Hi Pia,
> I extracted from the maxima, the t-value of each covariate for each
> condition and the degrees of freedom of the t statistics.
>
> And use the below formula to calculate the r Pearson correlations:
>
> r = (t^2/(t^2+df-1))^0.5
I think you're on the right track, except that the formula should be
r = (t^2/(t^2+df))^0.5
The (n-2) that commonly appears is actually the df, and not df-1,
since the correlation model includes a mean/intercept as well as the
regressor of interest.
> The formula obviously (as everything is squared) gives only positive
> correlations, even tough I know that the covariates in some cases were
> negatively correlated with the BOLD. Is there anyway to obtained back
> this information, I could always use the signs of the t statistics maybe?
This should be fine, and is in fact the approach taken in cg_spmT2x.m
of the vbm2 toolbox (I think a similar function is in Volkmar's
volumes toolbox. The relevant code fragment is:
t2x = sign(Z).*(1./((df(2)./((Z.*Z)+eps))+1)).^0.5;
http://dbm.neuro.uni-jena.de/vbm/vbm2-for-spm2/
http://sourceforge.net/projects/spmtools/
> Finally, doing the procedure above I obtained relatively very week
> correlations for all subjects and all conditions: r < 0.1; even though
> on a second level analysis they were significant different than zero,
> would such a weak correlation make sense or do they look too much like
> noise.
Maybe try with the corrected formula, and/or use one of the toolbox
versions, though I wouldn't expect the difference to be huge. Perhaps
it's just that a weak correlation found in all subjects can be
significant at the second level, though I'm not sure about that...
Hope this helps,
Ged.
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