ABSTRACT
Often one of the two categorical variables that are being related is an ordinal categorical variable, a set of categories that, unlike a nominal variable, has a meaningful order. Examples of ordinal categorical variables include the set of rating-scale categories Worse, Unimproved, Moderately Improved, and Much Improved; the set of attitudinal scale categories Strongly Agree, Agree, Disagree, and Strongly Disagree; the set of categories Applicant Accepted, Applicant on Waiting List, Applicant Rejected; and the scale from Introversion to Extroversion. The technical name for such ordinal categorical variables is ordered polytomy. The focus of this chapter is on some relatively simple methods for estimating an effect size in tables with two rows that represent two groups and three or more columns that represent ordinal categorical outcomes (2 × c tables). (The methods also apply to the case of two ordinal categorical outcomes. However, with fewer categories, the number of tied outcomes between the groups is more likely to increase, a matter that is discussed later in this chapter.) Table 9.1 provides an example with real data in which participants were randomly assigned to one or another treatment. Of course, the roles of the rows and columns can be reversed, so the methods also apply to comparable r× 2 tables. The clinical details do not concern us here, but we do observe that the Improved column reveals that neither Therapy 1 nor Therapy 2 appears to have been very successful. However, this result is perhaps less surprising when we note that the results were based on a 4-year follow-up study after therapy and the presenting problem (marital problems) was likely deteriorating just prior to the start of therapy. The data are from D. K. Snyder, Wills, and Grady-Fletcher (1991).
