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

Dummy variables

These are special and quite unusual variables that in some respects might be said to make a virtue of the ambiguity in defining different kinds of variable. At first sight, they seem to represent obvious examples of nominal and/or categorical variables, in that they only have two values. But rather than interpret these values in the way we normally would with a nominal variable – i.e. as being distinct but having no logical rank order or numerical significance – it is best to think of dummy variables as indicating the presence or absence of a certain characteristic. For example, did someone vote Conservative in the last election or not? Does someone have a university degree or not? Does someone describe their own health as good or not?

The beauty of dummy variables is twofold. First, we can easily transform any kind of variable into a dummy variable– or indeed into a series of dummy variables. Often, we want to do this with variables that have a nominal or ordinal level of measurement. The reason for this is because of the second dimension of the beauty of dummy variables: they do have a meaningful numerical quality, which is in fact rather similar to interval variables.

With dummy variables, we assign the value 0 to the absence of a characteristic of interest to us, and 1 tothe presence of that characteristic.

For example, for a dummy variable representing whether or not an individual has a university degree, we would assign a value of 1 to cases who do have a degree and 0 to those who don’t. The difference (or ‘distance’) between the only two possible values is therefore fixed at 1 – the difference between 0 and 1. We could interpret this as one unit on a scale of having or not having a degree.

In effect, what a dummy variable provides is a very simple interval variable, which may then be used in analytical approaches where interval or ratio level variables are essential. They are also very useful in analysis that is based on the probability of a particular characteristic being present or absent.This might seem a little abstract, but because the scale has only two points we do not have the problem we would have with an ordinal measure of education, namely that we cannot say that the difference between those with a degree and those with higher level school qualifications is, e.g. the same as the difference between any other two adjacent points on the scale, because there are only two points on the scale!

The main drawback of dummy variables is that they often simplify a more complex picture because we reduce variables to only two broad categories. However, if the category of interest is defined thoughtfully, this drawback can be ameliorated. Transforming a categorical variable with a number of values into a series of dummy variables can also help retain the complexity of the variable.