# Ordinal Variables

An ordinal variable is a categorical variable for which the possible values are ordered. Ordinal variables can be considered “in between” categorical and quantitative variables.

Example: Educational level might be categorized as
1: Elementary school education
3: Some college

•    In this example (and for many ordinal variables), the quantitative differences between the categories are uneven, even though the differences between the labels are the same. (e.g., the difference between 1 and 2 is four years, whereas the difference between 2 and 3 could be anything from part of a year to several years)
•    Thus it does not make sense to take a mean of the values.
•    Common mistake: Treating ordinal variables like quantitative variables without thinking about whether this is appropriate in the particular situation at hand.
•    For example, the “floor effect” can produce the appearance of interaction when using Least Squares Regression, when no interaction is present.1

Agresti (2010)1 discusses  methods that are appropriate for ordinal data.
Permutation tests2 (also known as randomization tests) can also be used on ordinal data.

Notes:
1.  Agresti, Alan (2010) Analysis of Ordinal Categorical Data, Wiley
2. See, e.g.:
Moore, Thomas (2010), Using baboon “mothering” behavior to teach permutation tests, Cause Webinar, http://www.causeweb.org/webinar/teaching/2010-09/.
Video and power-point slides. A gentle introduction to permutation tests.
Eddington, Eugene S., Randomization Tests, 1995, Marcel Dekker
Good, P. (2005) Introduction to Statistics Through Resampling Methods and R/S-PLUS. Wiley.

Last updated June 1, 2011