Hypothesis Test to Compare Two Paired Binomial Proportions: Assessment of 24 Methods

The comparison of two paired binomial proportions is a topic of interest in statistics, with important applications in medicine. There are different methods in the statistical literature to solve this problem, and the McNemar test is the best known of all of them. The problem has been solved from a conditioned perspective, only considering the discordant pairs, and from an unconditioned perspective, considering all of the observed values. This manuscript reviews the existing methods to solve the hypothesis test of equality for the two paired proportions and proposes new methods. Monte Carlo simulation methods were carried out to study the asymptotic behaviour of the methods studied, giving some general rules of application depending on the sample size. In general terms, the Wald test, the likelihood-ratio test, and two tests based on association measures in 2 x 2 tables can always be applied, whatever the sample size is, and if the sample size is large, then the McNemar test without a continuity correction and the modified Wald test can also be applied. The results have been applied to a real example on the diagnosis of coronary heart disease.