PERMANOVA pseudo-F from a distance matrix

SS_T = (1/N) sum_{i<j} d_ij^2; SS_W = sum_{i<j} d_ij^2 eps_ij/n_g; F = (SS_A/(a-1)) / (SS_W/(N-a)) with SS_A = SS_T - SS_W.

Usage

Permanova(X, group, aitchison = TRUE)

Arguments

X

Rows are compositions (positive) or numeric vectors.

group

Group label per row.

aitchison

Take clr coordinates before measuring distance.

Value

List with F, SSA, SSW, SST, df1, df2, N, a, sizes.

References

Anderson (2001), Austral Ecology 26(1), 32-46, Equations (3)-(5), in their standard published form.

Examples

V <- c(1, 2, 3, 4, 5, 6, 7, 8)
Permanova(V, V)
#> $F
#> [1] Inf
#> 
#> $SSA
#> [1] 0
#> 
#> $SSW
#> [1] 0
#> 
#> $SST
#> [1] 0
#> 
#> $df1
#> [1] 7
#> 
#> $df2
#> [1] 0
#> 
#> $N
#> [1] 8
#> 
#> $a
#> [1] 8
#> 
#> $sizes
#> [1] 1 1 1 1 1 1 1 1
#> 
#> $method
#> [1] "PERMANOVA pseudo-F on Aitchison distances (Anderson 2001)"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"