Measuring ordinal association in situations that contain tied scores

Abstract

The construal of ties is critical for assessing the association between two variables. Ties should be excluded when the investigator's data-collection procedure forces ties to occur (e.g., a J-place rating scale is used to rate K items, with J < K; a criterion variable contains fewer than K possible outcomes per item). Four measures arising from excluding or including ties on 2 ordinal variables are Goodman & Kruskal's G, Somer's dyx, Kim's dyx, and Wilson's e. In contrast to measures having variance-accounted-for interpretations, probabilistic interpretations developed here can be applied meaningfully both to ordinal-scaled variables and to stronger scales. Recommendations are offered for which measure to use in various situations.