Block 14
Objective 5: How to select the appropriate measure of association

We have just covered quite a bit of information–information about a confounding array of nominal- and ordinal-level measures of association. As a result of this inundation of information, you may still be confused about the appropriate measure to use. Remember we said that selection depends on the level of measurement, the size of the table, and whether you hypothesize a direction in a relationship, or specify causality. Confusing, right? The purpose of Table 14-11 is to alleviate some of your confusion by giving you help in selecting the appropriate measure of association.

Table 14-11. Choosing the Appropriate Measure of Association

Measure of Association Table Size Asymmetrical/ Symmetrical General Comments
Nominal Measures      
Phi coefficient 2 by 2 Symmetrical Limited by the size of the table.
Cramer's V Any size Symmetrical Preferable to C. Because it can attain a value of 1.0.
Contingency coefficient (C) Larger tables Symmetrical Upper limit is somewhat less than 1.0.
Lambda Any size Asymmetrical PRE measure. Can underestimate the degree of the relationship.
Ordinal Measures      
Gamma Any size Symmetrical PRE measure. Can overestimate the degree of relationship.
Tau b Square tables Symmetrical PRE measure. Limited by shape of table.
Tau c Any size Symmetrical PRE measure. More useful than tau b.
Sommer's D Any size Asymmetrical PRE measure. Use when you know the direction of the relationship.