This paper deals with nonparametric methods for hypothesis testing with special regard to permutation tests. After the role of parametric and nonparametric methods for hypothesis testing is debated, fundamental historical aspects of permutation tests are reviewed. Then theoretical and practical features of these tests are presented and discussed in a non-technicalway, the main aim being that of emphasizing both their theoretical rigour and high practical efficacy. Such qualities also pertain to a recently proposed method for the analysis of complex multivariate and multiaspect problems. In our opinion, permutation tests do not seem to enjoy the consideration they deserve in a vast part of the scientific world.
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