scholarly journals A study on Freeman-Tukey test statistic under the symmetry model for square contingency tables

2021 ◽  
Vol 42 (2) ◽  
pp. 441-451
Author(s):  
Sayiter YILDIZ ◽  
Can Bülent KARAKUŞ
Keyword(s):  
Contingency Tables ◽  
Test Statistic ◽  
Tukey Test ◽  
Symmetry Model

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.

scholarly journals Extensions to the Kruskal-Wallis test and a generalised median test with extensions

1997 ◽  
Vol 1 (1) ◽  
pp. 13-25 ◽  
Author(s):  
J. C. W. Rayner ◽  
D. J. Best
Keyword(s):  
Null Hypothesis ◽  
Treatment Effects ◽  
Contingency Tables ◽  
Higher Order ◽  
Fixed Number ◽  
Equal Treatment ◽  
Order Moment ◽  
Test Statistic ◽  
Median Test ◽  
Type Data

The data for the tests considered here may be presented in two-way contingency tables with all marginal totals fixed. We show that Pearson's test statistic XP2 (P for Pearson) may be partitioned into useful and informative components. The first detects location differences be tween the treatments, and the subsequent components detect dispersion and higher order moment differences. For Kruskal-Wallis-type data when there are no ties, the location component is the Kruskal-Wallis test. The subsequent components are the extensions. Our approach enables us to generalise to when there are ties, and to when there is a fixed number of categories and a large number of observations. We also propose a generalisation of the well-known median test. In this situation the location-detecting first component of XP2 reduces to the usual median test statistic when there are only two categories. Subsequent components detect higher moment departures from the null hypothesis of equal treatment effects

scholarly journals Measure of Departure From Local Symmetry for Square Contingency Tables

2019 ◽  
Vol 8 (2) ◽  
pp. 140
Author(s):  
Yusuke Saigusa ◽  
Mitsuhiro Takami ◽  
Aki Ishii ◽  
Sadao Tomizawa
Keyword(s):  
Shannon Entropy ◽  
Diversity Index ◽  
Contingency Tables ◽  
Local Symmetry ◽  
Harmonic Mean ◽  
Symmetric Structure ◽  
Symmetry Model

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.

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