scholarly journals Decompositions of Symmetry Using Generalized Linear Diagonals-Parameter Symmetry Model and Orthogonality of Test Statistic for Square Contingency Tables

2013 ◽  
Vol 03 (06) ◽  
pp. 9-13 ◽  
Author(s):  
Kouji Yamamoto ◽  
Motoki Ohama ◽  
Sadao Tomizawa
Keyword(s):  
Contingency Tables ◽  
Test Statistic ◽  
Symmetry Model ◽  
Parameter Symmetry

scholarly journals Orthogonal decomposition of the sum-symmetry model for square contingency tables with ordinal categories: Use of the exponential sum-symmetry model

2021 ◽  
Vol 58 (2) ◽  
pp. 95-104
Author(s):  
Shuji Ando
Keyword(s):  
Contingency Tables ◽  
Decomposition Theorem ◽  
Real Data ◽  
Exponential Sum ◽  
Orthogonal Decomposition ◽  
Global Symmetry ◽  
Asymptotic Equivalence ◽  
Artificial Data ◽  
Test Statistic ◽  
Symmetry Model

Summary In the existing decomposition theorem, the sum-symmetry model holds if and only if both the exponential sum-symmetry and global symmetry models hold. However, this decomposition theorem does not satisfy the asymptotic equivalence for the test statistic. To address the aforementioned gap, this study establishes a decomposition theorem in which the sum-symmetry model holds if and only if both the exponential sum-symmetry and weighted global-sum-symmetry models hold. The proposed decomposition theorem satisfies the asymptotic equivalence for the test statistic. We demonstrate the advantages of the proposed decomposition theorem by applying it to datasets comprising real data and artificial data.

Was This in Your Statistics Textbook? IV. Frequency Data

1989 ◽  
Vol 25 (1) ◽  
pp. 11-25
Author(s):  
D. J. Finney
Keyword(s):  
Statistical Analysis ◽  
Contingency Tables ◽  
The Other ◽  
Frequency Data ◽  
Significance Tests ◽  
Test Statistic ◽  
Jumping To Conclusions ◽  
Proper Role ◽  
Measure Of Association

SUMMARYObservations that are frequencies rather than measurements often call for special types of statistical analysis. This paper comments on circumstances in which methods for one type of data can sensibly be used for the other. A section on two-way contingency tables emphasizes the proper role of χ2 a test statistic but not a measure of association; it mentions the distinction between one-tail and two-tail significance tests and reminds the reader of dangers. Multiway tables bring new complications, and the problems of interactions when additional classificatory factors are explicit or hidden are discussed at some length. A brief outline attempts to show how probit, logit, and similar techniques are related to the analysis of contingency tables. Finally, three unusual examples are described as illustrations of the care that is needed to avoid jumping to conclusions on how frequency data should be analysed.

scholarly journals Test of Association in the Presence of Complex Environment

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-6 ◽  
Author(s):  
Muhammad Aslam ◽  
Osama H. Arif
Keyword(s):  
Contingency Tables ◽  
Complex Environment ◽  
Test Statistic ◽  
Test Of Independence ◽  
The Real ◽  
Classical Statistics ◽  
Neutrosophic Statistics

A new test of independence under neutrosophic statistics for testing the association between two criteria of classification is presented in this paper. The necessary contingency tables for the neutrosophic population and the neutrosophic sample are presented. The test statistic of the proposed test is introduced under neutrosophic statistics. A real example from education is selected to explain the proposed test. From the real example, it is concluded that the proposed test of independence is more informative, flexible, and suitable to be applied under uncertainty as compared to the existing test under classical statistics.

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