4: Tests for Ordinal Data and Small Samples

Overview Section

So far, we've dealt with the concepts of independence and association in two-way tables assuming nominal classification. The Pearson and likelihood test statistics introduced do not assume any particular ordering of the rows or columns, and their numeric values do not change if the ordering is altered in any way. If a natural ordering exists (i.e., for ordinal data), we can utilize it to potentially increase the power of our tests. In the last section, we will consider a test proposed by R. A. Fisher for two-way tables that is applicable when the sample size is small and/or cell counts are small, and the large-sample methodology does not hold. But before getting into testing and inference, we revisit some measures of association and see how they can accommodate ordinal data.

Upon completion of this lesson, you should be able to:

  Objective 4.1
Interpret appropriate summary measures of ordinal data.
  Objective 4.2

Determine appropriate score assignments for ordinal data.

  Objective 4.3
Measure evidence for association between two ordinal variables.