Hi,
I'm afraid we won't be able to look at additional examples until
we're finished with the next release but I can give you a quick
'ANOVA->GLM cookbook':
(i) when setting up the GLM design matrix in my mind there is no
difference between what are factors and what are levels: in an ANOVA
the different combinations are cells in the ANOVA table while in the
GLM equivalent design they turn into EVs with blocks of 1s - the only
questions are how many of these EVs you end up having and what to do
with the mean. Every ANOVA cell you need modelling will become a
single EV to be included in your GLM. That is, a 3x2 ANOVA gives you
8 regressors if you don't have repeated measures and 9 regressors if
you do. For a 2x3 anova there then are 6/7 regressors.
(ii) the contrasts are relatively easy to calculate using the logic I
described in our previous email exchange
(iii) As steve said the complexity comes in when you try to create
the relevant F statistics: the GLM F's are always relative to the
residual noise variance - if you want them relative to the amount of
variance explained by one or a set of GLM EVs (or equivalently
relative to the sum-of-squares explained by a factor/level) you
simply form the quotients of the two, that is, if F_AR is the
default GLM estimated F-test on a part of your design A against the
overall residual sum-of-squares (and similarly for F_BR) then F_AR/
F_BR calculates the amount of variance that A explains relative to B,
i.e. gives you rfx of factorial anovas, see the notes after the 2x2
and 3x2 examples at http://www.fmrib.ox.ac.uk/fsl/feat5/index.html
If you need more help please feel free to email again once FSL 4.0 is
out
hope this helps
Christian
On 27 Jul 2007, at 00:32, Sophie Anisa wrote:
> On 7/26/07, Steve Smith <[log in to unmask]> wrote: Hi Sophie,
> yes you're probably right that 2x3 isn't quite the same as
> 3x2, although presumably the difference really only comes down to
> which set of options you want to describe different factors and
> levels as fixed or random (see for example the table at the bottom of
> http://www.fmrib.ox.ac.uk/fsl/feat5/
> detail.html#ANOVA3factors2levels ).
>
> Hello Steve
>
> And thank you for replying to my question. I am sorry however, but
> I must disagree with you! As I understand it a 2 factor by 3 level
> design
> (2x3) is *very* different from a 3 factor by 2 level design (3x2).
> The former
> involves 6 unique conditions, the latter 8 (2x2x2). Hence, no simple
> rearrangement or relabelling from fixed to random can map 6 to 8
> dimensions. More particularly, for a FEAT setup, the latter can be
> modelled by binary classications in the structure of the FEAT design
> matrix, making it easy to do intra-level comparisons. The former
> cannot,
> as it is it necessary to do separate events for each level.
>
> I'm afraid that the number of possibilities for ANOVA designs is
> endless so we can't provide examples for all of them!
>
> Of course I must sympathise with your positition! But I am so very
> stuck at the moment as I just cannot get my head around this. I just
> do not see how to make the design matrix for such a higher order
> model.
> I guess from the later post of at least one other person (Kristofer
> Kinsey)
> I am not alone!
>
> So rather than asking for all possible examples, please please please
> could you provide ONE example of a higher order ANOVA where there
> is more than 1 factor (e.g. 2) and these factors are at more than 2
> levels
> (e.g. 3)? I think the simplest example of this is the 2x3 design
> (and yes
> I know this is what I originally asked for but feel free to give a
> better
> example if it is more helpful)...
>
> merci
>
> Sophie
____
Christian F. Beckmann
University Research Lecturer
Oxford University Centre for Functional MRI of the Brain (FMRIB)
John Radcliffe Hospital, Headington, Oxford OX3 9DU, UK.
[log in to unmask] http://www.fmrib.ox.ac.uk/~beckmann
tel: +44 1865 222551 fax: +44 1865 222717
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