Dear all,

I am somewhat new to fMRI and would be grateful for some insight into contrast weighting in 2nd-level gPPI (bivariate regression) analyses.

The data used an event-related design with six within-subjects conditions. I had thought that within-subject contrasts reflect linear combinations of regression coefficients–for example:
• Conditions selected: Cond1, Cond2
• Between-condition contrast: [0.5 0.5]
• Model: y = 0.5*BetaCond1 + 0.5*BetaCond2 + 0*BetaCond3 + 0*BetaCond4 + 0*BetaCond5 + 0*BetaCond6
• Interpretation: Regions showing greater connectivity during Cond1 and Cond2, relative to an implicit baseline

However, I see in the SPM.mat file that the actual model does not use a weighting of 0.5 but rather sqrt(0.5):
• Conditions: Cond1, Cond2
• Contrast: [0.5 0.5]
• SPM.mat description: 0.707107*Cond1 + 0.707107*Cond2

This is true when I take the difference between task conditions as well:
• Conditions: Cond1, Cond2
• Contrast: [1 -1]
• SPM.mat description: 0.707107*Cond1 - 0.707107*Cond2

And in case it is relevant, the weighting is perhaps proportional to the number of conditions included in the contrast:
• Conditions: Cond1, Cond2, Cond3, Cond4
• Contrast: [0.25 0.25 0.25 0.25]
• SPM.mat description: 0.5*Cond1 + 0.5*Cond2 + 0.5*Cond3 + 0.5*Cond4

I must be missing something key in gPPI, or perhaps contrasts more generally, and haven't been able to find an answer. Any help would be very much appreciated!

Thank you,
Sara