9 Categorical Inference

Categorical outcomes are analyzed according to whether observations are independent or paired.

For independent groups, Pearson’s chi-square test or Fisher’s exact test assesses association between categorical variables. The choice between them depends mainly on whether the expected cell counts are large enough for the chi-square approximation. For binary outcomes measured twice in the same participants, the observations are paired and McNemar’s test is used instead.

9.1 Choosing the categorical test

Data structure Condition Test
independent categorical observations expected counts adequate Pearson chi-square test
independent categorical observations expected counts sparse Fisher’s exact test
paired binary observations same participants measured twice McNemar’s test

For independent observations, a practical criterion for using the Pearson chi-square approximation is based on the expected cell counts, not the observed counts: no expected count should be below 1, and no more than 20% of expected counts below 5. If these conditions are not met, Fisher’s exact test is preferred.