PERMANOVA is frequently used in microbiome studies when analyzing beta diversity. While I know that basics of PERMANOVA are similar to ANOVA (with some differences related to permutation), I have a hard time understanding the logic of this analysis in the context of beta diversity analysis.
- In particular, we perform statistical tests for vectors of data, e.g., to compare the abundance of OTU X in cases vs. abundance of OTU X in controls. When working with beta diversity though we deal with a distance matrix (e.g. based on Bray-Curtis) for pairs of samples and not vectors. Can someone please explain to me what quantities are compared against each other using PERMANOVA?

- Should one compute different distance matrices for each category (e.g., one for cases and one for controls) or just one matrix that includes samples from all categories?
Many thanks!