Choice of column scores for testing independence in ordered 2 X K contingency tables

The numerous statistical methods for testing no association between a binary response (rows) and K ordered categories (columns) group naturally into two classes: those that require preassigned numerical column scores and those that do not. An example of the former would be a logistic regression analysis, and of the latter would be a Wilcoxon rank-sum test. In this paper we demonstrate that the perceived advantage of not preassigning scores is illusory. We do this by presenting an example from our consulting experience in which the midrank scores used by the rank tests that do not require preassigned scores are clearly inappropriate. Our recommendations are to assign reasonable column scores whenever possible, and to consider equally spaced scores when the choice is not apparent. Midranks as scores should always be examined for their appropriateness before a rank test is applied.