Hi Liron,

Fred is right and I was somewhat mixing the description for looking at the effect sizes in seed-to-voxel vs. ROI-to-ROI analyses. Let me see if I can elaborate a bit with an example in order to clarify this. If you are performing ROI-to-ROI analyses, and you have three subject groups and perform a [1 -1 0; 0 1 -1] between-group comparison, you could get something like the following:

https://drive.google.com/open?id=0B4jW8HPqnNiuU0ctZkxjYkNycGs&authuser=0

For this analysis, the connectivity between the seed area (MPFC) and target area (Amygdala r) reads the following stats:
beta = 0.13; F(2,22)=5.81; p=.009398

If instead you used a contrast [1 -1 0; 0 1 -1; 1 0 -1] (where the last row is redundant) you would read the following stats:
beta = 0.14; F(2,22)=5.81; p=.009398

Despite the apparent different beta values the two analyses are exactly equivalent (note that the F-stats, p-values, and degrees of freedom are exactly the same). Those beta values shown in the results table are simply showing the norm of a multi-variate effect-size vector. If you click 'import values' and get a new second-level covariate listing the subject-specific connectivity values between these two areas, you can use Tools.Calculator to actually see the 'expanded' beta values that result in these different norms. To do so click on Tools.Calculator, select as 'outcome variable' the newly defined 'conn between MPFC and Amygdala' variable, and select as 'predictor variables' the same 'group1', 'group2', and 'group3' effects as in the original analysis. If you enter as a between-subjects contrast the matrix [1 -1 0; 0 1 -1] you will get something like the following:

https://drive.google.com/open?id=0B4jW8HPqnNiuVjc0REJJMV91OW8&authuser=0

which reads the following stats:
beta = [0.06 -0.11]; F(2,22)=5.81; p=.009398

As you see here, the F-stats and p-values are exactly the same as before, but now Calculator is showing you the actual multi-dimensional (in this case two-dimensional, because your contrast matrix has two rows) effect-size vector. In this example the 0.06 value represents the average difference in connectivity between the first and second groups, and the -0.11 value represents the difference in connectivity between the second and third groups, and the norm of the [0.06 -0.11] vector is the "beta=0.13" value that was shown in the original display.

If you enter instead the contrast matrix [1 -1 0; 0 1 -1; 1 0 -1] you will get something like the following:

https://drive.google.com/open?id=0B4jW8HPqnNiuRlZ4SU1MTDhhdnM&authuser=0

which reads these stats:
beta = [0.06 -0.11 -0.051]; F(2,22)=5.81; p=.009398

which are, again the same stats as before, but now Calculator is showing you the actual three-dimensional (because the contrast matrix in this case has three rows) effect-size vector for this contrast. In this example the 0.06 and -0.11 values are just the same as in the example above, and the -0.051 value represents the difference in connectivity between the first and third groups (unsurprisingly that value -0.051 is the same as the sum of the average difference in connectivity between the first and second groups 0.06, and the average difference in connectivity between the second and third groups -0.11, i.e. -0.051 = 0.06 + -0.11), and the norm of the [0.06 -0.11 -0.051] vector is the "beta=0.14" value that was shown in the original display.

So summarizing, when looking at the differences between three groups, one typically uses the contrast [1 -1 0;  0 1 -1] to test for any between-group differences because it provides a simple parsimonious representation of the between-group differences being tested. It would be just the same to use instead a contrast like [1 -1 0; 0 1 -1; 1 0 -1], or any other combination such as [1 0 -1;0 1 -1] or [1 -1 0;1 0 -1], etc., and even highly redundant ones like [1 -1 0; 1 0 -1;-1 1 0;0 1 -1;-1 0 1;0 -1 1]... All of those would lead to exactly the same statistical test (same F-stats, p-values, degrees of freedom), since these statistical tests are invariant to any rank-preserving transformation of the chosen contrasts and all of them test for any between-group differences, even if each of them will show different effect-size beta values in the results table (simply because those values reflect the norm of the vector composed of the particular combination of between-group differences chosen).

Hope this helps clarify
Alfonso

Originally posted by Fred Uquillas: