Three non-parametric permutation tests comparing means and medians were implemented: (1) the Fisher-Pitman permutation test which tests if two distributions have the same mean and variance, (2) the Independence Test which tests if the LOR is independent of group assignment (i.e., PAE or COA), and (3) the Savage Test, which tests if one distribution is larger than the other. The R package coin (Conditional Inference Procedures in a Permutation Test Framework) was used to implement the permutations and computations (https://cran.r-project.org/web/packages/coin/index.html). The approximate distribution of the test statistic was estimated using Monte Carlo resampling, applying 10,000 permutations per test.
