Goodman and Kruskal's Tau-b as Correlation Ratio

Kenneth E. Southwood
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Kenneth E. Southwood: University of Illinois at Urbana-Champaign

Sociological Methods & Research, 1974, vol. 3, issue 1, 82-110

Abstract: It is shown that Goodman and Kruskal's Tau-b, a PRE coefficient of association between two nominal variables, is a more general form of the correlation ratio. Deriving from this, it is shown that similar correlation ratios can be derived for relationships between independent ordinal and interval variables and a dependent nominal variable. It is suggested that this makes it possible to express the relationship between any variable at any level of measurement-nominal, ordinal, or interval-in terms of linear equations and correlation ratios, and that this provides a useful and conceptionally parsimonious technique for practitioners. It also opens the way to greater flexibility in multivariate analysis using variables at different levels of measurement.

Date: 1974
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Persistent link: https://EconPapers.repec.org/RePEc:sae:somere:v:3:y:1974:i:1:p:82-110

DOI: 10.1177/004912417400300104

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