Open AccessMeasure of Departure From Local Symmetry for Square Contingency Tables
Author(s) -
Yusuke Saigusa,
Mitsuhiro Takami,
Aki Ishii,
Sadao Tomizawa
Publication year - 2019
Publication title -
international journal of statistics and probability
Language(s) - English
Resource type - Journals
eISSN - 1927-7040
pISSN - 1927-7032
DOI - 10.5539/ijsp.v8n2p140
Subject(s) - contingency table , mathematics , measure (data warehouse) , symmetry (geometry) , entropy (arrow of time) , square (algebra) , contingency , combinatorics , statistics , computer science , geometry , data mining , physics , quantum mechanics , linguistics , philosophy
For square contingency tables, this paper considers the local symmetry model which indicates that there is a symmetric structure of probabilities for only one of pairs of symmetric cells. Also it proposes the measure to express the degree of departure from the local symmetry model. The measure is expressed as the weighted harmonic mean of the diversity index including the Shannon entropy. Examples are given.