permutations: Permutation tests in Vegan
Description
Unless stated otherwise, vegan currently provides for two types of
permutation test:
- Free permutation ofDATA, also known as randomisation,
and
- Free permutation of DATA within the levels of a factor
variable.
code
strataenumerate
- 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