Richard Gonzalez
Center Director, Research Center for Group Dynamics, Institute for Social Research
Director, BioSocial Methods Collaborative, RCGD
Amos N Tversky Collegiate Professor, Psychology and Statistics, LSA
Professor of Marketing, Stephen M Ross School of Business
Professor of Integrative Systems and Design, College of Engineering
| E-mail: | Email Richard Gonzalez |
| Address: | Research Center for Group Dynamics Institute for Social Research University of Michigan 426 Thompson Street Ann Arbor, Michigan 48106 |
| Phone: | 734-647-6785 |
Measuring the degree of ordinal association between two variables
In this paper Tom Nelson and I review several alternative measures of association. Most researchers make ordinal statements such as “when one variable goes up, the other goes down.” But then they assess such an ordinal statement with a Pearson correlation or a linear regression. There are better measures available as reviewed in this paper. We also address the thorny issue of how to handle ties in data.
Gonzalez, R. & Nelson, T. O. (1996). Measuring ordinal association in situations that contain tied scores. Psychological Bulletin, 119, 159-165. doi:10.1037/0033-2909.119.1.159 PMid:8559859
Tom Nelson passed away Jan 2005.
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, Somers’s d, Kim’s d.x, 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.
