We have discussed briefly the McNemar test and
proposed its modification which intrinsically and
structurally adjusts the test statistic for the possible
presence of tied responses between the sampled
populations of case and control subjects which may be
data on any scale of measurement. The proposed test
statistic is shown to be more efficient and hence likely
to be more powerful than the regular McNemar test
statistic. The method also enables the researcher
readily estimate not only the chances that among a
randomly 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 is illustrated with some data.