Measures of Association

The measures of association refer to a wide variety of coefficients (including bivariate correlation and regression coefficients) that measure the strength and direction of the relationship between variables; these measures of strength, or association, can be described in several ways, depending on the analysis.

There are certain points that a researcher should know in order to better understand the measures of statistical association.

  • First, the researcher should know that measures of association are not the same as measures of statistical significance.  It is possible for a weak association to be statistically significant; it is also possible for a strong association to not be statistically significant.
  • For measures of association, a value of zero signifies that no relationship exists.  In a correlation analysis, if the coefficient (r) has a value of one, it signifies a perfect relationship on the variables of interest. In regression analyses, if the standardized beta weight (β) has a value of one, it also signifies a perfect relationship on the variables of interest.  The researcher should note that bivariate measures of association (e.g., Pearson correlations) are inappropriate for curvilinear relationships or discontinuous relationships.
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Resources

Berry, K. J., & Mielke, P. W. (1992). A family of multivariate measures of association for nominal independent variables. Educational and Psychological Measurement, 52(1), 41-55.

Cohen, J., & Nee, J. C. (1984). Estimators for two measures of association for set correlation. Educational and Psychological Measurement, 44(4), 907-917.

Gibbons, J. A. (1985). Shrinkage formulas for two nominal level measures of association. Educational and Psychological Measurement, 45(3), 551-566.

Gibbons, J. D. (1993). Nonparametric measures of association. Thousand Oaks, CA: Sage Publications.

Keown, L. L., & Hakstian, A. R. (1973). Measures of association for the component analysis of Likert scale data. Journal of Experimental Education, 41(3), 22-27.

Kim, S., & Olejnik, S. (2005). Bias and precision of measures of association for a fixed-effect multivariate analysis of variance model. Multivariate Behavioral Research, 40(4), 401-421.

Kraemer, H. C. (2000). Measures of association. In Encyclopedia of psychology (Vol. 5, pp. 135-139). Washington, DC: American Psychological Association.

Krieger, A. M., & Green, P. E. (1993). Generalized measures of association for ranked data with an application to prediction accuracy. Journal of Classification, 10(1), 93-114.

Liebetrau, A. M. (1983). Measures of association. Newbury Park, CA: Sage Publications.

Siegel, S. (1956). Nonparametric Statistics For The Behavioral Sciences. New York: McGraw-Hill.

Stevens, J. P. (1972). Global measures of association in multivariate analysis of variance. Multivariate Behavioral Research, 7(3), 373-378.

Wilcox, R. R. (2007). Local measures of association: Estimating the derivative of the regression line. British Journal of Mathematical and Statistical Psychology, 60, 107-117.