Bioinformatics Asked on April 4, 2021

Could you please help me to understand what is the difference between Permutational multivariate analysis of variance (PERMANOVA,adonis) and Variance partitioning

(permutest).

I understood that permutest is used to confirm the PERMANOVA result that differences in PERMANOVA is not due to dispersion.

```
###adonis_calculation
BC <- phyloseq::distance(phyloseq_prop, "bray")
pmv =adonis(BC ~Season*Region, as(sample_data(physeqN3), "data.frame"),permutations = 5000)
pmv
Call:
adonis(formula = BC ~ Season * Region, data = as(sample_data(physeqN3), "data.frame"), permutations = 5000)
Permutation: free
Number of permutations: 5000
Terms added sequenti
Total 99 19.8578 1.00000 ally (first to last)
Df SumsOfSqs MeanSqs F.Model R2 Pr(>F)
Season 1 1.8586 1.85862 12.036 0.09360 2e-04 ***
Region 1 2.4218 2.42183 15.682 0.12196 2e-04 ***
Season:Region 1 0.7522 0.75222 4.871 0.03788 2e-04 ***
Residuals 96 14.8251 0.15443 0.74656
```

Many thanks

Permutational Multivariate Analysis of Variance (PERMANOVA) assumes no distribution which means it is a non-parameteric statistical test. According to the assumption of PERMANOVA test, each group must have same dispersion in the data. Before performing any statistical test, we must check the underlying assumptions. Variance partitioning (permutest) is a confirmatory test to check the assumption (similar dispersion). You can use permutest.betadisper for permutest. After that you can perform PERMANOVA test using adonis().

Interpretation of PERMANOVA test –

If p value is small (<0.05 ) we reject the null hypothesis (No difference between the groups) otherwise we accept the null hypothesis (Significant difference between the groups).

Coefficient of determination, R-squared value indicates the variation in the distances being explained by groups under the study. Higher value indicates a better fit.

You can further look into the confidence interval for each group.

Hope this confirms the answer to your question.

Correct answer by Elucidata on April 4, 2021

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