Paul R. Yarnold
Optimal Data Analysis, LLC
Rectangular categorical designs (RCDs) are among the most prevalent designs in science. Categorical designs involve categorical measures. Examples of categorical measures include gender with two response categories (male, female), color with three response categories (red, blue, green), or political affiliation with many response categories. RCDs cross-tabulate two or more categorical variables that have a different number of response options: that is, there are more columns than rows in the cross-tabulation table, or the opposite is true. Analysis via chi-square doesn’t enable researchers to disentangle effects which are identified in such designs, especially when the number of response options is large—as are typically used for attributes such as ethnicity, marital status, type of health insurance, or state of residence, for example. This article demonstrates how to disentangle effects within rectangular (or square) cross-classification tables using UniODA, and demonstrates this first for a sample of n=1,568 patients with confirmed or presumed Pneumocystis carinni pneumonia (PCP) measured on city and gender, and a second time for n=144 ESS and ESP values arising in a comparison of analysis of qualitative strength categories achieved by models identified using raw or z-score data.