  I'm not really sure what you exactly mean by a block, but normally we would expect that to represent a period of time where a particular condition was presented.  I think this might be what you mean, but I'm concerned that you only have one block for each condition, as we normally recommend more repetitions than this, in order to get better statistical power.  But maybe your "block" is actually a set of what I call a "block".  It would be good if you could clarify these points.

> Questions
> 1a) Should I model the habituation in the 3rd column of my ev file? I know in the 3 column format I could put my modulation vector in the last column but will I be able to do this for both the linear and curvilinear trend?
> OR
> 1b) Should I simply model the linear and curvilinear trend under the STATS > Contrasts and F-Tests?

You can model things in different ways.  One option is to have separate EVs for each condition and then form contrasts across them.  Another option is to form different EVs for each desired combination (e.g. mean, linear, quadratic).  I would recommend the former, as it allows for modelling effects that don't fit exactly with your quadratic model, and hence will reduce the residual noise.  However, if you have a very low number of repetitions then the latter model can have some advantages with respect to DOF.  It would help if you could clarify about the number of timepoints, how you define a run, and what constitutes a "block".

> 2) Also, how does one go about testing a linear versus a non-linear model? Should I run the group with both models and see which is more significant- we have reason to believe that we will see a “U” curve based on previous literature but want to also assess linear. After I rule out a model, should I then rerun the analysis with only one model.

You can just use one model with the two varieties of contrasts and see whether you get results for the linear or non-linear contrast.  If you want to also see areas that respond with either linear or non-linear then you can use an F-test over these two t-contrasts.

> 3) We were also going to do an ROI analysis to get a better estimate of what the data curves look like in our two regions of interest. Would it be better to do this first to get an estimate and then just analyze with one model?

No - don't do this, as it is circular and statistically dodgy. You should decide on your contrasts in advance and look at both.  However, doing an ROI analysis to look at the curves is fine, but avoid using it to determine the contrasts of interest and also avoid interpreting any p or R values for correlations of the ROI outputs if they were created within statistical masks made by the non-ROI analysis (as this too is circular and problematic).

> 4) We are looking at this data in a two groups- what if one group shows linear and the other is curvilinear? How would the between groups stats be conducted in this event?

You can formulate differences between either linear contrasts in the groups or non-linear contrasts between the groups, and if you put an F-test over these two group difference contrasts then you will be able to see group differences driven by either linear or non-linear changes, or both.

All the best,
	Mark