Hi @devonorourke,
I want to address your goals. As you've described them, I don't think they're possible.
There is no statistical test that I can come up with that will let you compare categorical data when you only have one sample per category. The test - regardless of the type of test - relies on a distribution of data. And, the only way to characterise this distribution is to have multiple samples. (You can look at continuous variables because they're essentially sampling a distribution by themselves, and so unique values are fine.) This isn't a QIIME-specific limitation, this is a stats thing.
I also worry that you might be missing a concept with statistical tests.
- Permanova, mantel and bioenv look at differences associated with distances (beta diversity).
- Kruskal Wallis looks at alpha-diversity related differences
- ANCOM works on feature-based differences
So, ANCOM can help you determine if there are individual features that describe the differences between your two groups. ANCOM cannot help you determine if there's a difference in the distances themselves. Does that make sense?
Luckily, though, you may have another solution. If you think there might be features of the sites you could try a couple of things:
- Run your favorite geographical distance metric and then use a mantel test to compare with the continuous variable. (Although TBH, you might need to take this into python or R, Im approaching this from a more theoretical perspective ATM). This will tell you whether closer samples look more similar. It can be used with any pair of distance metrics you want to try.
- Pick individual features of your metadata and then compare the data on that basis. For instance, are sites with higher elevation similar?
- Use a broader classification of site (i.e. country, etc).
Hope that helps!
Best,
Justine