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Nominal-Level Variables, I

In: The Measurement of Association

Author

Listed:
  • Kenneth J. Berry

    (Colorado State University, Department of Sociology)

  • Janis E. Johnston

    (Alexandria)

  • Paul W. Mielke Jr.

    (Colorado State University, Department of Statistics)

Abstract

This chapter examines chi-squared-based measures of association designed for two categorical variables. Four measures are introduced that are notoriously difficult to interpret because they do not norm properly between the limits of 0 and 1: Pearson’s ϕ 2, Tschuprov’s T 2, Cramér’s V 2, and Pearson’s C coefficient of contingency. A chi-squared-based alternative is proposed that norms properly between 0, corresponding to independence, and 1, corresponding to perfect association. Finally, the relationship between chi-squared and Pearson’s product-moment correlation coefficient is examined for r×c contingency tables.

Suggested Citation

  • Kenneth J. Berry & Janis E. Johnston & Paul W. Mielke Jr., 2018. "Nominal-Level Variables, I," Springer Books, in: The Measurement of Association, chapter 0, pages 73-138, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-98926-6_3
    DOI: 10.1007/978-3-319-98926-6_3
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