Hi Bettyann,
I think you have answered your own question very well. For functional
connectivity, correlation is what you're after, and the z-score is a
simple transformation of the correlation coefficient and thus provides
the same information. Beta weights in that case are far more difficult
to interpret in terms of connectivity. Another way of looking at it is
that betas will tell you something about time-locked amplitude,
whereas z-scores will tell you something about the degree of
time-locking.
-Tom
Centre for Integrative Neuroscience & Neurodynamics
School of Psychology and CLS
University of Reading
Ph. +44 (0)118 378 7530
[log in to unmask]
http://www.personal.reading.ac.uk/~sxs07itj/index.html
On Thu, May 10, 2012 at 8:51 PM, bettyann <[log in to unmask]> wrote:
> Hi, I'm back with another round of seed-based functional connectivity analysis questions. Hooray!
>
> Round 1 for US$100 / 62 GBP / 77 EUR:
> Again with the 'z-score v beta weight as a measure of functional connectivity' question.
>
> I've created plots and run regression analysis of dependent variable z-score (or beta weight) v independent variable TestScore. I get similar but different results when using z-scores or beta weights. But sometimes I get very different results typically due to noisy data. For example, after doing a linear regression of z-score v TestScore, I get a p-value of 0.03. If I do a linear regression of beta weight v TestScore, I get a p-value of 0.98 because one beta weight is crazy large -- an order of magnitude larger than any other beta weight.
>
> This all makes sense to me -- noisy data needs to be down-weighted. And that's what a z-score (or t-stat) does: z = (beta weight) / variance.
>
> So I wonder if anyone can help me understand the benefits of using beta weights as a measure of functional connectivity. My hesitation about using beta weights is exactly what my analysis reveals -- beta weights do not include a noise factor.
>
> While thinking about 'why beta' I was thinking about the statistical meaning of beta in a GLM analysis. What does this beta weight represent?
>
> Classical answer:
> For every 1 unit increase in my independent variable X, there is a beta-many unit increase in my dependent variable, Y.
>
> I'm not sure how to apply this classical answer to my analysis of comparing time courses.
>
> But I do understand that with some monkeying around I can transform my z-score to a correlation coefficient, r (where 'monkeying around' is a Fisher transform). And correlation is exactly what I'm trying to assess between my seed time course and the time course of each voxel in my image.
>
> Using z-score as a measure of functional connectivity makes sense to me because it represents a measure of correlation. A z-score also includes a noise weighting factor.
>
> Using beta as a measure of functional connectivity is more obscure for me. I would be most appreciative of others' insights and explanations.
>
> Stay tuned for:
> Round 2 for US$500 / 310 GBP / 386 EUR:
> Assessing change in functional connectivity between pre- and post-conditions using randomise.
>
> Stay tuned!
>
> And, seriously, thanks.
> * ba
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