A robust nonparametric test which is an alternative to the paired t-test. This test makes the basic assumption that there is information
only in the signs of the differences between paired observations, not in their sizes.
Take the paired observations, calculate the differences, and count the number of
s
and
s
,
where
is the sample size. Calculate the binomial coefficient
Then
gives the probability of getting exactly this many
s and
s if positive and negative
values are equally likely. Finally, to obtain the P-value
for the test, sum all the coefficients that are
and divide by
.