Two by Two Contingency Tables

Abstract Two by two contingency tables are generated by cross classifying subjects by two binary variables. In such tables, one may be interested in testing for an association between the two variables, and, if it is found, then also in estimating the strength of the association. The χ 2 test of independence and Fisher's exact test are illustrated to test independence. The difference in proportions, relative risk, and odds ratio are shown to measure the association. Sensitivity, specificity, the false positive rate, and the false negative rate are used to evaluate a test method. Simpson's paradox is introduced to illustrate the difference between marginal tables and partial tables.