Binary matched-pairs data occur commonly in longitudinal studies, such as in cross-over experiments. Many analyses for comparing the matched probabilities of a particular outcome do not utilize pairs having the same outcome for each observation. An example is McNemar's test. Some methodologists find this to be counterintuitive. We review this issue in the context of subject-specific and population-averaged models for binary data, with various link functions. For standard models and inferential methods, pairs with identical outcomes may affect the estimated size of the effect and its standard error, but they have negligible, if any, effect on significance. We also discuss extension of this result to matched sets. Copyright © 2003 John Wiley & Sons, Ltd.