Hi Tom, 

Many thanks for the reply - can I clarify the following:


>Say you have 3 groups - A, B and C, a single behavioural measure (X) in
>> each, and a single confounder (Y) in each such as age which could
>> theoretically affect both data (FA/MD) and X.
>>
>> If the purpose of the analysis was to compare the nature of data-behaviour
>> correlations between groups, whilst allowing for the confounding factor of
>> age within each group, would the following be correct, where Ev1=GpA,
>> Ev2=GpB, Ev3=GpC, Ev4=X in GpA, Ev5=X in GpB, Ev6=X in GpC, Ev7=age in GpA,
>> Ev8=age in GpB, Ev9=age in GpC
>>
>>         Ev1 Ev2 Ev3 Ev4 Ev5 Ev6 Ev7 Ev8 Ev9
>> Sub1   1     0    0    -2    0    0   3     0    0
>> Sub2   0     1    0     0    3     0    0    6    0
>> Sub3   0     0    1     0    0     2    0    0   -4
>>
>
>Let me relabel your EVs:
>
>GrA GrB GrC  XA XB XC  AgeA AgeB AgeC
>
>
>Gr{A,B,C} model of  the main effect of Group
>X{A,B,C} model of the covariate-by-Group interaction
>Age{A,B,C} model of the age-by-Group interaction
>
>
>Firstly, remember that when you fit interactions, the main effects are very
>difficult to interpret.  So in this model I won't do any contrasts involving
>the first three columns.

I only want to use this model to specifically compare FA/MD-behaviour
correlations between groups.  That is, the contrasts would be similar to the
ones described below, with zeros in Ev1 to 3 at all times.  In order to look
at main effects (ie compare the FA and MD in gp A with B and C) I would only
have a model with Evs1-3 and appropriate contrasts - hopefully you think
this is ok ?

>
>Second, as I've droned on about before, over-all de-meaning of covariates is
>usually only important when fitting fMRI data, or any sort of differenced
>data.  As you're modelling (positive) FA data, this isn't so much of a issue
>here (you can or cannot demean the entire covariate, and results will be the
>same either way).  Likewise, because of Gr{A,B,C} modelling the main effect
>of group, centering a covariate within each group is done automatically and
>doesn't need to be done explicitly.

This confuses me.  I understand that the -D option would not be needed with
randomise here as the Evs1 to 3 encompass group means.  But do I still not
have to demean age/covariates entered into other Evs (I am also looking at
MD in addition to FA) - this is the impression I have got looking at other
posts on correlation analyses in TBSS.  Certainly when I have looked at
single group with a two covariates to assess correlations between FA/MD in
the group and the covariate of interest, I only got interpretable results
when I demeaned the covariates manually.  Why is it different in this case?

>
>>
>> If this is right are the following contrasts and my interpretations
>> correct:
>>
>> 0 0 0 1 -1 0 0 0 0 = where is the correlation between data in Gp A and X
>> bigger than the correlation between data in Gp B and X, whilst allowing for
>> any effect age may have on data and X within each group
>>
>
>Yup.
>
>
>> 0 0 0 1 0 0 0 0 0 = where is there a positive correlation between data in
>> Gp
>> A and X whilst allowing for the effect age may have on data and X within Gp
>> A.
>>
>
>Yup.
>
>
>>
>> If this is correct:
>>
>> 1) Adding any other confounding variables within groups would involve again
>>  splitting then into three groups and demeaning in each group before
>> padding
>> with 0s ?
>>
>
>Yes, but, again, demeaning is not needed.
>
>
>> 2) As this design gets bigger, is it better to analyse using a single large
>> group like this or would it be better to split into 2 analyses one with Gp
>> A
>> and B and another with Gp A and C (where A is control group)
>>
>
>Depends on the question.  The more different factors/questions you add into
>a model, the bigger assumptions you make.  Even with the non-parametric
>randomise, you are making a homogeneity assumption... under the null
>hypothesis, after discounting any nuisance factors, the distribution of the
>data is the same in every group modelled.  The smaller the model, the
>smaller the scope of this homogeneity assupmtion.  The only flip side
>relates to the variance and permutations; variance can be difficult to
>estimate with few subjects (less than 20, especially less than 10) and so
>considering a larger model with more observations to contribute to a
>variance estimate can help; likewise, if you have a tiny amount of data you
>may not get enough permutations to have a reasonable test, and again you
>might be served better by a bigger model.
>
>3) If one did not split age into 3 groups but included it as a single Ev
>> across all 3 groups and applied a similar contrast to the above what would
>> be the interpretation of this or would it be nonesensical ?
>>
>
>Good point.  It is simply a question of whether you believe you need a
>group-by-covariate interaction.  I.e. for each covariate, consider if you
>need to let it vary by group.  If it is *not *a reasonable concern that it
>could be different in each group, then you can include the covariate as a
>single regressor and don't worry about the covariate-by-group interaction.

I understand - I do definitely think that some of my covariates will be
different in different groups, and hence I think I need to include a
co-variate by group interaction.

Thanks for your help and patience.

Mahinda