Measuring ordinal association in situations that contain tied scores. [article]. - Gonzales, Richard
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 L. A. Goodman and W. H. Kruskal's (1954) G. R. H. Somers's (1962; see record 1968-12971-001) dyx, J. O. Kim's (1971) dy.x, and T. P. Wilson's (1974) 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. -- (from the author)