Visualization for Departures from Symmetry with the Power-Divergence-Type Measure in Square Contingency Tables
Wataru Urasaki, Tomoyuki Nakagawa, Jun Tsuchida, Kouji Tahata
TL;DR
This paper introduces a new method for visualizing symmetry departures in square contingency tables using a modified divergence statistic.
Contribution
A novel correspondence analysis approach is proposed that allows for consistent visualization of symmetry departures across different datasets.
Findings
The modified divergence statistic enables visualization of symmetry departures independent of sample size.
The CA plot includes two principal axes with equal contribution rates for consistent comparison.
Confidence regions are added to improve the accuracy of the visualization.
Abstract
When the row and column variables consist of the same category in a two-way contingency table, it is called a square contingency table. Since square contingency tables have an association structure due to the concentration of observed values near the main diagonal, a primary objective is to examine symmetric relationships and transitions between variables. Various models and measures have been proposed to analyze these structures to understand the changes between two variables’ behavior at two-time points or cohorts. This is necessary for a detailed investigation of individual categories and their interrelationships, such as shifts in brand preferences. We propose a novel approach to correspondence analysis (CA) for evaluating departures from symmetry in square contingency tables with nominal categories, using a modified divergence statistic. This approach ensures that well-known…
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Taxonomy
TopicsSensory Analysis and Statistical Methods · Psychometric Methodologies and Testing · Cognitive and psychological constructs research