USING STATISTICS: Spotting and Avoiding Them
An ordinal variable is a
categorical variable for which the possible values are ordered. Ordinal
variables can be considered “in between” categorical and
Example: Educational level
might be categorized as
1: Elementary school education
2: High school graduate
3: Some college
4: College graduate
5: Graduate degree
• 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.
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
Video and power-point slides. A gentle
introduction to permutation tests.
Eddington, Eugene S., Randomization
, 1995, Marcel Dekker
Good, P. (2005) Introduction to
Statistics Through Resampling Methods and R/S-PLUS
Last updated June 1, 2011