## Statistical Science

- Statist. Sci.
- Volume 7, Number 1 (1992), 131-153.

### 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.

#### Article information

**Source**

Statist. Sci. Volume 7, Number 1 (1992), 131-153.

**Dates**

First available in Project Euclid: 19 April 2007

**Permanent link to this document**

http://projecteuclid.org/euclid.ss/1177011454

**Digital Object Identifier**

doi:10.1214/ss/1177011454

**Mathematical Reviews number (MathSciNet)**

MR1173420

**Zentralblatt MATH identifier**

0955.62587

**JSTOR**

links.jstor.org

**Keywords**

Categorical data chi-squared tests computational algorithms conditional inference Fisher's exact test logistic regression loglinear models odds ratios sufficient statistics

#### Citation

Agresti, Alan. A Survey of Exact Inference for Contingency Tables. Statist. Sci. 7 (1992), no. 1, 131--153. doi:10.1214/ss/1177011454. http://projecteuclid.org/euclid.ss/1177011454.

#### See also

- See Comment: Edward J. Bedrick, Joe R. Hill. [A Survey of Exact Inference for Contingency Tables]: Comment. Statist. Sci., Volume 7, Number 1 (1992), 153--157.Project Euclid: euclid.ss/1177011455
- See Comment: Diana E. Duffy. [A Survey of Exact Inference for Contingency Tables]: Comment. Statist. Sci., Volume 7, Number 1 (1992), 157--160.Project Euclid: euclid.ss/1177011456
- See Comment: Leonardo D. Epstein, Stephen E. Fienberg. [A Survey of Exact Inference for Contingency Tables]: Comment. Statist. Sci., Volume 7, Number 1 (1992), 160--162.Project Euclid: euclid.ss/1177011457
- See Comment: Svend Kreiner. [A Survey of Exact Inference for Contingency Tables]: Comment: Exact Inference in Multidimensional Tables. Statist. Sci., Volume 7, Number 1 (1992), 163--165.Project Euclid: euclid.ss/1177011458
- See Comment: D. Y. Lin, L. J. Wei. [A Survey of Exact Inference for Contingency Tables]: Comment. Statist. Sci., Volume 7, Number 1 (1992), 166--167.Project Euclid: euclid.ss/1177011459
- See Comment: Cyrus R. Mehta. [A Survey of Exact Inference for Contingency Tables]: Comment: An Interdisciplinary Approach to Exact Inference for Contingency Tables. Statist. Sci., Volume 7, Number 1 (1992), 167--170.Project Euclid: euclid.ss/1177011460
- See Comment: Samy Suissa. [A Survey of Exact Inference for Contingency Tables]: Comment. Statist. Sci., Volume 7, Number 1 (1992), 170--172.Project Euclid: euclid.ss/1177011461
- See Comment: Alan Agresti. [A Survey of Exact Inference for Contingency Tables]: Rejoinder. Statist. Sci., Volume 7, Number 1 (1992), 173--177.Project Euclid: euclid.ss/1177011462