SUMMARY OF COMMON MEASURES OF ASSOCIATION
Pearson product-moment r: For measuring relationships between two variables when both are
continuous and the relationship is rectilinear. The coefficient of correlation is most reliable when
based upon a large number of observations.
The correlation ratio eta: For measuring relationships between two continuous variables that are
related in a curvilinear fashion.
Spearman's rank difference coefficient rho rs: For measuring the association between two
rankings. The measure is based on the difference between ranks. It is primarily used where
rankings of individual cases on two variables are available so that ranking range from 1 to N for
each variable. Rho will have a value of +1.0 for a perfect match of ranks, to a value of -1.0 if the
ranks are exactly opposite.
Gamma G: For measuring the association between two ordinal variables, each of which is
arranged in rank order. Gamma can always achieve the limiting values of -1.0 or +1.0 regardless
of the number of ties between the pairs in the data.
Lambda : For measuring the association between two bivariate distributions where both variables
are interpreted to be nominal variables. Lambda simply reverses the role of two variables
predicting x from information about y.
Multiple correlation coefficient R: For measuring the maximum relationship that may be
obtained between a combination of several continuous (independent variables) and some other
continuous (dependent) variable.
Partial correlation coefficient r12.3: For measuring the relationship between two continuous
variables with the effects of a third continuous variable (or several others) held constant.
Biserial r: For measuring relationships when one variable is recorded in terms of a dichotomy
and the other is continuous. Biserial r assumes that the individuals in each of the two categories
represent a complete distribution (i.e., not just the two extremes), that the dichotomized variables
are really continuous and normally distributed, and that the relationship between the two
variables is rectilinear.
Point biserial r: For measuring the relationship between a truly dichotomous variable and a
continuous variable.
Contingency coefficient c: For measuring the association between two variables that can b e
classified into two or more categories, but when the categories themselves are not quantitative.
Phi coefficient o: For measuring the association between two variables that are truly
dichotomous. Compare with Yule's Q for appropriate use.
Kendall coefficient of concordance B: For measuring the degree of agreement among m sets of n
ranks. If we have a group of n objects by each of m judges, the coefficient of concordance tells us
the degree of agreement among the m sets of ranks.
Source: Miller, D. C. (1991). Handbook of research design and social measurement (5th ed.).
Newbury Park, CA: Sage.