Dear Darren & list,
Apologies - have gived bad advice in last email.
d gitelman wrote:
> Will and Volkmar
>
> Thanks for your detailed replies. I want to follow-up on some of the answers
> and combine Will's two recent replies.
>
>> If you think about this contrast in the following way I hope
>> you can see why it is invalid. Consider first, just the part
>> of your design matrix for the first 9 subjects (ie. the first
>> group). This contains the 9 subject effects and the 3
>> condition effects. Now, if you try doing a [1 0 0] contrast
>> here, this will be invalid; we can only use contrasts that
>> look for differences among the conditions (you know this from
>> your later reply to Matt :-)). The same consideration goes
>> for the second part of the design matrix; you can't do a [-1
>> 0 0]. Therefore its not surprising you can't do [1 0 0 -1 0
>> 0] for the whole design matrix.
>
> I think I understand this now. One has to account for the subject means and
> one can only look at differential effects.
>
>> This logic also means you can't test for eg. a main effect of group !!
>> Which is of course a main reason for setting up the design in
>> the first place.
>
My mistake here. You *can* test for the group effects and interactions
as Volkmar instructed !
> Here I have a question. I had understood from Volkmar's reply that testing
> group effects was possible using the contrast.
>
> 3*1/N1*ones(1,N1) -3*1/N2*ones(1,N2) 1 1 1 -1 -1 -1
>
This will test for the overall difference (or difference in means)
between groups (ie. collapsing across conditions).
The logic here is as follows. First apply the operator
1/N1*ones(1,N1) to the first N1 columns. This will give you the
average of the first N1 columns. Do the same for the next N2 columns.
Now your design just has group effects and condition effects.
The contrast is then
3 -3 1 1 1 -1 -1 -1
Dividing by 3 gives
1 -1 1/3 1/3 1/3 -1/3 -1/3 -1/3
This has two parts. The first,
1 0 1/3 1/3 1/3 0 0 0
is the mean effect for group 1. The second
0 -1 0 0 0 -1/3 -1/3 -1/3
is (minus) the mean effect for group 2.
So, 3 -3 1 1 1 -1 -1 -1 tests for the difference in means between the
two groups.
> I assumed the first 21 columns incorporated the part of the between groups
> contrast that is due to the subject effects (or something like that).
> Assuming this is true, by the way, would the F-test for the group effect be
> the same as the t-test or would I have to split up the condition effects
> like so.
> 1/N1*ones(1,N1) -1/N2*ones(1,N2) 1 0 0 -1 0 0
> 1/N1*ones(1,N1) -1/N2*ones(1,N2) 0 1 0 0 -1 0
> 1/N1*ones(1,N1) -1/N2*ones(1,N2) 0 0 1 0 0 -1
> these may be equivalent but I'm not sure
>
This will be the interaction. A difference between groups in condition
1, 2, 3 or any combination therof.
Again, the logic being 1/N1*ones(1,N1) -1/N2*ones(1,N2) converts
the subject effects to group effects. The first row
1 -1 1 0 0 -1 0 0
then has two parts. The first
1 0 1 0 0 0 0 0
is the average response to condition 1 in group 1. The second
0 -1 0 0 0 -1 0 0
is (minus) the average response to condition 1 in group 2. ETC ...
>> So, my advice is as follows. Don't use designs that mix (i)
>> within-subject effects (ie. condition) with (ii) between
>> subject effects (group).
>
> probably good advice...
>
>> Within-subject designs with just 1 factor (eg. 'condition') are fine.
>>
>> You can test for between group differences in working memory
>> as follows.
>> Take two levels of working memory eg. condition 3 minus condition 1.
>> Make this contrast for each subject at the first level. Then
>> use these differential contrasts in a two sample t-test at
>> the second level (where the two samples are the two groups).
>
> I had done that, but my hope in doing the anova is that by properly
> estimating the within subject measures I might gain a bit of power.
>
>> Thinking further on this, if you were to also create the
>> within subject contrast cond2 minus cond 1, for each subject
>> at the first level, then you could enter the 2 contrasts per
>> subject into a second level analysis. You would'nt then need
>> the subject effects at the 2nd level as you have used
>> differential contrasts at the first level. So, you could have
>> a 2x2 design at the second level with 1 factor group, and the
>> other factor (differential) condition. (Again I stress you don't have the
>> subject effects at 2nd level). This should work. (So the key
>> is to use differential contrasts at the first level and don't
>> have subject effects at the second).
>
> This sounds good, but I have questions about the implementation.
>
> In my simple minded way I assume that if I have differential condition
> effects of (3-1) and (2-1) then both the main effects of condition and the
> the interactions won't have the proper differential condition term, i.e.,
> I'd end up with (3-1) - (2-1) = 3-2, which is not the between condition
> comparison I want (I want 3-1). If I want to end up with 3-1 I thought I
> would enter the differential contrasts of (3-2) and (1-2). This seems to
> produce a vaguely similar but not identical result to the t-test of 3-1 (see
> attached gif showing some overlap between the results but also non-overlap
> areas).
>
> Anyway, IF as I noted above I can use the original anova with subject
> effects AND the group contrasts I noted above (in reference to question 1)
> are correct, then I'll go with that.
>
>
Yes, I think you can. You should go with that.
Sorry for the confusion I introduced earlier.
Best,
Will.
>> Happy New Year,
>
> you too.
>
> Darren
>
>
>
> ------------------------------------------------------------------------
>
--
William D. Penny
Wellcome Trust Centre for Neuroimaging
University College London
12 Queen Square
London WC1N 3BG
Tel: 020 7833 7475
FAX: 020 7813 1420
Email: [log in to unmask]
URL: http://www.fil.ion.ucl.ac.uk/~wpenny/
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