Randomization test

A randomization test compares a statistic with values obtained by applying transformations that preserve the joint distribution under the null hypothesis.

A permutation test uses relabelings of observations as its null-preserving transformations and computes a p-value from the resulting orbit of the test statistic.

A sign-flip randomization test independently multiplies observations by signs in $\{-1,1\}$. It is finite-sample exact for a zero-centered null when the joint distribution is invariant under those sign changes.