Title: Categorical variables
Course: UGQuants (SSPS) > Section: Introduction to Quantitative Analysis

Categorical variables

These most obviously relate to the nominal level of measurement. Variables that have distinct categories with no underlying order or meaningful numerical quality can be straightforwardly defined as categorical. For example,the categories male and female are usually regarded as distinct, rather than points on any sort of underlying continuum where we could, theoretically at least, attempt to measure degrees of ‘maleness’ or ‘femaleness’. You may also see such variables described as ‘qualitative’, which essentially reflects the fact that the numerical values in themselves have no significance.

However, this description can be a little confusing given that we can and do often want to employ such variables for quantitative analysis! Such variables are also sometimes described as ‘discrete’ variables. However, it could be argued that any variable that cannot be defined as a continuous variable in the strictest sense (i.e. as being theoretically measurable to infinitesimally small degrees) should be defined as a discrete variable. This would mean, e.g., that even a variable such as total population of a country would be regarded as a discrete variable because it is not possible to measure fractions of people. But in practice we would not normally define such a variable as categorical. The reason for this relates again to different approaches to analysis. The type of analysis we apply to categorical variables usually assumes a fairly limited number of categories (and hence values), whereas we tend to adopt quite different approaches to continuous (or approximately continuous) variables, which tend to take a great many different values.

Although in a strict sense variables measured at the ordinal level should be defined as categorical we should also be aware of complexity that is in some ways similar to that discussed on Ambiguities in defining levels of measurement. For example, if we have a variable for an individual’s general interest in politics that takes a small range of values from ‘very interested’ to ‘not at all interested’, clearly we could argue that this is a categorical (and certainly discrete) variable in that it is not possible, for example, for any case to have a value somewhere between ‘very interested’ and ‘quite interested’.

On the other hand, we could argue that our range of values does reflect an underlying continuum on which we could theoretically measure degrees of interest in politics to infinitesimally small degrees. Even though in practical terms it is unlikely that we ever could or would want to do this, we could argue that the variable does therefore have a more ‘quantitative’ or continuous character. A similar logic might be applied to argue that numerical scales may legitimately be treated as interval or even ratio variables. As always, the ultimate definition has most significance in terms of the analytical approach we choose to adopt to data arising from this variable. Our decisions in this regard may not be perfect, but they should be practical, rational and justifiable.