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A Similarity between Goodman and Kruskal's Tau and Kendall's Tau, with a Partial Interpretation of the Latter

1962; Volume: 57; Issue: 300 Linguagem: Inglês

10.1080/01621459.1962.10500818

1537-274X

Robert H. Somers,

Multi-Criteria Decision Making

Abstract This paper deals with the population interpretations of measures of association for cross classifications. A new pair of (asymmetric) coefficients is introduced and interpreted. They are shown to be related both to Kendall's τb and to Goodman and Kruskal's τ, and their relation to Kendall's τc is discussed. Second, Goodman and Kruskal's τ is interpreted as an analogue of the correlation ratio, suitable for unordered categorical data. This interpretation rests on a certain function, designated the “ordinal analogue of the variance,” of a univariate (ordered) frequency distribution, which enters into both Kendall's τb and Goodman and Kruskal's τ.