Exploring the Application of Categorical Data Analysis in Examining Nominal and Ordinal Variables Relationships

Posted: Mar 25, 2014

• Chloe Robinson
• Chloe Rodriguez
• Daniel Harris

Abstract

Categorical data analysis represents a fundamental branch of statistical methodology with widespread applications across scientific disciplines. Despite its importance, conventional approaches to analyzing relationships between nominal and ordinal variables remain constrained by methodological limitations that restrict their analytical power and interpretative value. Traditional methods such as chi-square tests, Fisher's exact tests, and various measures of association often fail to capture the complex, multi-dimensional nature of relationships between categorical variables of different types. This research addresses these limitations by developing an innovative framework that integrates concepts from topological data analysis with information theory to provide deeper insights into the structural relationships between nominal and ordinal variables. The methodological gap in current categorical data analysis lies in the treatment of nominal and ordinal variables as fundamentally separate entities with distinct analytical requirements. While nominal variables represent categories without inherent ordering, and ordinal variables maintain a meaningful sequence, their interaction in real-world datasets often creates complex relational patterns that conventional methods struggle to characterize. Existing approaches typically either reduce ordinal variables to nominal status, losing valuable ordering information, or impose parametric assumptions that may not hold in practice. This research bridges this gap by developing a non-parametric framework that preserves the unique characteristics of both variable types while enabling comprehensive analysis of their interrelationships.