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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