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Effects on Mantel-Haenszel Chi-square Statistic of Scores in Ordered Two-way Contingency Tables

Year 2020, , 1060 - 1070, 26.09.2020
https://doi.org/10.17798/bitlisfen.662229

Abstract

Analysis of association between ordinal categorical variables has been widely considered especially in social and medical studies. It is known that ordering instead of nominal categorical data has several advantages for researchers. Mantel-Haenszel chi-square statistic, which is known as the appropriate statistics to detect the association between ordinal variables, was considered the linear trend for ordinal data to test independence. In this study, integer, midrank, exponential, Van der Waerden and joint scores were compared with a Monte Carlo simulation study to evaluate power of statistics. Although integer scoring is generally prefered when using the statistic, it is seen that Van der Waerden also performes well.

References

  • [1] Jeong H.C., Jhun M.,Kim D. 2005. Bootstrap tests for independence in two-way ordinal contingency tables, Computational Statistics&Data Analysis, 48:623-631.
  • [2] Aktaş S. 2016. Power divergence statistics under quasi independence model for square contingency tables, Sains Malaysiana, 45(10):1573-1578.
  • [3] Agresti A. 2007. An Introduction to Categorical Data Analysis. New Jersey: Wiley.
  • [4] Agresti A. Analysis of Ordinal Categorical Data, John Wiley&Sons, Inc. Publication, 2010.
  • [5] Gong H. 2012. Modeling and measuring association for ordinal data, University of Regina, Faculty of Graduate Studies and Research, 73s, Reginas, Canada.
  • [6] Anderson C.J. 2017. Statistical inferences for ordinal variables in 2-way tables, Department of Educational Psychology, University of Illinois. https://www.coursehero.com/file/22519849/2way-ordinal-beamer-online/. (Erişim Tarihi: 16.09.2019).
  • [7] Chen H.W.N. 2014. The assignment of scores procedure for ordinal categorical data, Hindawi Publishing Corporation, The Scientific World Journal. http://dx.doi.org/10.1155/2014/304213.
  • [8] Mantel N., Haenszel W. 1959. Statistical aspects of the analysis of data from retrospective studies of disease. Journal of the National Cancer Institute, 22: 719-748.

İki-yönlü Olumsallık Tablolarında Skorların Mantel-Haenszel Ki-kare İstatistiği Üzerine Etkileri

Year 2020, , 1060 - 1070, 26.09.2020
https://doi.org/10.17798/bitlisfen.662229

Abstract

Sıralı kategorik değişkenler arasındaki birliktrlik
analizi özellikle sosyal ve tıbbi çalışmalarda yaygın olarak düşünülmektedir.
Sınıflama kategorik veri yerine sıralamanın araştırmacılar için birçok avantaja
sahip olduğu bilinmektedir. Sıralı değişkenler arasındaki birlikteliği kontrol
etmek için uygun bir istatistik olarak bilinen Mantel-Haenszel ki-kare
istatistiği, bağımsızlığı test etmek için sıralı verilerde doğrusal eğim olarak
düşünülmektedir. Bu çalışmada, Mantel-Haenszel ki-kare istatistiğinin gücünü
değerlendirmek için bir Monte Carlo benzetim çalışması yardımıyla tamsayı,
mid-rank, üstel, Van der Waerden ve ortak skorlar düşünüldü. Tamsayı skorlama
genellikle Mantel-Haenszel ki-kare istatistiği kullanıldığı zaman tercih
edilmesine rağmen, Van der Waerden de iyi bir performans göstermiştir. 

References

  • [1] Jeong H.C., Jhun M.,Kim D. 2005. Bootstrap tests for independence in two-way ordinal contingency tables, Computational Statistics&Data Analysis, 48:623-631.
  • [2] Aktaş S. 2016. Power divergence statistics under quasi independence model for square contingency tables, Sains Malaysiana, 45(10):1573-1578.
  • [3] Agresti A. 2007. An Introduction to Categorical Data Analysis. New Jersey: Wiley.
  • [4] Agresti A. Analysis of Ordinal Categorical Data, John Wiley&Sons, Inc. Publication, 2010.
  • [5] Gong H. 2012. Modeling and measuring association for ordinal data, University of Regina, Faculty of Graduate Studies and Research, 73s, Reginas, Canada.
  • [6] Anderson C.J. 2017. Statistical inferences for ordinal variables in 2-way tables, Department of Educational Psychology, University of Illinois. https://www.coursehero.com/file/22519849/2way-ordinal-beamer-online/. (Erişim Tarihi: 16.09.2019).
  • [7] Chen H.W.N. 2014. The assignment of scores procedure for ordinal categorical data, Hindawi Publishing Corporation, The Scientific World Journal. http://dx.doi.org/10.1155/2014/304213.
  • [8] Mantel N., Haenszel W. 1959. Statistical aspects of the analysis of data from retrospective studies of disease. Journal of the National Cancer Institute, 22: 719-748.
There are 8 citations in total.

Details

Primary Language English
Journal Section Araştırma Makalesi
Authors

Ezgi Nazman 0000-0003-0189-3923

Hülya Olmuş 0000-0002-8983-708X

Publication Date September 26, 2020
Submission Date December 20, 2019
Acceptance Date July 7, 2020
Published in Issue Year 2020

Cite

IEEE E. Nazman and H. Olmuş, “Effects on Mantel-Haenszel Chi-square Statistic of Scores in Ordered Two-way Contingency Tables”, Bitlis Eren Üniversitesi Fen Bilimleri Dergisi, vol. 9, no. 3, pp. 1060–1070, 2020, doi: 10.17798/bitlisfen.662229.



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