Goodman and Kruskal's Tau-b as Correlation Ratio

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.

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