Abstract
This chapter focuses on measures of association for nominal- and ordinal-level variables. We begin with a discussion of why it is important to distinguish between statistical significance and strength of association. Measures of association for nominal and ordinal variables allow researchers to go beyond a simple chi-square test for independence between two variables and assess the strength of the relationship. The measures of association discussed in this chapter are the most commonly used measures of association for nominal and ordinal variables. For 2 × 2 tables, the measures of association discussed are the phi (φ) coefficient, the risk ratio, and the odds ratio. Cramer’s V is like the phi coefficient but can handle tables with more than two rows and/or columns. Goodman and Kruskal’s tau and lambda are measures of association that are not based on the proportional reduction in error, or PRE. PRE measures tell us how much knowledge of one measure helps to reduce the errors we make in defining the values of a second measure. There are four common measures of association for ordinal variables: gamma (γ), Kendall’s τb and τc, and Somers’ d. These measures of association for ordinal variables also all have proportional reduction in error interpretations.
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Notes
- 1.
For a description of the study, see Britt (2001).
- 2.
For all calculations of prediction errors, we have rounded the result to the nearest integer.
- 3.
All the measures of association for ordinal variables that we discuss here are for grouped data that can be represented in the form of a table. In Chap. 14, we discuss another measure of association for ordinal variables—Spearman’s r (rs)—that is most useful in working with ungrouped data, such as information on individuals. The difficulty we confront when using Spearman’s r on grouped data is that the large number of tied pairs of observations complicates the calculation of this measure of association. Spearman’s r is a more appropriate measure of association when we have ordinal variables with a large number of ranked categories for individual cases or when we take an interval-level variable and rank order the observations (see Chap. 14).
- 4.
These two tau measures are different from Goodman and Kruskal’s tau, which measures the strength of association between two nominal variables.
- 5.
For a more detailed discussion of these issues, see Gibbons (1993).
References
Britt, C. L. (2001). Health consequences of criminal victimization. International Review of Victimology, 8, 63–73.
Cohen, J. (1988). Statistical power analysis for the behavioral sciences. Hillsdale, NJ: Lawrence Erlbaum.
Gibbons, J. D. (1993). Nonparametric measures of association. Newbury Park, CA: Sage.
Greenberg, D. F. (1999). The weak strength of social control theory. Crime and Delinquency,45(1), 66–81.
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Weisburd, D., Britt, C., Wilson, D.B., Wooditch, A. (2020). Measures of Association for Nominal and Ordinal Variables. In: Basic Statistics in Criminology and Criminal Justice. Springer, Cham. https://doi.org/10.1007/978-3-030-47967-1_13
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DOI: https://doi.org/10.1007/978-3-030-47967-1_13
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