Categorical Variables

What are Categorical Variables?

Remember that univariate data, also known as one-variable data, are observations that are made on the individuals in a population or sample. That data comes in different types, like qualitative, quantitative, categorical, continuous, discrete, and so on. In particular, you will be looking at categorical variables, which are also often called categorical data. Let's first look at the definition.

Categorical variables are qualitative variables because they deal with qualities, not quantities. So, some examples of categorical data would be hair colour, the type of pets someone has, and favourite foods. On the other hand things like height, weight, and the number of cups of coffee that someone drinks per day would be measured numerically, and so are not categorical data.

Categorical vs. Quantitative Data

Now you know what categorical data is, but how is that different from quantitative data? It helps to look at the definition first.

Quantitative data usually answers questions like "how many" or "how much". For example quantitative data would be collected if you wanted to know how much people spent on buying a cell phone. Quantitative data is often used to compare multiple sets of data together. For a more complete discussion of quantitative data and what it is used for, take a look at Quantitative Variables.

Categorical vs. Continuous Data

All right, what about continuous data? Can that be categorical? Let's take a look at the definition of continuous data.

A good example of continuous data is height. For any of the numbers between \(4 \, ft.\) and \(5 \, ft.\) there could be someone of that height. In general, categorical data is not continuous data.

Types of Categorical Variables

There are two main types of categorical variables, nominal and ordinal.

Ordinal Categorical Variables

An example of ordinal categorical data would be the survey at the start of this article. It asked you to rate satisfaction on a scale of \(1\) to \(5\), meaning there is an implied order to your rating. Remember that numerical data is data that involves numbers, which the survey example does have. So it is possible for survey data to be both ordinal and numerical.

Nominal Categorical Variables

Suppose a survey asked you what kind of housing you live in, and the options you could pick from were dorm, house, and apartment. Those are examples of named categories, so that is nominal categorical data. In other words, if it has a named category but isn't numerically ordered, then it is a nominal categorical variable.

Categorical Variables in Statistics

Before you go on to look at more examples of categorical variables, let's look at some of the advantages and disadvantages of categorical data.

On the advantage side are:

• The results are very straightforward because people only get a few options to choose from.

• Because the options are laid out ahead of time, there are no open-ended questions that need to be analyzed. Categorical data is called concrete because of this property.

• Categorical data can be much easier to analyze (and less expensive to analyze) than other kinds of data.

On the disadvantage side are:

• In general, you need to get quite a few samples to make sure the survey accurately represents the population. This can be expensive to do.

• Because the categories are laid out at the start of the survey, it isn't very sensitive. For example, if the only two options for hair colour on a survey are brown hair and white hair, people will have trouble deciding which category to put their hair colour in (assuming they have any at all). This can lead to non-responses, and people making unanticipated choices on what their hair color is which skews the data.

• You can't do quantitative analysis on categorical data! Because it isn't numerical data you can't do arithmetic on it. For example, you can't take a survey satisfaction of \(4\), and add it to a survey satisfaction of \(3\) to get a survey satisfaction of \(7\).

You can see a summary of the advantages and disadvantages of categorical variables in statistics in the following table:

Collecting Categorical Data

How do you collect categorical data? This is often done through interviews (either in person or on the phone) or surveys (either online, in the mail, or in person). In either case, the questions asked are not open-ended. They will always ask people to choose between a specific set of options.

Categorical Data Analysis

The collected data then needs to be analysed, so how do you analyze categorical data? Often it is done with proportions or percentages, and it can be in tables or graphs. Two of the most frequent ways to look at categorical data are bar charts and pie charts.

Like and Didn't Like Bar Chart

Pie chart showing percentage of people who liked or didn't like the soda

Either one gives you a visual comparison of the data. For many more examples of how to construct a chart for categorical data, see Bar Graphs.

Examples of Categorical Variables

Let's look at some examples of what categorical data can be.

Let's look at another example.

Let's change what you are asking in your survey a bit.

So how do you compare categorical variables anyway?

Correlation Between Categorical Variables

Suppose you asked your friends whether or not they liked a particular movie, and whether they paid less than \($5\), between \($5\) and \($10\), or more than \($10\) to see it. Those are two categorical variables, so how can you compare them? Is there any way to see if how much they paid to see the movie influenced how much they liked it?

One thing you can do is look at comparative bar charts of the data, or at a two-way table. You can find more information about those in the article Bar Graphs. The other thing you can do is a more official kind of statistical test, called a chi-square test. This topic can be found in the article Inference for Distributions of Categorical Data.