Description Usage Arguments Details Value Author(s) References Examples
This function computes Mantel's permutation test for similarity of two matrices. It permutes the rows and columns of the second matrix randomly and calculates a Zstatistic.
1 2  mantel.test(m1, m2, nperm = 999, graph = FALSE,
alternative = "two.sided", ...)

m1 
a numeric matrix giving a measure of pairwise distances, correlations, or similarities among observations. 
m2 
a second numeric matrix giving another measure of pairwise distances, correlations, or similarities among observations. 
nperm 
the number of times to permute the data. 
graph 
a logical indicating whether to produce a summary graph (by default the graph is not plotted). 
alternative 
a character string defining the alternative
hypothesis: 
... 
further arguments to be passed to 
The function calculates a Zstatistic for the Mantel test, equal to the sum of the pairwise product of the lower triangles of the permuted matrices, for each permutation of rows and columns. It compares the permuted distribution with the Zstatistic observed for the actual data.
The present implementation can analyse symmetric as well as (since version 5.1 of ape) asymmetric matrices (see Mantel 1967, Sects. 4 and 5). The diagonals of both matrices are ignored.
If graph = TRUE
, the functions plots the density estimate of
the permutation distribution along with the observed Zstatistic
as a vertical line.
The ...
argument allows the user to give further options to
the plot
function: the title main be changed with main=
,
the axis labels with xlab =
, and ylab =
, and so on.
z.stat 
the Zstatistic (sum of rows*columns of lower triangle) of the data matrices. 
p 
Pvalue (quantile of the observed Zstatistic in the permutation distribution). 
alternative 
the alternative hypothesis. 
Original code in S by Ben Bolker, ported to R by Julien Claude
Mantel, N. (1967) The detection of disease clustering and a generalized regression approach. Cancer Research, 27, 209–220.
Manly, B. F. J. (1986) Multivariate statistical methods: a primer. London: Chapman & Hall.
1 2 3 4 5 6 7 8  q1 < matrix(runif(36), nrow = 6)
q2 < matrix(runif(36), nrow = 6)
diag(q1) < diag(q2) < 0
mantel.test(q1, q2, graph = TRUE,
main = "Mantel test: a random example with 6 X 6 matrices
representing asymmetric relationships",
xlab = "zstatistic", ylab = "Density",
sub = "The vertical line shows the observed zstatistic")

$z.stat
[1] 5.129018
$p
[1] 0.121
$alternative
[1] "two.sided"
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