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Mixed-Level Variables

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Abstract

This chapter describes measures of association for two variables at different levels of measurement, e.g., a nominal-level independent variable and an ordinal- or interval-level dependent variable, and an ordinal-level independent variable and an interval-level dependent variable. This chapter begins with discussions of three measures of association for a nominal-level independent variable and an ordinal-level dependent variable: Freeman’s θ, Agresti’s \(\hat{\delta}\), and Piccarreta’s \(\hat {\tau }\). This chapter continues with a discussion of measures of association for a nominal-level independent variable and an interval-level dependent variable: the correlation ratio η 2, 𝜖 2, and \(\hat {\omega }^{2}\).

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Notes

  1. 1.

    Unconventionally, Freeman’s θ was first presented in an introductory textbook on Elementary Applied Statistics and not in a journal article.

  2. 2.

    For a discussion of Bross’s ridit analysis, see Chap. 6, Sect. 6.7.

  3. 3.

    Sample B simply because it is the smaller of the two samples.

  4. 4.

    Coincidentally, in this example the sum of the n 1 = 9 rank scores in Sample B is also 60.

  5. 5.

    In the literature, \(\hat {r}^{2}\) is variously termed “adjusted” or “shrunken” r 2.

  6. 6.

    Emphasis in the original.

  7. 7.

    Note that, in this case, the sum of squared deviations is divided by N, not N − 1.

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Authors and Affiliations

  1. Department of Sociology, Colorado State University, Fort Collins, Colorado, USA

    Kenneth J. Berry

  2. Alexandria, Virginia, USA

    Janis E. Johnston

  3. Department of Statistics, Colorado State University, Fort Collins, Colorado, USA

    Paul W. Mielke Jr.

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  1. Kenneth J. Berry
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  3. Paul W. Mielke Jr.
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Berry, K.J., Johnston, J.E., Mielke, P.W. (2018). Mixed-Level Variables. In: The Measurement of Association. Springer, Cham. https://doi.org/10.1007/978-3-319-98926-6_8

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