Decomposition of measure from symmetry for analyzing collapsed ordinal square contingency tables
Satoru Shinoda, Kouji Yamamoto, Sadao Tomizawa · Communication in Statistics- Theory and Methods · 2023
In some situations, square contingency tables with ordered categories are analyzed by considering collapsed tables where adjacent categories are combined. This study proposes measures to represent the degree of departure from symmetry using collapsed tables. The proposed measures are defined as the arithmetic mean of submeasures of each collapsed 3 × 3 table. Additionally, a theorem affirms that the value of the measure for symmetry is equal to the sum of the value of the proposed measures. Finally, examples are given.