Categorical variable analyses: Chi-square, Fisher exact, and Mantel-Haenszel

Categorical variables represent data that may be divided into groups. As such, the values in the categorical variable analysis represent a count of the data that fit the categorical description. Some of the more common examples of categorical variable analysis include the chi-square, Fisher exact, and Mantel-Haenszel tests. Paramount to the selection of the most appropriate test is an understanding of what questions are being answered and which assumptions can be satisfied by the data at hand. The chi-square test is fairly robust, but the Fisher exact test is preferred for sample sizes that may lead to small cell counts on cross-tabulation. The need for adjustment due to confounding or stratification on important factors can be achieved with the Mantel-Haenszel test. In general, these tests attempt to evaluate the discrepancy between the numbers observed in the data against the numbers that would be expected under the predefined null hypothesis. Developing an appreciation for the nuances of categorical variable analysis can help clinical researchers make appropriate inferences and avoid erroneous conclusions.