Hello Haley,

They seem to have divided their samples into different groups using the method discussed earlier in their text. They use the PERMANOVA to test if the samples differ between groups. This they find and they use Kruskal Wallis to find which groups differ from which. 

I hope this helps. Best,

Patrick

PERMANOVA is a Multivariate ANOVA with permutations. It is meant to test differences between groups like an ANOVA test, but with a lot of variables (which are the OTUs abundances, for instance), and with permutations to avoid possible biases. If it is statistically significant, it usually tells you that the distribution and abundances of two groups, are different. 

PERMANOVA is useful to measure the effect of the host or other factors on the structure of microbial assemblages 

Here's the original paper: Article A new method for non-parametric multivariate analysis of variance

As stated earlier PERMANOVA is a permutational multivariate anova. But maybe it would help to understand how the test is most often used in microbial ecology. Say you have an ordination–like a PCA, NMDS, PCoA, whatever–and in this ordination you are showing gut microbiome samples from a sick host and a well host. The samples from either host overlap a little, but don't totally overlap. You want to know if folks that are sick have a different gut microbial assemblage than the folks that are healthy. A PERMANOVA lets you statistically determine if the centers (centroids) of the cluster of samples for the sick person differs from the center of the samples for the healthy person. Just like an ANOVA lets one tell if the mean value differs among treatment groups, so the PERMANOVA lets one determine if centroids differ in ordinations. In other words, the PERMANOVA tells you the chances of observing the ordination you observed, or one with even less overlap, given no difference between the gut microbes of the healthy and sick people. Note that the PERMANOVA is not done on the actual ordination but is done on the underlying distance matrices. You can perform a PERMANOVA on other multivariate data, but I think every time I have seen somebody use a PERMANOVA in ecology it is to test if centroids of distance matrices differ. Note that PERMANOVAs can miss a lot, so they shouldn't be the only analytical technique used. Whenever possible, doing some species-specific analyses can provide extra insight. Hope this helps.

Haley Hallowell

PERMANOVA, which is a permutation multivariate (and therefore non-parametric) analysis of variance, using some distance measure that considers double absences - for example, Hamming distance - or, if using the consumption frequency, perhaps distance Euclidean or from Manhattan.

Haley Hallowell

MANOVA, or its PERMANOVA variation, is commonly used to analyze data from experiments whose design fits the test assumptions (McCune & Grace, 2002).

ANOSIM is very robust when we have only two groups for which we want to compare the difference.

When we have more than two groups, the most recommended procedure is Multi-Response Permutation Procedure (MRPP).

MRPP is a non-parametric procedure very similar to ANOSIM, differing only in the test statistic.

In addition, MRPP is usually used when there are more than two groups to test for difference (McCune & Grace, 2002; p.188), while ANOSIM is more recommended when there are two groups.

This is a good one------

permanova - Microbiome@GitHub

microbiome.github.io › tutorials › PERMANOVA

Group-wise comparisons of microbiome composition. Leo Lahti, Sudarshan Shetty et al. 2019-12-25

hi, Haley

PerMANOVA analysis (also called NPMANOVA, Adonis analysis) is a multivariate analysis of variance with distance matrix as the object. From my perspective, it's necessary to cooperate with each other to prove that the differences between groups are indeed significant.

Whence, PERMANOVA can be used to analyze the interpretation of sample differences by different grouping factors, and displacement test can be used for significance statistics. In ecological statistics, PERMANOVA can be used (it is often used together with ranking analysis, and for PERMANOVA, it is often used together with PCoA ranking analysis to explain the problem) to see whether there are significant differences in community composition and structure in different environments.

"I think every time I have seen somebody use a PERMANOVA in ecology it is to test if centroids of distance matrices differ" Hope this helps.

Thank you it helps. Understand PERMANOVA test, but can somebody explain "centroid of distance matrices"