Title: Comparing other measures of distribution
Course: UGQuants (SSPS) > Section: Associations Between 2 Variables

Comparing other measures of distribution

Analysis of the association between categorical and ratio/interval variables is not limited to a comparison of means. For example, we could consider how standard deviations vary across the categories shown. For example, in table 9, although the mean age of non-voters is lower than voters, the standard deviation of age is higher among this group (approximately 19 years) than among voters (approximately 17 years). In other words, on average the age of non-voters is more spread out around the mean than for voters.

Comparing standard deviations may not offer such an obvious way of exploring association as comparing means, at least not in terms of one variable (potentially) ‘influencing’ another, but if we remember that a core objective of analysing association is to compare how the distribution of values for one variable varies across different categories of another variable, then we can see that standard deviation is relevant: e.g. we could find that values of a ratio variable varied hardly at all within one or some categories of a nominal variable but varied greatly for others.

We could also compare other features of distribution such as range or quartiles, but, rather than presenting such comparison in, e.g., tabular form, data visualisation can be used very effectively to show the association between ratio/interval and categorical variables in more graphical form.