I am comparing the differences in microbiome community composition between animals according to three different dietary regimes: hay, green vegetation, and restricted feed. Looking at a PCoA plot, the centroid and dispersion of the restricted feed group is obviously different from the two others, and comparing bray-curtis distances with the vegan::adonis() function yields a high R squared and a significant p-value. The green vegetation and hay groups appear the same, but running an adonis test comparing these two groups yields a significant p-value (albeit a very low r squared value of 0.02). Must I reject the null hypothesis that the hay fed group and the green vegetation groups are homogeneous, despite the low r-squared value and the disagreement with the PCoA plot results?
So you should reject the null on the basis of low p. The rˆ2 value simply shows that other factors also account for the relationship. Maybe change the Green Vegetation dots to green and the Hay dots to red?
Principal component analysis can not be used to find the difference. It is used for the variation of multiply independent parameters.
Nice graph. Hay and green grass cover the same space in the PC 1 and 2 and are together distinct from the "restricted feed" along the PC 1. That makes me wonder what the "restricted feed" is. Also the sameness of green grass and hay is interesting, although not surprising from an ecological and farming perspective.
Hi Claire, you might already have answer to this, but I found the answer to your question in this blog:
https://chrischizinski.github.io/rstats/adonis/
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