permutations: Permutation tests in Vegan

Description

From version 2.2-0, vegan has significantly improved access to restricted permutations which brings it into line with those offered by Canoco. The permutation designs are modelled after the permutation schemes of Canoco 3.1 (ter Braak, 1990).

vegan currently provides for the following features within permutation tests:

Free permutation ofDATA, also known as randomisation,

Free permutation of DATA within the levels of a grouping variable, Restricted permutations for line transects or time series, Permutation of groups of samples whilst retaining the within-group ordering, Restricted permutations for spatial grids, Blocking, samples are never permuted between blocks, and Split-plot designs, with permutation of whole plots, split plots, or both.

Arguments

emph

DATA
DATA
p
p
p
p
p
without
p
DATA
DATA
DATA
Restricted permutations; using the permute package

pkg

permute
vegan
vegan
permute
vegan
vegan
vegan
vegan
permute
permute
vegan
vegan
permute
permute

code

vignette("permutations",
  package = "permute").

enumerate

An appropriate test statistic is chosen. Which statistic is chosen should be described on the help pages for individual functions.

item

The value of the test statistic is evaluate for the observed data and analysis/model and recorded. Denote this value $x_0$.
The DATA are randomly permuted according to one of the above schemes, and the value of the test statistic for this permutation is evaluated and recorded.
Step 3 is repeated a total of $n$ times, where $n$ is the number of permutations requested. Denote these values as $x_i$, where $i = 1, ..., n$
Count the number of values of the test statistic, $x_i$, in the Null distribution that are as extreme as test statistic for the observed data $x_0$. Denote this count as $N$.
We use the phrase as extreme to include cases where a two-sided test is performed and large negative values of the test statistic should be considered.
The permutation p-value is computed as $$p = \frac{N + 1}{n + 1}$$

eqn

$n = 100$

deqn

$$p_{\mathrm{min}} = \frac{1}{n + 1}$$

strong

conservative
including

References

Manly, B. F. J. (2006). Randomization, Bootstrap and Monte Carlo Methods in Biology, Third Edition. Chapman and Hall/CRC. Phipson, B., & Smyth, G. K. (2010). Permutation P-values should never be zero: calculating exact P-values when permutations are randomly drawn. Statistical Applications in Genetics and Molecular Biology, 9, Article 39. DOI: 10.2202/1544-6115.1585 ter Braak, C. J. F. (1990). Update notes: CANOCO version 3.1. Wageningen: Agricultural Mathematics Group. (UR).