A Survey of Exact Inference for Contingency Tables

Abstract

The past decade has seen substantial research on exact inference for contingency tables, both in terms of developing new analyses and developing efficient algorithms for computations. Coupled with concomitant improvements in computer power, this research has resulted in a greater variety of exact procedures becoming feasible for practical use and a considerable increase in the size of data sets to which the procedures can be applied. For some basic analyses of contingency tables, it is unnecessary to use large-sample approximations to sampling distributions when their adequacy is in doubt. This article surveys the current theoretical and computational developments of exact methods for contingency tables. Primary attention is given to the exact conditional approach, which eliminates nuisance parameters by conditioning on their sufficient statistics. The presentation of various exact inferences is unified by expressing them in terms of parameters and their sufficient statistics in loglinear models. Exact approaches for many inferences are not yet addressed in the literature, particularly for multidimensional contingency tables, and this article also suggests additional research for the next decade that would make exact methods yet more widely applicable.