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 permutation tests, permute in Python and permuter in R, which include a comprehensive code base to implement common permutation tests as well as the code to implement each of the book's case studies.

This text may serve as an introduction to permutation tests for researchers, a handbook for researchers hoping to use the open source code, and a textbook in a graduate-level statistics or data science course.

Key Features:

• Examines the most up-to-date methodologies of univariate and multivariate permutation testing.
• Includes real case studies from both experimental and observational studies.
• Presents and discusses solutions to the most important and frequently encountered real problems in multivariate analyses.

Together with a wide set of application cases, the Authors present a thorough theory of permutation testing both with formal description and proofs, and analysing real case studies. Graduates, practitioners and researchers, working in different scientific fields such as engineering, biostatistics, psychology or medicine will benefit from this book.