and the ‘tsmethod’ options work in the way one would expect. So although McNemar’s test
was developed as a two-sided test, we can easily get one-sided exact McNemar-type Tests.
For two-sided tests we can get three different versions of the two-sided exact McNemar’s
test using the three ‘tsmethod’ options. In the appendix we show that all three two-sided
methods give the same p-value and they all are equivalent to the exact version of McNemar’s
test. So there is only one defined exact McNemar’s test. The difference between the
’tsmethod’ options is in the calculation of the confidence intervals. The default is to use
’central’ confidence intervals so that the probability that the true parameter is less than the
lower 100(1 − α)% confidence interval is guaranteed to be less than or equal to α/2, and
similarly for the upper confidence interval. These guarantees on each tail are not true for
the ’minlike’ and ’blaker’ two-sided confidence intervals.
Using x defined earlier, here is the exact McNemar’s test with the central confidence
intervals: