A directional measure for reverse global symmetry in square contingency tables with application to unaided vision data

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Abstract

The reverse global symmetry model in square contingency tables with ordinal categories is useful for analyzing whether the probability that the sum of row and column levels is larger than the reference value is equal to the probability that the sum of row and column levels is smaller than the reference value. This study proposes a directional measure that represents the degree of departure from the reverse global symmetry model. There are two kinds of direction with respect to the departure from the reverse global symmetry model. The existing measure, however, cannot discriminate between the two directions of reverse global asymmetry. The proposed measure can discriminate the direction. The proposed measure is useful for comparing degrees of departure from the reverse global symmetry model in several data. This study shows advantages of the proposed measure by (i) using two artificial data, in which the existing measure has the same value, and (ii) applying to real-world data of unaided vision.

Original languageEnglish
Pages (from-to)273-283
Number of pages11
JournalMetron
Volume79
Issue number3
DOIs
Publication statusPublished - Dec 2021

Keywords

  • Asymmetry
  • Compare
  • Ordinal category
  • Reverse diagonal cell
  • Symmetry

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