The exact analysis of contingency tables in medical research

A unified view of exact nonparametric inference, with special emphasis on data in the form of contingency tables, is presented. While the concept of exact tests has been in existence since the early work of RA Fisher, the computational complexity involved in actually executing such tests precluded their use until fairly recently. Modern algorithmic advances, combined with the easy availability of inexpensive computing power, has renewed interest in exact methods of inference, especially because they remain valid in the face of small, sparse, imbalanced, or heavily tied data. After defining exact p-values in terms of the permutation principle, we reference algorithms for computing them. Several data sets are then analysed by both exact and asymptotic methods. We end with a discussion of the available software.