Title: Using tables for measures of association
Course: UGQuants (SSPS) > Section: Association for Nominal and Ordinal Variables

Using tables for measures of association

Often we want to measure the strength of relationship between two variables represented in a table.  And often with tables we are using nominal or ordinal data. and here we can, for example, calculate the differences in percentages (or proportions) in the rows or columns of a table.

Our previous example shows the relationship between gender and voter turnout. We can display the information again, this time with column percentages. These will give us the proportion of women who voted and the proportion of men who voted in the last UK general election.  Note that if we showed the row percentages, this would give us the % of voters who were men and who were women.

Table 2: Gender and voter turnout, UK

Voted | Gender
Male | Female | Total
Yes | 724 (71.3%) | 947 (72.6%) | 1671
No | 292 (28.7%) | 358 (27.4%) | 650
Total | 1016 | 1305 | 2321

Source: ESS 5

Why might we be interested in the relationship between these two variables?  Perhaps we think that women are less likely to be engaged in policy areas that are affected by decisions at the national government, and are more likely to be interested in public areas decided by local or regional levels of government, and for this reason they might be less likely to participate in general elections.  Or perhaps we think that women are more likely to feel a sense of civic duty or sense of solidarity with the political community and are more likely to vote.  What the percentages show is that women are slightly more likely to vote than men, but the differences are very modest.  But how far apart would the figures need to be for us to claim that gender has an impact on voting?

This is where measures of association come in. Such tests summarise the relationship between two variables, and the particular measure of association we use will typically depend on two things:

 | The level of measurement of our data (nominal, ordinal, interval, ratio)
 | The structure of our data (whether a particular variable has two categories or three or more)

The most simple measures of association are for nominal or ordinal variables that each have two categories (i.e. in a 2x2 table).  One of these is called Yule’s Q.