ABSTRACT
This chapter introduces the theory of univariate and multivariate permutation tests, and shows the advantage of using such nonparametric procedures instead of traditional parametric solutions. It presents two important properties of univariate and multivariate permutation tests, specifically the equivalence of permutation statistics and the so-called finite sample consistency. Permutation tests for group randomized trials are appropriate and solutions are more general and powerful than asymptotic counterparts in that they require fewer distributional assumptions. For nonparametric methods whose goal is to develop a global test suitable for the problem of comparing curves, there are two main approaches in the literature: permutation-based solutions and nonparametric regression solutions. The concept of permutationally equivalent statistics is useful in simplifying computations and sometimes in facilitating the establishment of the asymptotic equivalence of permutation solutions with respect to some of their parametric counterparts.
