The test compares the two off-diagonal cells in the 2 × 2 table: units classified differently under the two conditions. Their imbalance indicates that changes favor one condition more than the other. Concordant pairs, which retain the same classification, add no directional evidence, so including them in the comparison would not address the paired difference directly.
Concordant outcomes are observations with the same category under both conditions, so they do not distinguish which condition produces more positive or negative classifications. They still belong in the study's paired dataset and table, but the inferential comparison is driven by the two types of change. This separation explains why the test can set aside their lack of change.
The exact binomial procedure is appropriate for small samples, where relying on a chi-square approximation may be less suitable. For larger paired datasets, the chi-square approximation provides the usual route described for the test. In either case, the calculation evaluates the same question: whether the two discordant counts support a difference in paired proportions.
First record each subject's or matched unit's classification under both conditions. Then cross-tabulate those paired results into a 2 × 2 contingency table, separating unchanged classifications from changes. The two off-diagonal counts become the critical inputs, while the diagonal counts document concordance. This organization preserves the pairing that the analysis requires.
Before-and-after studies, matched case-control designs, diagnostic test comparisons, and other repeated-measures research are appropriate settings. In each case, the outcome is recorded for the same subjects or matched units under two conditions, allowing changes within pairs to be examined. The method is especially relevant when the outcome is categorical and the research question concerns paired proportions.
A significant result indicates that the discordant classifications are sufficiently unbalanced to support a difference between the paired proportions. To determine the direction, inspect which off-diagonal cell is larger: that cell represents the more frequent type of change between conditions. Interpretation therefore combines the significance result with the observed pattern of changes in the 2 × 2 table.