# Adonis vs. Anosim vs. Permanova

Hi!

I'm a bit of a newbie with stats and I'm still trying to fully grasp things. I'm a bit confused on what exactly the test statistics are telling me for PERMANOVA (pseudo-F), ADONIS (R2) and ANOSIM (R), and what exactly I should be using for my question, that is: are there significant differences between locations?

From what I understand of permanova, pseudo-F tells me the ratio of between-group variation and within-group variation. A larger pseudo-F value means that the between-group variation is greater than the within-group variation (so like, the variation between locations is greater than the variation between samples within one location?) But I'm not sure what I'm comparing this number against. Are values 1-3 really low? Also, I noticed that this value is the same as the F.Model value in the ADONIS output. What is the relationship between PERMANOVA and ADONIS?

For ANOSIM, the R-value tells me if groups of samples are significantly different. In my case 0.44...is probably not statistically different? What does it mean that the R-value is 0.7 between two locations but the total R-value is much lower than that? Doesn't that explain some significant difference?

And for ADONIS, the R2-value tells me how much can be explained by the variable. So in my case, only 19% of variation can be explained by location differences.

Problem is, 0.44 doesn't seem suuuuper low to me...so I feel like there is a difference between locations, but why is the R2 value so low? Am I just being biased and misinterpreting?

Sorry for all the questions!

uu-location-significance-permanova.qzv (385.0 KB)
uu-location-significance-anosim.qzv (385.0 KB)

4 Likes

See here for more description of this test and its interpretation. See also the original PERMANOVA paper, the vegan-R adonis documentation, and other links on that webpage.

They are different implementations of the same test. The `adonis` action in QIIME 2 supports multi-factor PERMANOVA tests. The `beta-group-significance` action only supports one factor but generates useful plots.

Yes all of these tests appear significant (look at the P values) but only a portion of the variation is explained by location. This is normal and your R2 values actually look quite good; R2=0.19 may not sound like a lot, but many many factors shape microbiomes at different sites and so R2 values are often < 0.5, simply because the microbiome is not very simple.

7 Likes

In terms of R intrepetation, can I link you to a recent Nature paper where they had an Adonis R^{2} less than 0.06. (Check figure 1). Im actually amazed youâ€™re getting an R^{2} in the double digits, your explanatory factors must be large, or your sample homogenous and/or relatively small.

3 Likes

Thanks both @Nicholas_Bokulich and @jwdebelius for your replies! I will check these papers out. I donâ€™t know how when I google these cites donâ€™t come up, or I just miss them, so thank you for taking the time to link them to me. I was looking up other factors to explain variation, such as species and plant part type (leaf or stem) the R2 values were about 4-8% for that, so good to know that this is normal.

And yes @jwdebelius, unfortunatley my sample size is quite small (n < 50)

1 Like

The best thing to do if you have multiple factors in your experiment is to test these multiple factors.

Run adonis with a formula such as `location+plantspecies+plantpart`

1 Like

Woah, what just happenedâ€¦ I did run adonis for the factors, but individually, and now I am getting different R2 values. So originally I ran

â€“i-distance-matrix core-metrics-results-all-filtered/unweighted_unifrac_distance_matrix.qza
â€“p-formula Species

â€“i-distance-matrix core-metrics-results-all-filtered/unweighted_unifrac_distance_matrix.qza
â€“p-formula â€śLocationID+Species+LeaforStemâ€ť

And for species, for example, the R2 value of species on itâ€™s own was 0.08934, but with the other factors taken into account, itâ€™s now 0.068488. Interestingly, the R2 value for Location stayed the same. Is this what it means by â€śmulti-way ADONIS testsâ€ť? Is it basically like, some factors may have been influencing others and the test is now taking that into account? And with what I did before, the test just looked at one factor discretely and it didnâ€™t take into account the influence of other factors? (Sorry for the messy sentences)

4 Likes

Yes, yes, and yes! You can even make more complicated formulae, e.g., see if there is an interaction between factors by using the `*` operator instead of `+` (but beware, interactions can get very complicated to interpret! especially if you have > 2 levels of interaction)

4 Likes

Excellent! Thank you for all your help!!! I feel a lot better about interpreting my results now

2 Likes

This topic was automatically closed 31 days after the last reply. New replies are no longer allowed.