Drawbacks to integer scoring for ordered categorical data

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.