Measures of Association

Aside from describing variables and relationships, and noting central tendencies, or the degree of variation in samples, we also use numbers to describe the magnitude, or strength of relationships.

We use different statistics to express how associated variables might be, depending upon the type of data we’ve used in our sample, nominal, ordinal, interval, or ratio.

Measures of association for nominal data include lambda, tau, the phi coefficient, the contingency coefficient, Yule’s Q, and Cramer’s V.

For ordinal data we use gamma, Kendall’s coefficient of concordance (W), Somer’s D, and Spearman’s rank-order correlation coefficient.

Linear relationships between 2 variables on interval or ratio scales use Pearson product moment correlation coefficient ® or the coefficient of determination (r squared).
If data is not linear, we use eta.