# Confirmation about PERMANOVA and Variance partitioning (permutest)

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

• Fair question, but I do think it would use some references and reasoning why you think they should (not) be the same thing. Also could be better suited for cross-validated (the statistical Stack Exchange web). Jan 15 at 14:45
• Thanks, I understand that permutest can be done to validate the permanova (adonis) result, and if permutest result is not significant then this means we can be more confident that our adonis result is a real result, and not due to differences in group dispersions. Jan 18 at 11:40
• Great, I recommend to edit the question. Also, your comment kind of sound you know the answer already. Is you just need a confirmation, you could really make it easier for someone to answer if you provide relevant links. Jan 18 at 11:56
• This is done; thanks! Jan 18 at 22:18

## 1 Answer

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 –

1. 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).

2. 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.