Title: Comparing means
Course: UGQuants (SSPS) > Section: Associations Between 2 Variables

Comparing means

In analysing the association between categorical and ratio/interval variables, an effective approach is therefore to combine the characteristics of both types of variables and present a tabular list of all the categories (values) of the nominal or ordinal variable, showing the mean value of the ratio/interval variable for the cases in each category of the nominal/ordinal variable. This gives us a straightforward way of examining whether and to what extent the value a case takes for the ratio/interval variable varies depending on which value it takes for the nominal/ordinal variable. In this analysis, the presentation of the data is the same whether we conceptualise the ratio/interval variable as the independent or dependent variable, because it is never legitimate to calculate and compare the ‘mean’ values of nominal or ordinal variables.

However, to satisfy ourselves that it is logically possible for the ratio/interval variable to be either the independent or the dependent variable depending on the other variable, consider these two examples which use the same ratio variable:

1) In examining the association between income and occupation, it would be logical to understand income as the dependent variable: it seems much more likely that the type of job we have would influence our level of income than vice versa.

2) However, in examining the association between income and housing, it would be logical to understand income as the independent variable: it seems much more likely that our income would influence the kind of house we live in (and whether, e.g., we own it or not) than vice versa.

The following tables give examples of comparing the mean values of ratio/interval variables across categories of ordinal/nominal variables in order to assess the association between the variables.

Table 9:

Voted in national election | Mean age in years | N
Yes | 52.1 | 1,630
No | 40.7 | 646
All | 48.9 | 2,277

Source: European Social Survey, 2010

Note: 137 cases have been excluded because they were not eligible to vote. A further 8 have been excluded because they did not answer or did not know the answer to one or both of the questions.

Table 9 provides a concise representation of an evident association between age and voting: on average, non-voters are younger than voters.

As with exploring association of two categorical variables via contingency tables, when comparing means to explore associations our objective is not merely to establish the nature of any association, but also to theorise (either before or after the analysis) as to why such an association does (or indeed does not) exist.

Here, for example, we might theorise that...