help > RE: atan(r) values of second level results
Dec 17, 2014  02:12 AM | Alfonso Nieto-Castanon - Boston University
RE: atan(r) values of second level results
Hi Michael,

This is a very interesting and complex question. First, in your particular example you are using PPI analyses using regression (bivariate) measures, so the actual values that are entered into your second-level analyses would be regression coefficients (instead of Fisher-transformed correlation coefficients) associated with the interaction between the "psychological effect" (your task) and the "physiological effect" (the source ROI), and the interpretation of these effect-size measures is not straightforward. In particular effect sizes in PPI analyses do not represent absolute measures of connectivity during your task conditions but rather relative measures of connectivity-changes associated with the presence of your task. If using a block design, and PSC analysis units, for example, one possible way to characterize the units of these regression coefficients would be something along the lines of how much the ratio "percent-signal-change in target ROI/voxel for each unit percent-signal-change in source ROI/seed" changes in the presence of your task (compared to a common baseline condition that includes the entire acquisition), so the ~.17 difference between the -.054 and .116 effect sizes represents a difference of .17 between conditions in the ratio above (not a difference between conditions in Fisher-transformed correlation values).

Last, regarding what constitutes "high" or "low" correlation values, in practice for ROI-to-ROI analyses average resting-state correlation values between two ROIs have a distribution like the attached figure, where most (~90%) of the significant ROI-to-ROI connections show absolute correlations below .30, and many (~50%) show correlations below .10 (again only considering the significant ROI-to-ROI connections; e.g. P-fdr<.05). Of course, this touches on the question of the difference between statistical significance and practical significance, but that is probably the topic for a longer discussion (see for example Friston 2014 "Sample size and the fallacies of classical inference").

Best
Alfonso 
Originally posted by Michael King:
Hi, 

I'd like to follow up on this post after searching on a similar head-scratcher. I see the difference between the two Z/z values above, thanks. However, I'm unsure how r-values of 0.05-0.29 are considered correlated; these values seems low.

In our groups work, we're comparing two conditions. There is a strong effect size and near significant p (p=0.0527) when I compare connectivity values (i.e. fisher transformed Z-values) between conditions but the individual conditions don't seem very correlated with the task (they have mean fisher values of -0.05411 and 0.116). 

Other information:
I performed a PPI (regression (bivariate)) analysis with 14 subjects. 

Michael
Attachment: fig01.jpg

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Crystal Goh Jun 2, 2012
Alfonso Nieto-Castanon Jul 8, 2012
Patrick McConnell Dec 20, 2014
Alfonso Nieto-Castanon Dec 21, 2014
Patrick McConnell Dec 21, 2014
Alfonso Nieto-Castanon Dec 24, 2014
Patrick McConnell Dec 24, 2014
Patrick McConnell Jan 8, 2015
Alfonso Nieto-Castanon Dec 27, 2014
Patrick McConnell Jan 7, 2015
Alfonso Nieto-Castanon Jan 15, 2015
Patrick McConnell Jan 22, 2015
Michael King Dec 16, 2014
RE: atan(r) values of second level results
Alfonso Nieto-Castanon Dec 17, 2014
Michael King Dec 17, 2014
Michael King Dec 17, 2014