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.
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
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
> 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.
> Happy New Year,
you too.
Darren
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