Preliminaries (Building Blocks)

Abstract

In Section 6.1.1 we argued that the p-values of two-sample tests cannot be based anymore on the parametric bootstrap method, because this technique presumes that the null hypothesis specifies some parameterised parametric distribution. On the other hand, most two-sample tests can be based on an asymptotic null distribution that can be derived from a central limit theorem, or from the application of the continuous mapping theorem and the weak convergence of the empirical process. Although the general two-sample null hypothesis is less parametric than the one-sample null hypothesis, we show here that this null hypothesis even allows us to obtain an exact null distribution. This means that the p-values computed from this null distribution are correct, even for very small sample sizes. Exact null distributions are often enumerated using permutations of observations. In this case we use the term permutation null distributionand tests based on it are referred to as permutation tests