Multiple Correlation and Ordinally Scaled Data

Four alternative measures of multiple correlation for ordinally scaled data are discussed: Goodman and Kruskal's gamma, Somers' dyx, Kendall's tau-c, and a new measure, gamma-k. They differ in their assumptions about the circumstances in which predictions should be evaluated, and also in their properties. Gamma and dyx may both decrease in value, implying a reduction in predictability, with the introduction of an additional predictor. By contrast, tau-c and gamma-k do not fall in value.