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vegan (version 2.0-10)

permutations: Permutation tests in Vegan

Description

Unless stated otherwise, vegan currently provides for two types of permutation test:
  1. Free permutation ofDATA, also known as randomisation, and
Free permutation of DATA within the levels of a factor variable.

Arguments

emph

  • DATA
  • DATA
  • DATA
  • DATA
  • DATA
  • DATA

code

strata

enumerate

  1. 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 two 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 $i = 1, ..., n$
  • The values of the test statistic for the $n$ permutations of the DATA are added to the value of the test statistic for the observed data. These n + 1 values represent the Null or randomisation distribution of the test statistic. The observed value for the test statistic is included in the Null distribution because under the Null hypothesis being tested, the observed value is just a typical value of the test statistic, inherently no different from the values obtained via permutation of DATA.
  • The number of times that a value of the test statistic in the Null distribution is equal to or greater than the value of the test statistic for the observed data is recorded. Note the point mentioned in step 5 above; the Null distribution includes the observed value of the test statistic. Denote this count as $N$.
  • The permutation p-value is computed as $$p = \frac{N}{n + 1}$$

eqn

$n = 100$

deqn

$$p_{\mathrm{min}} = \frac{0 + 1}{n +1}$$

strong

including

See Also

permutest, permuted.index