Hi Alfonso,

This is excellent work, thank you!

Indeed, the necessity of orthogonalising the contrast weights when the number of levels > 2 is not something I had previously realised. I'm intrigued by this and certainly has given me some food for thought. I do not believe that SPM orthogonalises contrast weights by default and so this is something I'm going to dig into more to try and gain some intuition. 

Rather frustratingly, I notice that Penny and Henson do actually mention this in their SPM chapter, however it is relegated to a footnote and a short explanation in the appendices. I had missed this previously, hence the issue with implementing their approach. Perhaps more frustrating is the fact that Will Penny does not mention or implement this in the example on the SPM Wiki. Perhaps the assumption is that the non-sphericity correction will always be used? Nevertheless, this seems like such an important point that I've not seen made anywhere else previously.

Anyway, thank you for all the help and useful discussion. I hope you got something out of this as well and hasn't been seen as a waste of your time. Hopefully other people will find the discussion instructive as well.

Best wishes,
- Martyn