Title: Introduction: Association for nominal and ordinal variables
Course: UGQuants (SSPS) > Section: Association for Nominal and Ordinal Variables

Introduction to module 4.

This module introduces you to measures of association for nominal and ordinal variables.  Sometimes we refer to these as categorical or non-parametric variables.  The simplest way to look at the relationship between two such variables is to create a table.  You will already be familiar with tables. Any newspaper usually has several examples.  Their development as a proper scientific resource is relatively recent, occurring only across the last century or so. The key feature of any table, no matter how simple, is the presentation of data in such a way as to facilitate and highlight comparisons.

Before you create tables it is worth thinking about how we interpret the information presented.  It is good practice to start looking with more care at the tables that appear in monographs and research articles. More often than not the summary of the tables’ contents that authors present in their text is not the only possible interpretation.  Indeed sometimes it is a highly contentious one. It is tempting to rely on these interpretations instead of studying the table independently. Once you can interpret tables for yourself, you have the skills to critically evaluate the work of others.

Tables can be simple. We can present two frequency distributions side by side to show changes over time or they can summarize the relationship between two different variables.  Let us consider the relationship between gender and voting.  Looking at the following table, are women more likely to vote than men?

Table 1: Gender and voter turnout

Voted | Gender
Male | Female | Total
Yes | 724 | 947 | 1671
No | 292 | 358 | 650
Total | 1016 | 1305 | 2321

This is referred to as a crosstab or contingency table (insert link to relevant unit), as the results of one variable are assumed to be contingent on the results of another variable. Enabling the reader to quickly grasp the content of a table is important. In the example above, for example, presenting column percentages (insert link) would quickly reveal that voter turnout is very similar amongst men and women in the UK.Data source: European Social Survey (ESS), round 5, data for UK

We can of course construct tables to incorporate more than two variables and these may be used to make calculations of various measures that allow us to make comparisons of the strength of the relationship between pairs of variables.  Tables can also be used to work out models of various kinds for our data and look at residuals from the model.

Presentation is very important. A good clear table can convey more than several pages of words.  There are, however, some simple basic rules which, once applied, ensure that your table contains what it needs to, but stays uncluttered by unnecessary detail.