Dear Dr, Schrvder,
> We have conducted an 2x2 factorial PET-experiment with seven patients.
> The first factor was task (neutral task (NT) versus cognitive task
> (CT)), the second factor was treatment (with treatment (T+) and no
> treatment (T-). Each condition was repeated three times. The covariate
> was reaction time. Our hypothesis is that there is an increase in
> activation comparing (CT/T-)-(NT/T-)-((CT/T+)-(NT/T+)). We chose the
> Multi-subject: conditions only and get nice activation in the expected
> area. However is it appropriate to collapse the activation over
> subjects
> because of proportional scaling or is it better to choose the
> Multi-subject:cond x Subj interaction & covariates? (in this model the
> results differ considerably) We would suggest that because of the four
> conditions we used there are too less scans/condition to perform this
> analysis. What exactly is the statistical difference between both
> models?
The difference between the two models is that the second models subject
x condition interactions. In other words each subject can respond
differently to each condition. By omitting these interaction terms one
is treating the replictions within subject and over subjects as
repeated measures of the same thing. If there are no profound
interactions this will be a more sensitive analysis because you have
saved degrees of freedom to estimate the error variance. It does
however assume sphericity (i.e. the within and between-subject error
variances are the same and there are no correlations among the error
terms from each subject. The nature of the global normalization is
really incidental here.
> The second question concerns our covariate. We think that it
> is inappropriate to collapse all scans irrespectively if they are from
> one subject or from many. Is this right? But how to perform an analysis
> of covariance then? (which of the various PET models would be
> appropriate?)
By an analysis of covariance you could mean (i) assessing the amin
effect of RT. This is subject to the same distinction as the condition
effects: You could model a single column or model subject x covariate
interactions - it depends on whether the between-subject differences in
RT are large relative to within-subject and which you are interested
in. (ii) If you mean the RT x contrast (i.e. activation) interaction
this would be more complicated and would require you to model the
interaction explicitly. However the same distinction applies in
relation to within- and between-subject variability.
I hope this helps - Karl
|