Theory & Methods: Measure of Asymmetry for Square Contingency Tables Having Ordered Categories
Theory & Methods: Measure of Asymmetry for Square Contingency Tables Having Ordered Categories
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理论
DOI：
10.1111/1467-842x.00180
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发表时间：
2001
影响因子：
1.1
通讯作者：
Yusuke Hatanaka
中科院分区：
文献类型：
--
作者：
S. Tomizawa;N. Miyamoto;Yusuke Hatanaka
为了分析带有名义类别的方形列联表，Tomizawa及其同事考虑了代表偏离对称性程度的度量。本文提出了一个衡量的程度，表示平方列联表有序类别（而不是那些名义类别）的不对称性。所提出的度量使用Cressie-Read功率发散或Patil-Taillie多样性指数来表示，该指数定义为观测福尔斯行（列）类别i或以下以及列（行）类别j（> i）或以上的累积概率。衡量标准取决于列出类别的顺序。它应该是有用的比较程度的不对称的几个表与有序的类别。显示了测量值与正态分布之间的关系。
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.