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}

• 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.

Agresti (2010)

Permutation tests

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/.

Good, P. (2005) Introduction to Statistics Through Resampling Methods and R/S-PLUS. Wiley.

Video and power-point slides. A gentle
introduction to permutation tests.

Eddington, Eugene S., Randomization
Tests, 1995, Marcel DekkerGood, P. (2005) Introduction to Statistics Through Resampling Methods and R/S-PLUS. Wiley.

Last updated June 1, 2011