Dear all,
Thank you, Rik, for your answers and thank you, Antonia, for your contribution.
I have one more question regarding the between groups analysis.
As a reminder, I have two groups (15 and 13 subjects each) and have made
contrast images for each subject as follows, based on the three parameter
estimates for three basis functions (HRF + derivatives):
con1: 1 0 0 -1 0 0 (1st beta A > B)
con2: 0 1 0 0 -1 0 (2nd beta A>B)
con3: 0 0 1 0 0 -1 (3rd beta A>B)
Now I want to compare groups I and II, so I put the contrast images into
one way ANOVA without constant:
group 1: con1 group I
group 2: con2 group I
group 3: con3 group I
group 4: con1 group II
group 5: con2 group II
group 6: con3 group III
I say [yes] to non-sphericity correction.
Then is asks: replications are over? AND THIS THE PROBLEM.
The replications should be over subjects but my first group has 15 subjects
and the second one only 13.
So I put in "repl(15)" but then the pre-whitened design matrix looks weird.
The color changes for the first three columns (group I) but not for the
next three columns (group II). So I think the error covariance matrix is
not correct and furthermore is not the inhomogeneity of variance is not
modelled the same way for the two groups.
Because ultimately, I want to compare groups I and II for all three
parameters (F-test):
1 0 0 -1 0 0
0 1 0 0 -1 0
0 0 1 0 0 -1
and just for the first beta (t-test):
1 0 0 -1 0 0
Now I am wondering if the statistics is valid given that the design matrix
is not exactly correct.
Thank you for your help in advance.
Best,
Martin
At 09:44 AM 6/23/2005 +0100, Rik Henson wrote:
>>Martin wrote:
>>I have two groups: controls and schizophrenics. I used the canonical hrf +
>>the two derivatives in my model. I created the following contrasts for the
>>difference between A and B for each subject from each group:
>>[1 0 0 -1 0 0] canonical HRF A-B
>>[0 1 0 0 -1 0] temporal derivative A-B
>>[0 0 1 0 0 -1] dispersion derivative A-B
>>I was then able to examine the overall effect for _each group_ separately
>>using a one-way ANOVA (without constant term), modelling the three contrast
>>images as three groups using the F-contrast:
>>[1 0 0
>> 0 1 0
>> 0 0 1]
>
>>Antonia wrote:
>>I think this step is a mistake (one I was making until yesterday!). This
>>ANOVA means that you are looking for areas where the HRF, temp
>>and disp differ from each other, not where they differ from zero. So
>>if you had a giant effect with positive values for all 3 contrasts,
>>you wouldn't find it in this analysis. Can anyone confirm and suggest
>>the proper analysis, because I don't know what it is?
>
>No, Martin is correct. If the contrast images are already
>differences between conditions, then the F-contrast [1 0 0; 0 1 0; 0 0 1]
>is CORRECT for testing any
>differences between the conditions in the shape of
>the HRF (at least those shape differences that can be captured by the
>three basis functions).
>
>You are correct that an F-contrast that tested for
>differences between the basis functions would NOT
>be appropriate. However, such an F-contrast would be
>some rotation of [1 -0.5 -0.5; -0.5 1 -0.5; -0.5 -0.5 1]
>instead.
>
>And this is why it is important NOT to include a constant
>term in the ANOVA. If you do include one, you will
>find that you cannot evaluate the F-contrast [1 0 0; 0 1 0; 0 0 1],
>because the design matrix is now rank deficient and the
>contrast weights will need to sum to 1. You will also see
>that the default "effects of interest" contrast looks like [1 -0.5 -0.5;
>-0.5 1 -0.5; -0.5 -0.5 1], and so is not
>appropriate. You would need to redo without a constant.
>
>Finally, note that you should use "full" nonsphericity correction
>(ie non-identically distributed and non-independent (correlated
>errors)), because the (contrasts of) basis functions come from
>the same subjects, and have quite difference scalings, so both
>the variance and covariance of errors are likely to be nonspherical.
>
>
>>Martin wrote:
>>What if I want to compare the two groups now? Do I do a one-way ANOVA where
>>I enter six groups - one for each contrast for each group and then do an
>>F-contrast like:
>>[1 0 0 -1 0 0
>> 0 1 0 0 -1 0
>> 0 0 1 0 0 -1]
>>to get the overall effect?
>
>Yes. (If the contrast images were already differences between
>two conditions, then this would actually test the "Group X Condition
>interaction". To test the "main effect of Group", perform another
>ANOVA, but this time with the contrast images being the average
>(sum) of the two conditions, for each basis function).
>
>There is a slight problem here that this ANOVA really consists of
>one within-subject factor (basis function) and one between-subject
>factor (group), yet the SPM2 GUI does not allow you to specify a
>error covariance basis set (for nonsphericity correction) with only
>some (but not all) of the off-diagonal terms included. You can do this
>by hand in matlab (in a batch script), or you can wait until (hopefully)
>the whole "second-level" stats GUI options in SPM5 are over-hauled (about
>time!).
>But for now, I doubt there would be much harm in allowing "full"
>nonsphericity correction anyway, and hopefully ReML will estimate
>covariance terms close to zero for the between-subject covariances.
>
>
>>Can I do an equivalent of the t-test above, such as:
>>[1 0 0 -1 0 0] to find A>B group 1>2?
>
>Yes.
>
>Rik
>
>
>----------------------------------------
>Dr Richard Henson
>MRC Cognition & Brain Sciences Unit
>15 Chaucer Road
>Cambridge
>CB2 2EF, UK
>
>Tel: +44 (0)1223 355 294 x522
>Fax: +44 (0)1223 359 062
>
>http://www.mrc-cbu.cam.ac.uk/~rik.henson
>----------------------------------------
|