Linear rank tests are widely used when testing for independence against sto
chastic order in a 2 x J contingency table with two treatments and J ordere
d outcome levels. For this purpose, numerical scores are assigned, possibly
by default, to the J outcome levels. When the choice of scores is not appa
rent, integer (equally spaced) scores are often assigned. We show that this
practice generally leads to unnecessarily conservative tests. The use of s
lightly perturbed scores will result in a less conservative and uniformly m
ore powerful test.