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In a test, permutation test is used to estimate the null distribution of the test statistic from the sample.

In multiple comparison, what is the usage of permutation test?

Thanks!

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It is typically used for Weak FWER control.

It allows you to generate the distribution of your global test statistic under the global null.

As an example: consider the distribution of the minimal p-value (which tests for the global null) of correlated test statistics, testing for a difference between two groups. Label switching, which is justified only under the global null, will allow you to recover the distribution of this minimal p-value while accounting for the unknown dependence between the test statistics.

Note it is sometime possible to use permutations for strong FWER control, or FDR, but much more attention should then be given to the type of permutation which is permissible under the null.

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