Title: Measures of association: Things to consider
Course: UGQuants (SSPS) > Section: Association for Nominal and Ordinal Variables

Measures of association: Things to consider

We have encountered several statistical tests in this module. Here is a typification of them to enable you to quickly choose the right one for your analysis:

Data are: | Nominal | Ordinal
Yule's Q

Chi Square

Phi

Cramer's V

Lambda

Tau
Gamma

Test is a: | Correlation coefficient | PRE measure
 | Phi Cramer's V | Lambda Tau Gamma

Test is: | Symmetric | Asymmetric
 | Yule's Q Cramer's V | Lambda Tau

Test measures | Association only | Test of significance
Yule's Q
Chi

(Phi and Cramer's V)*

Tau

Gamma

There a number of things to note about the measures of association we have considered so far. First, Yule’s Q, Chi, Cramer's V, Tau and Lambda can all be used when our data are at the nominal level of measurement. They each assume that the values for each variable in our tables are mutually exclusive but have no other relationship. If we have the additional information that our values are ordinal on both variables, we can use another measure of association that makes use of this information: gamma.

Second, although Yule’s Q can take a negative value, indicating the direction of the association, care must be taken in interpreting this as it depends entirely on the ordering of the values in the rows and columns of our table. In a 2 x 2 table, simply changing the order of either a row or a column will reverse the sign.

Third, because they use different methods of calculation, although each measure will range from 0 to 1, they all do so in rather different ways, and give different results for the same set of data. Because of this it is vital, when comparing different pairs of variables, to use the same measure of association.

Fourth, because of the way they are calculated, Tau and Lambda are asymmetric measures of association. This means that if we consider the example we worked through above, had we used information on people's smoking habits to reduce our error in predicting their educational qualifications, instead of the other way around, we would have obtained a different value for the associations. Yule’s Q, and Cramer's V however, are symmetric; they give the same results regardless of which of our variables we imagine might have an impact on the other.