Which Statistical Test Should We Use for 2 x 2 Tables?

Categorical data analysis of 2 x 2 contingency tables is extremely common, not least because they provide odds and risk ratio statistics in medical research. The χ2 test is most often used, although some researchers use the likelihood ratio test (LRT). Does it matter which test is used? This paper argues that the LRT rather than the χ2 test should be used when we are interested in testing whether two variables are independent, as is typically the case. In contrast, the χ2 test should be reserved for where the data appear to match too closely a particular hypothesis (e.g. the null hypothesis), as may occur in the investigation of data integrity. Finally, it is argued that the evidential approach provides a consistent and coherent way in which tests can be made for each of these situations.