This paper develops a new test, the trinomial test, for pairwise ordinal data
samples to improve the power of the sign test by modifying its treatment of zero
diRerences between observations, thereby increasing the use of sample information.
Simulations demonstrate the power superiority of the proposed trinomial test statis-
tic over the sign test in small samples in the presence of tie observations. We also
show that the proposed trinomial test has substantially higher power than the sign
test in large samples and also in the presence of tie observations, as the sign test
ignores information from observations resulting in ties.
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