Pairwise comparison in betadisper - How to interpret the p value?

[lucasmoncao]

Hi, I'm doing a comparison between the quartiles. I would like to understand the differences between the "Observed p-value below diagonal, permuted p-value above diagonal"

Permutation test for homogeneity of multivariate dispersions
Permutation: free
Number of permutations: 999

Response: Distances
          Df  Sum Sq  Mean Sq      F N.Perm Pr(>F)    
Groups     3 0.21699 0.072329 7.5743    999  0.001 ***
Residuals 64 0.61115 0.009549                         
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Pairwise comparisons:
(Observed p-value below diagonal, permuted p-value above diagonal)
           Q1                Q2                 Q3                 Q4
Q1                         3.9000e-01   2.4300e-01   0.039
Q2 3.8410e-01                           6.0500e-01    0.001
Q3 2.3801e-01   5.8714e-01                             0.001
Q4 4.0773e-02.  8.3245e-06  3.9198e-07      

I need to describe in my master's work the p value between Q1 and Q4.

[jarioksa]

Observed p-values are calculated from analytic t-distribution (see ?pt), permuted p-values are evaluated from permutations. As to Q1 – Q4 pair, the reported values are so similar (0.041 vs 0.039) that probably the parametric assumptions of t-test are satisfied pretty well. See also ?TukeyHSD.betadisper.