Data017: Discrete and continuous variables, or, How to measure your nose(s)

When measuring variables in research, quantitative variables are a wonderful thing. Whenever you’re able to measure something – i.e., measure a quantity of something – as opposed to simply categorizing it, you have much richer, more statistically valuable information. (There are some important exceptions to this, but I’ll get to those another day.)

Quantitative variables can be broken down into two kinds: discrete quantitative variables and continuous quantitative variables. A discrete quantitative variable is one that can only take specific values. Examples include:

• The number of children in a family
• The number of times a person has been to Brazil
• The number of time someone has stuck calipers on your nose

Although this subcategory (i.e., discrete vs. continuous) doesn’t usually matter, it can make certain chart like histograms or scatterplots (which we will discuss later) look funny. There are, however, ways to deal with that, which we will also discuss later.

A continuous quantitative variable, on the other hand, is one that can theoretically be measured in infinitely small steps (what mathematicians call “an arbitrary level of precision”). Examples include:

• Distance between two people
• Time spent working on a puzzle
• The width of your nose in millimeters and fractions thereof

You can record distance, for example, as

• 4 feet
• 4.1 feet
• 4.121738502767485960… feet

There is a common error on this point that I have seen even in respectable statistics books. Many people call a variable continuous when they should call it quantitative. This is an error because a quantitative variable can also be discrete. In addition, people often use the term discrete to mean categorical, which is an error because discrete variables can also be quantitative. Ay yi yi… Data fans of the world: Please get it straight. I’ll thank you now.