Contingency Tables and Diagnostic Tests

Abstract

Contingency tables are a convenient form to report and analyze data that contain characteristics of two properties. In the simplest and most common form, each property has two possible outcomes, and the contingency table contains four numbers. Contingency tables are often used to test for the independence between the properties, although more complex hypothesis tests can also be performed. K. Pearson was the first to use an approximate $\chi ^2$ test for independence in contingency tables, while R.A. Fisher devised an exact method to do hypothesis testing on contingency tables based on the binomial distribution. Contingency tables are convenient for binary diagnostic testing and provide a convenient framework to study such properties as true or false positives, and the sensitivity and specificity of tests.