Abstract
This chapter covers how to measure the strength of the relationship between two ratio-/interval- and two ordinal-level variables. The walk-through starts out by visually examining the bivariate relationship between the two variables of interest using a scatterplot. This is important because it will inform us whether we measure the strength of the relationship using a Pearson’s correlation (parametric test for a linear relationship) or a Spearman’s rho/Kendall’s tau correlation (nonparametric test for a nonlinear relationship). The chapter draws on a dataset used by Patrick Sharkey et al. (2017) to study the effect of nonprofit organizations in the levels of crime.
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References
Cohen, J. (1988). Statistical power analysis for the behavioral sciences. Hillsdale, NJ: Lawrence Erlbaum.
Sharkey, P., Torrats-Espinosa, G., & Takyar, D. (2017). Community and the crime decline: The causal effect of local nonprofits on violent crime. American Sociological Review, 82(6), 1214–1240.
Sharkey, P. (2018). Replication data for, “Sharkey, P., Torrats-Espinosa, G., & Takyar, D. (2017). Community and the crime decline: The causal effect of local nonprofits on violent crime. American Sociological Review, 82(6), 1214-1240.” Retrieved March 30, 2020, from https://doi.org/10.7910/DVN/46WIH0, Harvard Dataverse, V2, UNF:6:kGD4YDh/xSMtgVJ6knZnmA== [fileUNF].
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Key Terms
- Covariation
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A measure of the extent to which two variables vary together relative to their respective means. The covariation between the two variables serves as the numerator for the equation to calculate Pearson’s r.
- Kendall’s tau
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Measures the strength and direction of two rank-ordered variables on a standardized scale between 0 and 1.0, whereby higher values indicate a stronger relationship.
- Linear relationship
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An association between two variables whose joint distribution may be represented in linear form when plotted on a scatter diagram.
- Pearson’s correlation coefficient
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See Pearson ’s r.
- Pearson’s r
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A commonly used measure of association between two variables. Pearson’s r measures the strength and direction of linear relationships on a standardized scale from −1.0 to 1.0.
- Scatterplot
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A graph whose two axes are defined by two variables and upon which a point is plotted for each subject in a sample according to its score on the two variables.
- Spearman’s correlation coefficient
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See Spearman ’s rho.
- Spearman’s rho (r s )
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A measure of association between two rank-ordered variables. Spearman’s rho measures the strength and direction of linear relationships on a standardized scale between −1.0 and 1.0.
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Wooditch, A., Johnson, N.J., Solymosi, R., Medina Ariza, J., Langton, S. (2021). Bivariate Correlation. In: A Beginner’s Guide to Statistics for Criminology and Criminal Justice Using R. Springer, Cham. https://doi.org/10.1007/978-3-030-50625-4_14
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DOI: https://doi.org/10.1007/978-3-030-50625-4_14
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