# [R] Permutation tests in {coin}

Henric Winell nilsson.henric at gmail.com
Thu Oct 10 23:55:20 CEST 2013

```Lars Bishop skrev 2013-10-05 22:17:
> Hello,
>
> I'm trying to get familiar with the coin package for doing
> permutation tests. I'm not sure I understand the documentation
> regarding the difference between distribution = "asymptotic" and
> "approximate" in the function independence_test.

The use of "asymptotic" or "approximate" leads to two different
approximations of the exact conditional distribution under the null
hypothesis.

The basis of 'coin' is a multivariate linear test statistic, and it can
be shown (Strasser and Weber, 1999) that its conditional distribution is
asymptotically normally distributed under the null hypothesis
("asymptotic").  Alternatively, another approximative conditional null
distribution can be obtained using conditional Monte Carlo procedures
("approximate").

> Are permutations of the test statistic actually computed in the
> asymptotic case, or only when the distribution is specified as
> approximate?

In the asymptotic case, the univariate normal distribution is used when
the test statistic is a scalar and the chi-squared distribution is used
when the test statistics is a quadratic form.  For a multivariate
maximum-type test, permutations may be used in the asymptotic case but
only in the sense that probabilities from the corresponding multivariate
normal distribution are obtained by numerical integration using Monte
Carlo procedures.  In the latter case, the 'mvtnorm' package is used and
further details can be found in its documentation.

In the approximate case, permutations are always used irrespective of
the type of test statistic.

> When should I use each option?

You should only use "asymptotic" in situations where you trust the
asymptotic approximation. ;-)  In all other cases, use "approximate" or,
if possible, "exact".

HTH,
Henric

>
> Thanks Lars.
>
> [[alternative HTML version deleted]]
>
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```

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