Complex multivariate testing problems are frequently encountered in many scientific disciplines, such as engineering, medicine and the social sciences. As a result, modern statistics needs permutation testing for complex data with low sample size and many variables, especially in observational studies. The Authors describe permutation tests from the point of view of experimental design, avoiding cumbersome mathematical details, and illustrate the process of devising an appropriate permutation test through case studies. In addition to the text, we contribute two open source packages for...