Modified McNemar Test

This paper proposes and presents a test statistic that intrinsically and structurally adjusts the usual McNemar test statistic for the possible presence of tied responses between the paired populations of cases and control subjects that may be measurements on any scale. The method also enables the researcher readily estimate not only the chances that among a random selected pair of case and control subjects the case responds positive and the control responds negative, or the case responds negative and the control responds positive, but also even when both case and control subjects have similar responses, it enables one easily estimate the probability that both respond positive or both respond negative. The proposed method, which is shown to be relatively more efficient and hence likely to be more powerful than the usual McNemar test statistic is illustrated with some data.