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 dichotomization
|
| 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 |
Bivariate Data 
