McNemar Exact Test
Track paired binary changes and enumerate the discordant outcomes behind an exact McNemar p-value.
Free theory articleTrack paired binary changes and enumerate the discordant outcomes behind an exact McNemar p-value.
Concept & interpretation
The McNemar Exact Test evaluates paired binary responses, such as evaluating successes before and after a treatment. Rather than modeling all outcomes, the exact test conditions only on the discordant pairs—the cases that changed state. Under the null hypothesis of marginal homogeneity, a discordant pair is equally likely to be a loss or a gain, leading to a binomial distribution for the test statistic.
Interactive Experiment
In the interactive module, you can directly adjust the number of losses and gains in a paired experiment setting. The visualizer graphs the probability mass function for the exact conditional binomial distribution.
- Adjust the Losses b slider to change the count of pairs transitioning from success to failure.
- Adjust the Gains c slider to change the count of pairs transitioning from failure to success.
- Observe the dynamically updated Statistic min(b, c) and exact conditional Exact Two-Sided p-value based on the specified pair counts.
Try it out in the matching experiment: https://riano.app/module/mcnemar-exact-test.