Hello Stefan, Stephen, Mirta, Rik & others
I think can help on some of this but there is also a question in here!
> 1.) Why do you need a 2-way ANOVA? The order of the 1st level regressors
> is 1=pre hrf, 2=pre temporal derivative(TD), 2=post hrf, 4=post TD. So,
> [1 0 -1 0] tests hrf and [0 1 0 -1] tests TD. If so, you get two con s
> images. Why would you need a 2-way ANOVA for this? Isn't it a oneway
> within-subjects ANOVA with 2 levels?
I agree it looks like it should be a one way ANOVA with two levels However
it's not within-subjects in the sense that the subject effects need to be
modelled at the second level. These are already 'accounted for' by virtue
of the fact that the contrasts entering from the 1st level are already
differences between conditions for each subject Likewise, the constant
isn't modelled at the second level because it isn't meaningful to 'account
for' the average of the canonical and TD effects Nonsphercity, however, is
modelled - firstly, because the variances of the two measures may differ
from one another (also applies when the ANOVA is between-groups). Where
it's a within-subjects ANOVA, as here, the off-diagonal (covariance) is
also modelled (if you say yes to the question about 'correlated repeated
measures' that means it's non-zero) - this may seem a little odd because
the effects of interest F contrast has only 1 degree of freedom when there
are 2 levels, and normally (eg in SPSS, etc) this doesn't require any
nonsphericity correction. However I believe that the non-zero off-diagonal
is modelled because it affects the parameter estimates via prewhitening -
is that right, anyone? The simplest rule of thumb is to say yes to the
first question whenever it is asked, and yes to the second question
whenever your 2nd level measures are from the same subjects
2.) Is it true that the 1st level
> t-contrasts test only for greater activations before than after (ie pre
> minus post)? If one wanted to test both tails (ie pre>post or post>pre),
> would it be correct to run F contrasts on the first level and take these
> to the second level?
If you take up the 1st level 't-contrasts' (actually contrasts, ie
differences in means, as opposed to t-tests) and do an 'effects of
interest' F test as Rik suggests, you will be looking at both tails. You
are then probably going to want to run post-hoc t-contrasts at the 2nd
level The other way around doesn't really make sense, the F test at the
first level says 'is anything going on for all linear combinations of these
effects' and so isn't 'reversible' at either level - if you take up the ess
image, ie the sum of squares for this contrast, to the second level, you
can't then 'reverse' it to get another tail.
hope this helps,
Alexa
|