Fundamentals of Statistics contains material of various lectures and courses of H. Lohninger on statistics, data analysis and here for more.

Measures of Association - an Overview

Relationships among two variables may be specified using many different measures. The following table gives an overview on the most important measures of association:

Measure Type of Variables Range    Remarks
phi-coefficient binary, dichotomous -1 ... +1 phi is numerically equal to Pearson's correlation coefficient if the states of the binary variables are encoded by 0 and 1
Cramer's V binary, dichotomous 0 ... +1 is derived from the phi-coefficient and is comparable to other measures of correlation
tetrachoric correlation coefficient binary, dichotomous -1 ... +1 is applied to artificially dichotomized variables, assuming that the variables were normally distributed before the dichotomisation
Spearman's rank correlation ordinal -1 ... +1 can be used for ordinal data, as well (in contrast to Pearson's correlation coefficient)
Pearson's correlation coefficient interval level -1 ... +1 the "classic" correlation coefficient; if the term "correlation coefficient" is used without any further specification, this particular correlation coefficient is usually meant
contingency coefficient chi ordinal 0 ... +1 the contingency coefficient specifies only the strength of a relationship but not its direction
biserial correlation coefficient dichotom/interval level -1 ... +1 is used for measuring the correlation between a dichotomous variable and a variable at the interval level
Kruskal's gamma
(Goodman & Kruskal)
ordinal -1 ... +1 comparable to Kendall's tau-a; should be used when the data contain a high portion of ties
Kendall's tau-a ordinal -1 ... +1 ties are not accounted for; samples containing many ties may result in invalid or misleading values of tau-a
Somers' d ordinal -1 ... +1 is a variant of Kruskal's gamma

Last Update: 2012-10-08