Improving and extending the McNemar test using the Bayesian method.

The well-known McNemar test assesses the difference between two correlated proportions in binary matched-pairs data. To improve the power of the McNemar test and extend it to related problems, we reinterpret the test in a Bayesian framework. Replacing the prior density by a more realistic one realizes a powerful test. We numerically investigate different choices of the prior density, which strongly affects the performance of the derived test. Furthermore, we compare the maximum actual levels of the proposed test with those of existing tests. The proposed test is advantageous for its wide extendibility. We combine the evidence from multiple strata by an approach that largely differs from existing methods. The test statistic is the product of the posterior probabilities of the alternative models in the multiple strata. The proposed test is validated in practical examples. Copyright © 2016 John Wiley & Sons, Ltd.