Hi VM,
I think the question is a bit ill posed... NPC combines the evidence against the null from the separate (partial) tests. It can be understood as a meta-analysis, except that, instead of summary results from different studies, we use the the actual subject-level data, and further, we use the same subjects, while taking into account, through permutation, the non-independence between the various measurements obtained per subject.
NPC can also be seen as a non-parametric counterpart to MANOVA with some nicer properties, such as the ability to identify the direction of the effects, both jointly or separately, and higher power, particularly as the number of modalities being combined increase.
The exact profile with which each partial test contribute to the final test is known from the combining function used with the test. See Figure 3 from our NPC
paper. As you can see, for some functions, even non-significant results can contribute (together with others) to a significant joint effect. This isn't the same as "how much each has contributed" because there are non-linearities in the way these functions become significant, even more so when they aren't independent.
Hope this helps!
All the best,
Anderson
