# 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.

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.