Abstract
Chapter 12 introduced eta (η) and the more general concept of measures of association. Eta is a descriptive statistic that allows us to define how strongly the categorical variable or sample in an analysis of variance is related to the interval-level variable or trait we examined across the samples. But there are many other useful measures of association that allow us to define relationships among variables. Over the next few chapters, we will focus on some of these that are particularly useful in studying criminal justice. We will still be concerned with statistical significance in these chapters, but we will examine not only whether a measure is statistically significant but also how strong the relationship is.
Keywords
- Ordinal Level Variables
- Victim-offender Relationship
- Concordant Pairs
- Discordant Pairs
- Affective Identification
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- 1.
See Jacob Cohen, Statistical Power Analysis for the Behavioral Sciences (Hillsdale, NJ: Lawrence Erlbaum, 1988), pp. 215-271.
- 2.
For a description of the study, see Chester L. Britt, "Health Consequences of Criminal Victimization," International Review of Victimology, 8 (2001): 63-73.
- 3.
For all calculations of prediction errors, we have rounded the result to the nearest integer.
- 4.
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 Chapter 14, we discuss another measure of association for ordinal variables—Spearman’s r (r s)—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 Chapter 14).
- 5.
These two tau measures are different from Goodman and Kruskal’s tau, which measures the strength of association between two nominal variables.
- 6.
David F. Greenberg, "The Weak Strength of Social Control Theory," Crime and Delinquency 45:1 (1999): 66-81.
- 7.
For a more detailed discussion of these issues, see Jean Dickson Gibbons, Nonpara-metric Measures of Association (Newbury Park, CA: Sage, 1993)
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Weisburd, D., Britt, C. (2014). Measures of Association for Nominal and Ordinal Variables. In: Statistics in Criminal Justice. Springer, Boston, MA. https://doi.org/10.1007/978-1-4614-9170-5_13
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DOI: https://doi.org/10.1007/978-1-4614-9170-5_13
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