When using a permutation test to assess the difference between two groups, why does the test remain valid even if the underlying distribution of the data is unknown or highly skewed?

A permutation test remains valid regardless of the underlying distribution because it relies on the principle of exchangeability under the null hypothesis. The null hypothesis in this context assumes that the two groups of data come from the identical probability distribution, meaning the group labels are essentially arbitrary. Because the null hypothesis assumes the labels do not influence the observed values, any observed difference between the groups is simply one possible ou....