Hi Arkan,

Some thoughts on your questions below

Hope this helps
Alfonso

Originally posted by Arkan Al-Zubaidi:
Briefly, after running first-level task-related analyses in SPM (we are not talking about connectivity analyses here, just standard functional task-related activation analyses) you would normally go to Contrast Manager and define there your contrasts of interest. Those contrasts are specified in terms of a contrast vector (as you mention) that simply defines the desired linear combination across your beta regressors (e.g. task minus baseline for a given subject). Each contrast that you define will create a con*.img volume which you would then typically enter into your second-level analyses. When using ART-based scrubbing regressors in your first-level model (e.g. in SPM's GUI 'Specify 1st-level', entering them in the 'Multiple regressors' field within the 'Data&Design' -> 'Subject/Session' options) you will typically simply disregard those regressors when defining your task-effects contrast vectors (simply enter 0's for all of the fields associated with the ART-based regressors). Once you have your contrast volumes for the task-effects (typically one volume per subject and per condition of interest) you would use SPM's GUI 'Specify 2nd-level' to define your second-level analyses and enter those volumes in the 'Design' -> 'Scans' field.

I was not being very clear probably. Both betaA and betaB are going to be estimated from your data (these are the regressors that SPM's first-level model estimates). betaA are the effects that you care about (e.g. the amount of task-related activation for a given subject) and the values that you are going to be entering into your second-level analyses (one value/volume per subject, for example to look at the average activation across all subjects). betaB are the effects of each outlier scan (e.g. difference between the observed BOLD signal at the outlier scan compared to the expected BOLD signal at that timepoint), and you typically do not care about these, nor are you going to do anything with the associated volumes. The point of entering these ART-based scrubbing regressors into your first-level model is not that you want to use that betaB information for anything, but rather to "free" the betaA values from unwanted influence of the outlier scans (which is captured by the betaB values).

If you are unclear how that works consider this example. Say you have a BOLD signal over five scans with values:
Y = 
 2
 7
 200
 4
 5

and you want to estimate the average BOLD signal using a design matrix:
A = 
 1
 1
 1
 1
 1

Let's say ART has identified the third scan as an outlier, so your new design matrix (including one new regressor for the identified outlier scan) is:
[A B] =
 1 0
 1 0
 1 1
 1 0
 1 0

When you use linear regression to fit the data Y (e.g. in Matlab use "beta = [A B]\Y") you will get:
 betaA = 4.5
 betaB = 195.5

Note that betaA is actually representing the average BOLD signal disregarding the 3rd scan (i.e. the average BOLD signal across the 1st, 2nd, 4th and 5th scans), and betaB is representing the departure between the third scan BOLD signal and that average. Also note that the estimated betaA value is going to be exactly the same if you change the 3rd value of Y from 200 to say 500 (that will only change the estimated betaB value, but not the estimated betaA value). This is the "invariance" I was referring to, and those betaA values (e.g. 4.5) are the values that you estimate in your first-level model for each subject and for each task effect and which you later enter into your second-level analyses to do group/population-level inferences (the betaB values, e.g. 195.5, you typically simply disregard / do not need to care about)
 
Hope this helps
Alfonso