Title: Yule’s Q
Course: UGQuants (SSPS) > Section: Association for Nominal and Ordinal Variables

Yule’s Q

Yule’s Q is a simple measure of association. It works for 2 x 2 tables only, but has a number of useful features, as well as being relatively simple to calculate.

Our 2 x 2 table must have 2 rows and 2 columns. We can label the cells in the tables with the letters a, b, c and d, as follows

IV
category 1
IV
category 2
DV
category 1
a
b
DV
category 2
c
d

The formula for Yule’s Q is as follows:

If there is a relationship in our data we would expect to see it in the diagonal axes of the table, in other words in cells a and d, or in cells b and c.

Let us work through an example used in Marsh (1988). This shows the workings for Yule’s Q comparing the proportion of the sons of fathers of two different classes (‘service/intermediate’ and ‘working’) who go to selective (i.e. private) and non-selective schools. The first figure in each cell shows the number of cases, while the second figure standardises that number by presenting it as a column percentage:

Father’s Social Class and Son’s School

School Type | Father's class | Total
Service/intermediate | Working class
Non-selective | 1792 (51%) | 3410 (76%) | 5202 (65%)
Selective | 1752 (49%) | 1060 (24%) | 2810 (35%)
Total | 3544 | 4470 | 8014

Source: Marsh 1988

We can see just by comparing the percentages that while almost half of the sons of intermediate/service class fathers go to selective schools only one quarter of the sons of working class fathers do so. There is a correlation between fathers’ class and sons’ school type. To provide a statistic that summarizes this correlation we can calculate Yule’s Q.

In the table below we pay attention, initially, to the number of cases in each cell rather than the proportions. We calculate Yule’s Q as follows:

Yule’s Q calculates this correlation at -0.52. Note that the minus sign in this result depends upon the ordering of the categories in the table. It tells us that sons with working class fathers (the higher nominal value of the Father's class variable) are less likely to go to selective schools (the higher nominal value of the School Type variable). Had we changed the order of either one of these categories then the value ofYules' Q would have been positive (Can you see why? if this is not clear try it for yourself: change the order of the categories for one of the variables and re-calculate Yule's Q).

If you want SPSS to calculate Yule's Q for two dichotomous variables, you can ask SPSS to calculate 'gamma', whose value is identical to Yule's Q for 2 x 2 tables.  Yule’s Q only works for 2 x 2 crosstabs, but, as we shall see, other coefficients are available for other types of table.

There is a video on how to obtain measures of association at the end of this module.