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Theory & Methods: Measure of Asymmetry for Square Contingency Tables Having Ordered Categories
Author(s) -
Tomizawa Sadao,
Miyamoto Nobuko,
Hatanaka Yusuke
Publication year - 2001
Publication title -
australian and new zealand journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 1369-1473
DOI - 10.1111/1467-842x.00180
Subject(s) - contingency table , mathematics , measure (data warehouse) , asymmetry , degree (music) , square (algebra) , statistics , divergence (linguistics) , index (typography) , symmetry (geometry) , combinatorics , data mining , geometry , computer science , linguistics , physics , philosophy , quantum mechanics , world wide web , acoustics
For the analysis of square contingency tables with nominal categories, Tomizawa and coworkers have considered measures that represent the degree of departure from symmetry. This paper proposes a measure that represents the degree of asymmetry for square contingency tables with ordered categories (instead of those with nominal categories). The measure proposed is expressed using the Cressie–Read power‐divergence or Patil–Taillie diversity index, defined for the cumulative probabilities that an observation falls in row (column) category i or below and column (row) category j (> i ) or above. The measure depends on the order of listing the categories. It should be useful for comparing the degree of asymmetry in several tables with ordered categories. The relationship between the measure and the normal distribution is shown.