Either approach is technically valid. Ultimately it comes down to what question you wish to ask of your data, and what granularity you wish your inferences to be performed at.
Consider the most obvious test case, where a voxel contains 2 fixels, only one of which is significant. The voxel-wise inference could be either significant or not. So we now have four cases:
Voxel-wise inference is significant; fixel results are projected to voxel. Both fixel-wise and voxel-wise statistical inference have produced at least one significant result in this voxel.
Voxel-wise inference is not significant; fixel results are projected to voxel.
Fixel-wise statistical inference produced at least one significant result; voxel-wise statistical inference gave no result.
Voxel-wise inference is significant; voxel results are projected to fixels.
One fixel reports statistical significance in fixel-wise statistical inference but not in voxel-wise inference; the other fixel reports no significance using either method.
Voxel-wise inference is not significant; voxel results are projected to fixels.
One fixel reports statistical significance using both methods; the other fixel reports significance in voxel-wise inference but not fixel-wise inference.
Question is whether you want to report 1 & 2, or 3 & 4.
It’s also worth noting that while projection of voxel data to fixels is unambiguous (just take the voxel value and assign all fixels in the voxel that value), projection of fixel data to a voxel is not; there is a statistical measure that must be taken across the values within those fixels within a particular voxel to produce a single scalar measure for that voxel. Here I’ve assumed that one has a binary mask - 1 for significant, 0 for not; and then the maximum value across fixels within a voxel is taken, such that for fixel-wise statistical inference, the voxel-wise value indicates whether or not any fixel in that voxel reached statistical significance. This is probably the most sensible, but it’s important to understand the ramifications of that choice, as it affects how the cases above would be both quantified and reported.
I think this is very much a separate question from the first, and would probably be better understood by disentangling the two as much as possible. Given this relates to correlations between specifically fixel-wise measures, it doesn’t explicitly relate to comparisons between fixel-wise and voxel-wise measures.
In short: Yes, but it requires some GLM trickery that is not yet present in the public MRtrix3 branch (but will be in the upcoming release). While this abstract reports specifically on comparisons between white-matter-based and grey-matter-based quantitative measures, parts of this methodology would be used to assess correlations between different white-matter-based fixel-wise metrics.
Voxel-wise inference is significant; fixel results are projected to voxel . Both fixel-wise and voxel-wise statistical inference have produced at least one significant result in this voxel.
Voxel-wise inference is not significant; fixel results are projected to voxel .
Fixel-wise statistical inference produced at least one significant result; voxel-wise statistical inference gave no result .
Voxel-wise inference is significant; voxel results are projected to fixels .
One fixel reports statistical significance in fixel-wise statistical inference but not in voxel-wise inference; the other fixel reports no significance using either method.
Voxel-wise inference is not significant; voxel results are projected to fixels .
One fixel reports statistical significance using both methods; the other fixel reports significance in voxel-wise inference but not fixel-wise inference.
For example in case 3 you mention Voxel-wise inference is significant but report no voxel-wise significance: One fixel reports statistical significance in fixel-wise statistical inference but not in voxel-wise inference; the other fixel reports no significance using either method.
Let’s say we have one voxel, with fixels that we label f1 and f2. We’ll constrain our example to the fixel-wise FD metric. For this metric, For f1, p<0.05; f2 is not statistically significant. We also have a voxel-wise metric that we’ll call V. Since it’s a voxel-wise metric, we project the value of metric V to both f1 and f2 using voxel2fixel.
Case 3: p<0.05 for V. Your reported results are:
For f1: FD is affected; V is also affected (“match”).
For f2: FD is not affected; V conversely is affected (“mismatch”).
Case 4: V is not statistically significant. Your reported results are:
For f1: FD is affected; V is however not affected (“mismatch”).
For f2: FD is not affected; V is also not affected (“match”).