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: