I have done NMDS plot and adonis for species composition data between two groups. adonis is giving me a significant p value indicating that the species composition between two groups are significantly different. But in the NMDS plot confidence ellipses of two groups are overlapping indicating that there is no difference between two groups.
Is it correct to write that the species composition between two groups are significantly different?
p-values enable the recognition of any statistically noteworthy findings. Confidence intervals provide information about a range in which the true value lies with a certain degree of probability, as well as about the direction and strength of the demonstrated effect. So they measure different things, even though there is some relationship, but they are not exact proxies of each other. If the p value is significant, there is definitely a significant difference between the two groups :)
A lot depends on how the "confidence ellipses" are constructed and what, therefore, they actually represent. If they were done using the bootstrap, as is done in Primer v7, I'd expect a metric MDS, so this is clearly something else.
The Permanova hypothesis is that the centroids of the different groups are in the same place in multivariate space. The test is done in the full space. The MDS ordination is a representation in 2 dimensions (or possibly 3) and however the ellipses are constructed they are also represented in that lower dimensional space. It is to be expected that in a higher-dimensional representation the ellipses would not, actually, overlap if the Permanova is significant.
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