A Lego System for Conditional Inference

Conditioning on the observed data is an important and flexible design principle for statistical test procedures. Although generally applicable, permutation tests currently in use are limited to the treatment of special cases, such as contingency tables or K-sample problems. A new theoretical framework for permutation tests opens up the way to a unified and generalized view. This article argues that the transfer of such a theory to practical data analysis has important implications in many applications and requires tools that enable the data analyst to compute on the theoretical concepts as closely as possible. We reanalyze four datasets by adapting the general conceptual framework to these challenging inference problems and using the coin add-on package in the R system for statistical computing to show what one can gain from going beyond the “classical” test procedures.