Testing for a lack of relationship among categorical variables

Abstract

Determining a lack of association among two or more categorical variables is frequently necessary in psychological designs such as comparative outcome analyses, assessments of group equivalence at a baseline level, and therapy outcome evaluations. Despite this, the literature rarely offers information about, or technical recommendations concerning, the appropriate statistical methodology to be used to accomplish this task. This paper explores two equivalence tests for categorical variables, one introduced by \textcite {rhv93} and another by \textcite {w10}, as well as a proposed strategy based on Cramèr's $V$ (\citeyear {c46}). A simulation study was conducted to examine and compare the Type I error and power rates associated with these tests. The results indicate that an equivalence-based Cramèr's $V$ procedure is the most appropriate method for determining a lack of relationship among categorical variables in two-way designs.

Keywords

• equivalence testing
• categorical variables
• frequency tables